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"text": "! Selbständigkeitserklärung\n\n \n\nDer Verfasser erklärt, dass er die vorliegende Arbeit selbständig, ohne fremde Hilfe und ohne Benutzung anderer als der angegebenen Hilfsmittel angefertigt hat. Die aus fremden Quellen (einschließlich elektronischer Quellen) direkt oder indirekt übernommenen Gedanken sind aus nahmslos als solche kenntlich gemacht. Die Arbeit ist in gleicher oder ähnlicher Form oder auszugsweise im Rahmen einer anderen Prüfung noch nicht vorgelegt worden. \n\nKöln, den 24.05.2018",
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"created": "20260602105229034",
"modified": "20260602105229034",
"page": "004",
"parent_section": "kolbe2018hubbard_H3"
},
{
"title": "kolbe2018hubbard_PARA_0007",
"text": "! Danksagung\n\n \n\nEinen ganz besonderen Dank sage ich meinem Betreuer Professor Ralf Bulla, der mir bei der Auswahl des Themas und der Interpretation der Ergebnisse sehr geholfen hat. \n\nBesonderen Dank auch Pd. Rochus Klesse, der sich die Zeit genommen hat, meine Arbeit zu lesen und sich als Zweitgutachter zur Verfügung gestellt hat. \n\nDes Weiteren danke ich meinen Kommilitonen für die anregende und aufschlussreiche Diskussionen. \n\nMeiner Familie und Freunden danke ich, weil sie mich beim Korrektur-Lesen dieser Arbeit unterstützt haben. \n\nZu guter Letzt sei den vielen Programmierern freier Software und anderer hilfreicher Werkzeuge gedankt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "005",
"parent_section": "kolbe2018hubbard_H4"
},
{
"title": "kolbe2018hubbard_PARA_0008",
"text": "! 1 Einleitung",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "006",
"parent_section": "kolbe2018hubbard_H5"
},
{
"title": "kolbe2018hubbard_PARA_0009",
"text": "Abbildung 1.1: Darstellung einer Heisenberg-Kette mit Übernächster-Nachbar-Wechselwirkung und sieben Plätzen \n\nDer Ausgangspunkt dieser Arbeit sind das Heisenberg-Modell und das Hubbard-Modell. Die Modelle beschreiben physikalische Eigenschaften in kondensierter Materie. Das Heisenberg-Modell beschreibt die Austauschwechselwirkung zwischen lokalisierten Elektronenspins. Lokalisierte Elektronenspins findet man in ferromagnetischen- oder antiferromagnetischen Isolatoren. Die Austauschwechselwirkung, zwischen den Elektronenspins wird durch die Kopplungkonstante {{kolbe2018hubbard_FO0007||FO}} beschrieben und ist der einzige freie Parameter in dem Modell. Das Hubbard-Modell beschreibt das Verhalten von delokalisierten Fermionen. Es beschreibt Eigenschaften von Metallen, Isolatoren, Metall-Isolatoren-Übergänge, Antiferromagnetismus, Ferromagnetismus und Supraleitung. Das Modell hat zwei frei wählbare Parameter und kann mit beliebig vielen Gitter-Konfigurationen untersucht werden. Es wird seid über 30 Jahren mit diesen Modellen geforscht und trotz ihrer Einfachheit haben sie nicht an Aktualität verloren[3]. \n\nIn dieser Arbeit wird die Spin-Korrelation für drei unterschiedliche Gitter-Konfigurationen, numerisch analysiert. Die Spin-Korrelation wird für den Grundzustand bestimmt. Der Hamilton, der die Dynamik der Objekte im Gitter beschreibt, wird für diese beiden Modellen bestimmt. Das Ziel dieser Arbeit ist es, mit dem antiferromagnetischen Heisenberg-Modell, das Phänomen der \"geometrische Frustration\" durch die Spin-Korrelation nachzuweisen. Für eine Heisenberg Kette, mit Störstellen an beiden Enden, wird mittels Spin-Korrelation der Nachweis erbracht, dass sich für {{kolbe2018hubbard_FO0008||FO}} ein Singulett-Zustand zwischen den Störstellen bildet. Für {{kolbe2018hubbard_FO0009||FO}} bildet sich der Singulett-Zustand zwischen der Störstelle und dem zweiten Gitterplatz. Es wird die Korrelation zwischen der Störstelle ( {{kolbe2018hubbard_FO0010||FO}} ) und dem vorletzten Gitterplatz ( {{kolbe2018hubbard_FO0011||FO}} ), für beide Grenzfälle, für verschiedene Ketten Längen ( {{kolbe2018hubbard_FO0012||FO}} ) untersucht. Es wird gezeigt, dass die Länge der Kette einen Einfluss auf die Spin-Korrelation hat. Mit Hubbard-Modell wird gezeigt, dass stark wechselwirkende Elektronen korrelieren und für {{kolbe2018hubbard_FO0013||FO}} eine antiferromagnetische Ordnung im Grundzustand einnehmen. Es wird gezeigt, dass durch die Wahl der Gitter-Konfiguration, die Elektronen daran gehindert werden können, die energetisch niedrigste antiferromagnetische Ordnung anzunehmen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "006",
"parent_section": "kolbe2018hubbard_H5"
},
{
"title": "kolbe2018hubbard_PARA_0010",
"text": "! 2 Grundlagen der Quanten-Mechanik\n\n \n\nIn diesem Teil der Arbeit werden einige Grundbegriffe der Quanten-Mechanik erklärt. Der Umgang mit Operatoren wird vorgestellt, soweit dies für die Modell-Rechnung relevant ist. Die Beschreibung von Vielteilchensystemen wird im Rahmen der Zweiten Quantisierung erläutert.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "007",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_PARA_0011",
"text": "!! 2.1 Hilbertraum und Eigenschaften von Operatoren\n\n \n\nIn der Quantenmechanik wird ein Zustand als ein Objekt im Hilbertraum beschrieben. Dieser Hilbertraum {{kolbe2018hubbard_FO0014||FO}} ist ein Funktionen-Raum über dem Körper {{kolbe2018hubbard_FO0015||FO}} der komplexen Zahlen. Der Hilbertraum umfasst die Menge der möglichen Zustände und wird deshalb Zustandsraum genannt. Für beliebige Zustandsvektoren {{kolbe2018hubbard_FO0016||FO}} und komplexe Zahlen {{kolbe2018hubbard_FO0017||FO}} gilt, die Existenz {{kolbe2018hubbard_FO0018||FO}} eines Null-Zustandsvektor {{kolbe2018hubbard_FO0019||FO}}, das {{kolbe2018hubbard_FO0020||FO}} in {{kolbe2018hubbard_FO0014||FO}} existieren und es gelten die folgenden Rechenregeln.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "007",
"parent_section": "kolbe2018hubbard_H7"
},
{
"title": "kolbe2018hubbard_PARA_0012",
"text": "\n\nIn dem Zustandsraum ist ein Skalarprodukt definiert. Das Skalarprodukt ist eine Abbildung (.,.): {{kolbe2018hubbard_FO0021||FO}} mit den Eigenschaften, linear im zweiten Argument, antillinear im ersten Argument, hermitesch und positiv definit[10]. Der Hilbertraum {{kolbe2018hubbard_FO0022||FO}} ist der Dualraum zu {{kolbe2018hubbard_FO0014||FO}} und wird aus der Menge der kovarianten Zustandsevektoren gebildet. In den Hilberträumen ist die duale Paarung eine nicht ausgeartete Bilinearform. Die duale Paarung {{kolbe2018hubbard_FO0023||FO}} dabei ist {{kolbe2018hubbard_FO0024||FO}} der kovariante Zustandsvektor. Ist der Hilbertraum reell, dann ist die duale Paarung, wie das Skalarprodukt, sesquilinear. Für einen komplexe Hilbertraum ist die duale Paarung bilinear. Die benutzte Notation wurde von Paul Dirac im Jahr 1931 eingeführt und später nach ihm \"Dirac-Notation\" benannt. Sie ist eine koordinatenfreie Darstellung von Zustandsvektoren. Dirac gab der Funktion {{kolbe2018hubbard_FO0025||FO}} den Namen bra-Vektor und die Funktion {{kolbe2018hubbard_FO0026||FO}} nannte er ket-Vektor. \n\nAn dieser Stelle werden einige Operatoren und deren Eigenschaften vorgestellt. \n- Lineare Operatoren \n\nEs seien {{kolbe2018hubbard_FO0027||FO}} zwei beliebige komplexe Zahlen und {{kolbe2018hubbard_FO0028||FO}} beliebige Vektoren des Hilber traums. Ein Operator {{kolbe2018hubbard_FO0029||FO}} ist linear, wenn er die folgende Gleichung erfüllt: \n{{kolbe2018hubbard_FO0030||FO}} \nAlso die Bedingung der Homogenität und der Additivität erfüllt. \n- Antilineare Operatoren \n\nEs seien wieder {{kolbe2018hubbard_FO0027||FO}} zwei beliebige komplexe Zahlen und {{kolbe2018hubbard_FO0028||FO}} beliebige Vektoren des Hilbertraums. Ein Operator  ist anti-linear wenn er die folgende Gleichung erfült:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "007",
"parent_section": "kolbe2018hubbard_H7"
},
{
"title": "kolbe2018hubbard_PARA_0013",
"text": "\n{{kolbe2018hubbard_FO0031||FO}} \nDer Operator erfüllt nicht die Bedingung der Homogenität, aber er ist additiv. \n- Selbstadjungierte Operatoren \n\nMan nennt einen Operator selbstadjungiert wenn gilt: \n{{kolbe2018hubbard_FO0032||FO}} und {{kolbe2018hubbard_FO0033||FO}} \n- Hermitescher Operatoren \n\nMan nennt einen Operator hermitesch wenn gilt: {{kolbe2018hubbard_FO0034||FO}} \nEin hermitescher Operator hat reelle Eigenwerte. Für eine messbare Größe, ist es ein notwendiges Kriterium, dass die Eigenwerte reell sind. \n- Unitäre Operatoren \n\nEin Operator heißt unitär wenn die folgende Beziehung gilt: \n{{kolbe2018hubbard_FO0035||FO}} \nDie Eigenwerte von U liegen alle auf dem komplexen Einheitskreis. \nEr kann einen Zustand transformieren, ohne deren Eigenschaften zu ändern[7].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "008",
"parent_section": "kolbe2018hubbard_H7"
},
{
"title": "kolbe2018hubbard_PARA_0014",
"text": "!! 2.2 Drehimpulsoperator\n\n \n\nDer Drehimpuls wird ausführlicher beschrieben, seine Eigenschaften werden im Verlauf der Arbeit immer wieder benötigt. Der klassische Drehimpuls wird durch die folgende Gleichung beschrieben.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "008",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0015",
"text": "\n\nMit dem Korrespondenzprinzip, wird der klassische Drehimpuls in die Quantenmechanik übersetzt und zum quantenmechanischen Drehimpulsoperator. Es wird {{kolbe2018hubbard_FO0036||FO}} und {{kolbe2018hubbard_FO0037||FO}} in die Drehim puls Gleichung eingesetzt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "008",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0016",
"text": "\n\nIn der Komponentenschreibweise erkennt man die zyklische Vertauschung der Ortsobservablen {{kolbe2018hubbard_FO0039||FO}} und der Impulsobservablen {{kolbe2018hubbard_FO0040||FO}}.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "008",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0017",
"text": "\n\nMan sieht, dass der Drehimpuls aus Observablen besteht. Der Orts- und Impulsoperator Vertau schen mit sich selbst, aber nicht mit einander. Mann kann berechnen, dass für die Komponenten des Drehimpulses gilt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "008",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0018",
"text": "\n\nFür den Levi-Civita-Tensor gilt:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0019",
"text": "\n\nMit dem Levi-Civita-Tensor {{kolbe2018hubbard_FO0041||FO}} kann man die Gleichungen definieren als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0020",
"text": "\n\nAlle Komponenten des Drehimpulsen vertauschen mit dem Operator {{kolbe2018hubbard_FO0043||FO}}",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0021",
"text": "\n\nEs kann eine beliebige Komponente des Drehimpulses {{kolbe2018hubbard_FO0045||FO}} gleichzeitig mit {{kolbe2018hubbard_FO0046||FO}} messen, da alle Komponenten des Drehimpulses mit dem Operator {{kolbe2018hubbard_FO0047||FO}} vertauschen {{kolbe2018hubbard_FN0001||FN}}. Man wählt traditionell die {{kolbe2018hubbard_FO0048||FO}}-Komponente des Drehimpulses. Die Eigenwerte von {{kolbe2018hubbard_FO0046||FO}} werden mit {{kolbe2018hubbard_FO0049||FO}} bezeichnet und Drehimpulsquantenzahlen oder Nebenquantenzahlen genannt. Die Eigenwerte von {{kolbe2018hubbard_FO0048||FO}} werden mit {{kolbe2018hubbard_FO0050||FO}} bezeichnet und magnetische Quantenzahlen des Drehimpulses genannt. Die magnetischen Quantenzahlen haben {{kolbe2018hubbard_FO0051||FO}} Werte für jeden Nebenquantenzahl. Man sagt, dass die magnetischen Quantenzahlen {{kolbe2018hubbard_FO0051||FO}}-fach entartet sind.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0022",
"text": "\n\nMan kann den Operator {{kolbe2018hubbard_FO0053||FO}} und {{kolbe2018hubbard_FO0053||FO}} durch die Leiteroperatoren {{kolbe2018hubbard_FO0054||FO}}und {{kolbe2018hubbard_FO0055||FO}}beschreiben. Die Leiteroperatoren sind zueinander adjungiert und hermitesch.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0023",
"text": "\n\nZu dem Aufsteigeroperator {{kolbe2018hubbard_FO0054||FO}}und dem Absteigeroperator {{kolbe2018hubbard_FO0055||FO}}gehören neue Vertauschungsrela tionen, die man über die Gleichung (2.7) ableiten kann[7].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0024",
"text": "\\footnotetext{\n{{kolbe2018hubbard_FN0001||FN}} In der Quantenmechanik kann man zwei Größen gleichzeitig messen wenn die Observablen die Vertauschungs relationen erfüllen.\n}",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "009",
"parent_section": "kolbe2018hubbard_H8"
},
{
"title": "kolbe2018hubbard_PARA_0025",
"text": "!! 2.3 Der Spin\n\n \n\nDer Spin ist eine Eigenschaft von Quanten-Teilchen und ist ein Analogon zum Drehimpuls aus der klassischen Mechanik. Er hat die gleichen mathematischen Eigenschaften wie der Drehimpuls[6]. Er ist kein normaler Drehimpuls, wie mittels Experimente gezeigt wurde. Man konnte messen, dass der Spin eines Elektrons ein magnetisches Momente erzeugt. Teilchen mit einem ganzzahligen Spin werden Bosonen genannt und die mit einem halbzahligen Spin Fermionen. Der Spin eines Elektrons, wird im zweidimensionalen Spinraum {{kolbe2018hubbard_FO0056||FO}} beschrieben. Das Elektron hat drei räumliche Freiheitsgrade und zwei zusätzliche Freiheitsgrade. Mann konnte zeigen, dass die zusätzlichen Freiheitsgrade genau zwei bestimmte Werte annehmen, ein Elektron hat daher zwei mögliche Spinausrichtungen. Es kann sich im Zustand {{kolbe2018hubbard_FO0057||FO}} befinden, bei dem der Spin nach oben ausgerichtet ist, oder in dem Zustand ↓ bei dem er nach unten ausgerichtet ist. Man wählt für den Spinraum die Basisvektoren {{kolbe2018hubbard_FO0058||FO}} und bildet eine Orthonomalbasis. Der abstrakte Zustand kann in einem Zweidimensionalen Vektorraum beschrieben werden[1]. Für die räumliche Ausrichtung der Basiszustände wählt man die {{kolbe2018hubbard_FO0059||FO}}-Achse. Einen allgemeinen Spin Zustand kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "010",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0026",
"text": "\n\nDabei sind {{kolbe2018hubbard_FO0060||FO}} komplexe Zahlen für die {{kolbe2018hubbard_FO0061||FO}} gilt. Wolfgang Pauli hat, im Jahr 1927, zur Beschreibung des Spins, die Pauli-Matrizen eingeführt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "010",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0027",
"text": "\n\nSie bilden die Basis für den vierdimensionalen Vektorraum aller komplexen hermiteschen {{kolbe2018hubbard_FO0063||FO}} Matrizen und für den aller komplexen {{kolbe2018hubbard_FO0063||FO}}-Matrizen. Mit den Matrizen können die Spinobserva blen geschrieben werden als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "010",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0028",
"text": "\n\nDie Pauli'schen Spinmatrizen {{kolbe2018hubbard_FO0064||FO}} erfüllen die folgenden Eigenschaften.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "010",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0029",
"text": "\n\nDabei ist {{kolbe2018hubbard_FO0066||FO}} der Antikommutator. Für den Spin gelten die Gleichungen (2.11) und (2.12) mit denen die folgenden Gleichungen berechnet werden.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "011",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0030",
"text": "\n\nDie Matrix Darstellung der Leiteroperatoren kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "011",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0031",
"text": "\n\nMit den Basisvektoren kann man die folgenden Gleichungen berechnen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229034",
"modified": "20260602105229034",
"page": "011",
"parent_section": "kolbe2018hubbard_H9"
},
{
"title": "kolbe2018hubbard_PARA_0032",
"text": "!! 2.4 Spin-Korrelation\n\n \n\nDie Korrelation ist allgemein ein Maß für eine Wechselbeziehung zwischen Zuständen, Messungen oder statistischen Variablen. Die Spin-Korrelationsfunktion berechnet Werte im Intervall {{kolbe2018hubbard_FO0067||FO}} und diese werden folgendermaßen interpretiert[8].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "011",
"parent_section": "kolbe2018hubbard_H10"
},
{
"title": "kolbe2018hubbard_PARA_0033",
"text": "\n\nDie Spin-Korrelation wird, für die Observable {{kolbe2018hubbard_FO0068||FO}} mittels des Erwartungswertes berechnet. Sie beschreibt die Korrelation, in Abhängigkeit von der Temperatur {{kolbe2018hubbard_FO0069||FO}}, zwischen zwei Spins an den Positionen {{kolbe2018hubbard_FO0070||FO}} im Gitter. Die Spin-Spin-Korrelationsfunktion wird geschrieben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "011",
"parent_section": "kolbe2018hubbard_H10"
},
{
"title": "kolbe2018hubbard_PARA_0034",
"text": "\n\nDabei ist {{kolbe2018hubbard_FO0071||FO}} ein Eigenzustand des Systems für das Energieniveau {{kolbe2018hubbard_FO0072||FO}} die Inverse Temperatur multipliziert mit der Boltzmankonstante und {{kolbe2018hubbard_FO0073||FO}} ist der Entartungsgrad. Die Spin Korrelation für den Grundzustand {{kolbe2018hubbard_FO0074||FO}} wird für {{kolbe2018hubbard_FO0075||FO}} berechnet und wird geschrieben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "011",
"parent_section": "kolbe2018hubbard_H10"
},
{
"title": "kolbe2018hubbard_PARA_0035",
"text": "\n\nDie Spin-Korrelation wird über die Entartung des Grundzustandes gemittelt. Dabei ist {{kolbe2018hubbard_FO0076||FO}} die Entartung des Grundzustandes.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H10"
},
{
"title": "kolbe2018hubbard_PARA_0036",
"text": "!! 2.5 Vielteilchen-Systeme\n\n \n\nIn dieser Arbeit werden Quanten-Systeme untersucht die aus mehreren Teilchen bestehen. Die bisher erklärten Begriffe gelten nur für ein einzelnes Quanten-Teilchen. Es wird der Hilbertraum erneut aufgegriffen und die Operatoren erweitert.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H11"
},
{
"title": "kolbe2018hubbard_PARA_0037",
"text": "!! 2.5.1 Der Hilbertraum\n\n \n\nEin System aus N-Quantenobjekten wird in einem Hilbertraum {{kolbe2018hubbard_FO0014||FO}} beschrieben, der aus {{kolbe2018hubbard_FO0012||FO}} Hilberträume {{kolbe2018hubbard_FO0077||FO}} mittels Tensorprodukt gebildet wird. Dabei beschreibt jeder Hilbertraum {{kolbe2018hubbard_FO0078||FO}} die Zustände eines Ein-Teilchen-Quantensystems.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H12"
},
{
"title": "kolbe2018hubbard_PARA_0038",
"text": "\n\nDer Zustandsvektor für das gesamten Systems wird durch das Tensorprodukt gebildet.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H12"
},
{
"title": "kolbe2018hubbard_PARA_0039",
"text": "\n\nDabei beschreibt {{kolbe2018hubbard_FO0079||FO}} genau ein Quantenobjekt[1].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H12"
},
{
"title": "kolbe2018hubbard_PARA_0040",
"text": "!! 2.5.2 Operatoren\n\n \n\nEin Operator {{kolbe2018hubbard_FO0080||FO}} aus dem Hilbertraum {{kolbe2018hubbard_FO0078||FO}}, wirkt in einem Vielteilchen-System auf das {{kolbe2018hubbard_FO0081||FO}}-te Teilchen. Es gilt:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H13"
},
{
"title": "kolbe2018hubbard_PARA_0041",
"text": "\n\nDabei ist {{kolbe2018hubbard_FO0082||FO}} und {{kolbe2018hubbard_FO0083||FO}}. Mann kann sie nicht addieren wie ein Vektor oder eine Zahl. Es muss zuerst das Tensorprodukt mit allen anderen {{kolbe2018hubbard_FO0084||FO}} Einheitsmatrizen gebildet werden. Man berechnet die Operatoren nach der folgenden Formel[1].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H13"
},
{
"title": "kolbe2018hubbard_PARA_0042",
"text": "!! 2.6 Zweite Quantisierung\n\n \n\nVielteichensysteme mit ununterscheidbaren Teilchen, wie Fermionen und Bosonen, können mit der Zweiten Quantisierung beschrieben werden. Mit dem Hubbard-Modell wird ein Vielteilchen System aus Fermionen beschrieben. Die Grundlage für das Modells ist die Zweite Quantisierung.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "012",
"parent_section": "kolbe2018hubbard_H14"
},
{
"title": "kolbe2018hubbard_PARA_0043",
"text": "!! 2.6.1 Hilbertraum\n\n \n\nDer Hilbertraum des Gesamtsystems wird aus {{kolbe2018hubbard_FO0012||FO}} identischen {{kolbe2018hubbard_FO0085||FO}} Hilberträumen mittels Ten sorprodukt gebildet. Der Hilbertraum für ein System aus {{kolbe2018hubbard_FO0012||FO}} ununterscheidbaren Teilchen ist definiert durch:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H15"
},
{
"title": "kolbe2018hubbard_PARA_0044",
"text": "\n\nDer symmetrische Hilbertraum {{kolbe2018hubbard_FO0086||FO}}beschreibt Bosonen und der antisymmetrische Hilbertraum {{kolbe2018hubbard_FO0087||FO}}Fermionen. Für den symmetrischen Hilbertraum sind die Ein-Teilchen Hilberträume definiert als {{kolbe2018hubbard_FO0088||FO}}und für den antisymmetrischen {{kolbe2018hubbard_FO0089||FO}}.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H15"
},
{
"title": "kolbe2018hubbard_PARA_0045",
"text": "!! 2.6.2 Vielteilchenwellenfunktion\n\n \n\nDie Wellenfunktion {{kolbe2018hubbard_FO0090||FO}} des gesamten Systems ist eine Linearkombination aus Produkten der Ein-Teilchen-Wellenfunktionen {{kolbe2018hubbard_FO0091||FO}} und ist definiert als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H16"
},
{
"title": "kolbe2018hubbard_PARA_0046",
"text": "\n\nDie {{kolbe2018hubbard_FO0012||FO}}-Teilchenwellenfunktion unterschiedet man wie die Hilberträume. Es gibt die symmetrische Wellenfunktion und antisymmetrischen Wellenfunktion.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H16"
},
{
"title": "kolbe2018hubbard_PARA_0047",
"text": "\n\nDabei ist {{kolbe2018hubbard_FO0092||FO}} die Permutation und es gilt für eine gerade Permutation {{kolbe2018hubbard_FO0093||FO}}. für eine ungerade Permutation {{kolbe2018hubbard_FO0094||FO}}. Die Permutation ist hier zu verstehen, als eine Umsortierung der Zahlen {{kolbe2018hubbard_FO0095||FO}}, sodass jede Zahl genau einmal Vorkommt. Dabei weist {{kolbe2018hubbard_FO0096||FO}} jeder Zahl {{kolbe2018hubbard_FO0081||FO}} eine neue Zahl zu. Die Bosonenzustände haben immer eine gerade Permutation. Die Fermionen haben entweder gerade oder ungerade Permutation[7]. Man kann die Vielteilchenwellenfunktion für Fermionen entsprechend der Gleichung (2.38) schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H16"
},
{
"title": "kolbe2018hubbard_PARA_0048",
"text": "\n\nDabei steht {{kolbe2018hubbard_FO0097||FO}} für die Slater-Determinante und beschreibt eine N-Teilchenbasis. Die Slater-Determinante ist definiert als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "013",
"parent_section": "kolbe2018hubbard_H16"
},
{
"title": "kolbe2018hubbard_PARA_0049",
"text": "\n\nDie Wellenfunktion {{kolbe2018hubbard_FO0098||FO}} mit {{kolbe2018hubbard_FO0099||FO}} beschreibt ein Fermion am Ort {{kolbe2018hubbard_FO0100||FO}} im {{kolbe2018hubbard_FO0101||FO}} Zustand. \"Sind in dem N-Teilchen-Zustand zwei Sätze von Quantenzahlen gleich {{kolbe2018hubbard_FO0102||FO}}, dann bedeutet dies, dass zwei Zeilen der Determinante gleich wären, dann wäre das Ergebnis Null. Die Wahrscheinlichkeit ist also Null, zwei Fermionen in demselben Ein-Teilchen-Zustand anzutreffen.\" {{kolbe2018hubbard_FN0002||FN}} Die Determinate setzt also in dieser Theorie das Pauli-Prinzip 3 um.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H16"
},
{
"title": "kolbe2018hubbard_PARA_0050",
"text": "!! 2.6.3 Der Fockraum\n\n \n\nDer Fockraum ist ein Hilbertraum mit dem man Zustände von Fermionen und Bosonen beschrei ben kann. In der zweiten Quantisierung wird oft damit gerechtnet, wie viele Teilchen sich in einem Zustand befinden. Dabei beschreibt {{kolbe2018hubbard_FO0103||FO}} die Anzahl der Teilchen in dem {{kolbe2018hubbard_FO0104||FO}} Zustand. Der Basis-Zustand wird geschrieben als {{kolbe2018hubbard_FO0105||FO}} und die Anzahl der Teilchen kann mit dem Besetzungszahloperator {{kolbe2018hubbard_FO0106||FO}} berechnet werden. Für den Basiszustand gilt:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H17"
},
{
"title": "kolbe2018hubbard_PARA_0051",
"text": "\n\nMan beschreibt einen beliebigen Zustand {{kolbe2018hubbard_FO0107||FO}} durch die geeignete Linearkombination der Basis zustände der {{kolbe2018hubbard_FO0108||FO}} Elektronen. Es gilt:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H17"
},
{
"title": "kolbe2018hubbard_PARA_0052",
"text": "\n\nDabei ist der Zustand {{kolbe2018hubbard_FO0107||FO}} ein Element des folgenden Vektorraums.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H17"
},
{
"title": "kolbe2018hubbard_PARA_0053",
"text": "!! 2.6.4 Erzeugungs- und Vernichtungsoperatoren\n\n \n\nFermionen können, mittels Tunneleffekt, auf einer Position verschwinden und auf einer anderen wieder auftauchen. Diesen Prozess nennt man Hopping und er wird durch die Erzeugungs- und Vernichtungsoperatoren beschrieben. Ein Fermion im Zustand {{kolbe2018hubbard_FO0104||FO}} an der Position {{kolbe2018hubbard_FO0081||FO}} wird durch den Operator {{kolbe2018hubbard_FO0110||FO}} erzeugt. Die Wirkung des Erzeugungsopertors auf einen fermionischen Ein-Teilchen-Zustand ist definiert als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0054",
"text": "\n\nMan kann den fermionische Ein-Teilchen-Zustand mit dem Erzeugungsoperator schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0055",
"text": "\\footnotetext{\n{{kolbe2018hubbard_FN0002||FN}} nach Nolting (2009), S. 22 \n3 Zwei identische Fermionen können nicht im gleichen Zustand existieren.\n}",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "014",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0056",
"text": "\n\nDabei ist {{kolbe2018hubbard_FO0111||FO}} der Vakuum-Zustand. Der Vernichtungsoperator ist der adjungierte Erzeugungsoperator {{kolbe2018hubbard_FO0112||FO}} und wird geschrieben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "015",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0057",
"text": "\n\nDie Erzeugungs- und Vernichtungsoperatoren sind im fermionischen Fall Anti-Kommutativ.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "015",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0058",
"text": "\n\nDer Besetzungzahloperator wird mittels der Erzeugungs- und Vernichtungsoperatoren gebildet. Er ist definiert als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "015",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0059",
"text": "\n\nDieser Operator vernichtet und erzeugt ein Teilchen an der Position und zählt die Anzahl der Teilchen im {{kolbe2018hubbard_FO0104||FO}} Zustand an der Position {{kolbe2018hubbard_FO0081||FO}}. Es gilt:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "015",
"parent_section": "kolbe2018hubbard_H18"
},
{
"title": "kolbe2018hubbard_PARA_0060",
"text": "!! 2.7 Die Geometrische Frustration\n\n \n\nDie \"Geometrische Frustration\" tritt in kondensierter Materie auf. Die Frustration charakterisiert ein System. Konkurrierende Wechselwirkung zwischen den Spins verhindert, dass der energetisch günstigste Zustand angenommen werden kann. Die \"Unordnung\" in einem System kann für Frustration verantwortlich sein. Die Frustration erhöht die Entartung des Grundzustandes und die Nullpunkts-Entropie. In dieser Arbeit wird die Frustration im antiferromagnetischen Heisenberg-Modell beobachtet. Die Frustration ist bei Gitter Konfigurationen mit ungerader Gitterplatz Anzahl zu beobachten. Sie kann ebenfalls auftreten für bestimmte Reichweiten der Wechselwirkung. Anhand von Abbildung (2.1) lässt sich das Phänomen erklären, es ist {{kolbe2018hubbard_FO0114||FO}} und {{kolbe2018hubbard_FO0115||FO}} für alle {{kolbe2018hubbard_FO0116||FO}}. Bezogen auf die Wechselwirkung {{kolbe2018hubbard_FO0117||FO}}, möchte der Spin den ↓ Zustand annehmen, aber die konkurrierende Wechselwirkung {{kolbe2018hubbard_FO0118||FO}} drängt ihn hingegen den ↑ Zustand anzunehmen. Der Spin unterliegt in diesem Fall der Frustration, verursacht durch eine konkurrierende Wechselwirkung.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "016",
"parent_section": "kolbe2018hubbard_H19"
},
{
"title": "kolbe2018hubbard_PARA_0061",
"text": "! 3 Einführung in die theoretischen Modelle\n\n \n\nIn dieser Arbeit werden verschiedene Gitter-Konfigurationen auf die Spin-Korrelation und Fermion-Korrelation untersucht. Das Heisenberg-Modell beschreibt Wechselwirkung zwischen Spins und das Hubbard-Modell die Wechselwirkung zwischen Fermionen. In diesem Abschnitt werden die Modelle erklärt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "017",
"parent_section": "kolbe2018hubbard_H20"
},
{
"title": "kolbe2018hubbard_PARA_0062",
"text": "!! 3.1 Das Heisenberg-Modell\n\n \n\nDas Heisenberg-Modell ist ein Quantenmechanischen-Modell mit dem man Ferromagnetismus, Antiferromagnetismus und Ferrimagnetismus in Festkörpern beschreiben kann. In dem Modell wird angenommen, dass in einem Gitter, auf jedem Gitterplatz {{kolbe2018hubbard_FO0081||FO}} jeweils ein lokalisierter Elektro nenspin {{kolbe2018hubbard_FO0119||FO}} ist. Auf den Gitterplätzen sind Ionen die eine unvollständig gefüllte Elektronenschale haben. Die Elektronenspins erzeugen ein lokalisiertes magnetisches Moment. Das Gitter wird als Bravais-Gitter {{kolbe2018hubbard_FN0001||FN}} beschrieben. Bei Selten-Erd-Systemen ist der Spin lokal, weil der Gesamt drehimpuls {{kolbe2018hubbard_FO0120||FO}} durch nicht gefüllte {{kolbe2018hubbard_FO0121||FO}}-Schalen zustande kommt [2]. Die Wechselwirkung zwischen den Spins ist eingeschränkt auf nächste Nachbarn. Das Gitter kann mit dem Gittervek-",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "017",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0063",
"text": "\ntor {{kolbe2018hubbard_FO0122||FO}} beschrieben werden. Die Austausch-Kopplung ist, wegen der Translationsinvarianz des Gitters, von {{kolbe2018hubbard_FO0123||FO}} abhängig. Die Austausch-Kopplung zwischen zwei Spins ist definiert als {{kolbe2018hubbard_FO0124||FO}} und es gilt das {{kolbe2018hubbard_FO0125||FO}} ist. Man kann nimmt eine Konstante Kopplung {{kolbe2018hubbard_FO0007||FO}} zwischen den Spins an. Der Hamilton Operator im Heisenberg-Modell ist definiert als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "017",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0064",
"text": "\n\nDas Skalar-Produkt der Vektor-Operatoren kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "017",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0065",
"text": "\n\nMann kann die {{kolbe2018hubbard_FO0126||FO}}-Komponenten des Spins durch die Gleichungen (2.21), (2.22) ersetzt und die folgende Form für den Hamilton-Operator berechnen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229035",
"modified": "20260602105229035",
"page": "017",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0066",
"text": "\\footnotetext{\n{{kolbe2018hubbard_FN0001||FN}} Ein regelmäßiges Punktgitter, dass mit einem Gittervektor {{kolbe2018hubbard_FO0127||FO}} vollständig beschrieben werden kann.\n}",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "017",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0067",
"text": "\n\nMan nennt {{kolbe2018hubbard_FO0128||FO}} ferromagnetische Kopplung, weil sich die Spins parallel einstellen. Für {{kolbe2018hubbard_FO0129||FO}} stellen sich die Spins bevorzugt antiparallel ein und man hat eine antiferromagnetische Kopplung. Für {{kolbe2018hubbard_FO0129||FO}} erwartet man, dass sich im Grundzustand eine Überstruktur {{kolbe2018hubbard_FN0002||FN}} bildet. Diese Überstruktur bildet sich nicht für jede Gitter-Konfiguration. In der Abbildung 3.1 wurde bereits ein Beispiel für geometrische Frustration gezeigt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "018",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0068",
"text": "\\footnotetext{\n{{kolbe2018hubbard_FN0002||FN}} Wenn sich zwei Unter-Gitter bilden, spricht man von einer Überstruktur. In Legierungen können sich bei niedriger Temperatur Überstrukturen bilden. Die Überstruktur von {{kolbe2018hubbard_FO0130||FO}} bildet z.B. ein sc-Gitter mit zweiatomiger Basis[4].\n}",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "018",
"parent_section": "kolbe2018hubbard_H21"
},
{
"title": "kolbe2018hubbard_PARA_0069",
"text": "!! 3.2 Das Hubbard-Modell\n\n \n\nDas Hubbard-Modell ist ein theoretisches Modell zur Beschreibung von Band-Magnetismus. Man kann mit dem Modell Systeme beschreiben, die einem Metall-Isolator Übergang aufweisen. Es beschreibt Ferro-, Antiferromagnetismus und Ferrimagnetismus. Es wird generell benutzt, um Systeme zu beschrieben mit korrelierten Elektronen, die starker Wechselwirkung ausgesetzt sind. In der aktuellen Forschungen wird es benutzt, um Hochtemperatursupraleiter im normal leitenden Zustand zu beschreiben. Es unterscheidet sich vom Heisenberg-Modell in dem Punkt, dass es nicht am Atomrumpf lokalisierte Elektronen beschreiben kann. Bei vielen bekannten Elementen {{kolbe2018hubbard_FO0131||FO}} und {{kolbe2018hubbard_FO0132||FO}} die ferromagnetische Eigenschaften aufweisen, sind die Elektronen nicht am Atomrumpf lokalisiert, sondern bilden Energie Bänder. Die magnetische Ordnung entsteht durch die magnetischen Momente, die von den beweglichen Bandelektronen erzeugt werden. Der Hamilton im Hubbard-Modell wird aus drei Termen gebildet. Das Hubbard-Modell hat drei freie Parameter. Elektronen können mittels Tunneleffekt endliche Potentialbarrieren überwinden, mittels der Colombwechselwirkung mit anderen Teilchen interagieren und sich trotzdem frei im Festkörper bewegen. Der Hamilton im Hubbard-Modell wird geschrieben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "019",
"parent_section": "kolbe2018hubbard_H22"
},
{
"title": "kolbe2018hubbard_PARA_0070",
"text": "\n\nDas Coulomb-Wechselwirkungspotential, der Ionen auf den Gitterplätze, wird durch den {{kolbe2018hubbard_FO0133||FO}} Term beschrieben und Interaction-Term genannt. Der Parameter {{kolbe2018hubbard_FO0134||FO}} wird Coulomb-Korrelation genannt und ist variabel. Der Hopping-Term {{kolbe2018hubbard_FO0135||FO}} beschreibt, das Hüpfen der Elektronen zwischen den Gitterplätzen, wird aus dem Tight-Binding-Modell abgeleitet und der Parameter {{kolbe2018hubbard_FO0136||FO}} ist variabel. Der Parameter {{kolbe2018hubbard_FO0136||FO}} beschreibt, dass Überlappungsintegral von zwei benachbarten Atomorbital Wellenfunktionen. Der Term {{kolbe2018hubbard_FO0137||FO}} ist der Energien-Term, er beschreibt die kinetische Energie der Elektronen, der Parameter {{kolbe2018hubbard_FO0138||FO}} und wird wegen der Teilchen-Loch-Symmetrie durch den Interaction-Parameter bestimmt. Die Zweite Quantisierung ist die theoretische Grundlage für",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "019",
"parent_section": "kolbe2018hubbard_H22"
},
{
"title": "kolbe2018hubbard_PARA_0071",
"text": "\ndas Modell. Der Hamilton wird mit den fermionischen Erzeugungs- und Vernichtungsoperatoren beschrieben und hat die folgende Form:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "019",
"parent_section": "kolbe2018hubbard_H22"
},
{
"title": "kolbe2018hubbard_PARA_0072",
"text": "! 4 Implementierung der Modelle\n\n \n\nIn diesem Abschnitt wird erläutert, wie die mathematischen Modelle mittels der Programmier sprache Julia implementiert wurden. Es werden Ausschnitte vom Programmcode gezeigt, sowie deren Verwendung und Funktionen erklärt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "020",
"parent_section": "kolbe2018hubbard_H23"
},
{
"title": "kolbe2018hubbard_PARA_0073",
"text": "!! 4.1 Das Heisenberg-Modell\n\n \n\nDie Basiszustände für einen Spin im Heisenberg-Modell sind der Up-Zustand {{kolbe2018hubbard_FO0057||FO}} und {{kolbe2018hubbard_FO0139||FO}} Down-Zustand. Eine Heisenberg-Kette mit {{kolbe2018hubbard_FO0012||FO}} Gitterplätzen hat {{kolbe2018hubbard_FO0140||FO}} Zustände. Die Zustände werden mit der Funktion (spin_state_Generator) in Abhängigkeit von {{kolbe2018hubbard_FO0012||FO}} erzeugt. Die Funktion berechnet {{kolbe2018hubbard_FO0140||FO}} Arrays. In jedem Array sind {{kolbe2018hubbard_FO0012||FO}} Werte gespeichert. Der jeweilige Gitterplatz wird durch die Position in dem Array beschrieben. Die Basiszustände werden durch zwei Werte {{kolbe2018hubbard_FO0141||FO}} und {{kolbe2018hubbard_FO0142||FO}} beschrieben. Die Funktion0( digits!(Array, j,Basis)) gibt ein Array für die Zahl j in der angegebenen Zahlen-Basis base {{kolbe2018hubbard_FO0143||FO}}, also in diesem Fall die Bit-Kombination zurück. Es wird also eine Matrix {{kolbe2018hubbard_FO0144||FO}} mit den Bit-Kombinationen aller Zahlen zwischen 0 und {{kolbe2018hubbard_FO0145||FO}} gebildet, damit sind alle Permutationen vollständig enthalten.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "020",
"parent_section": "kolbe2018hubbard_H24"
},
{
"title": "kolbe2018hubbard_PARA_0074",
"text": "\n\nDie Spin-Operatoren sind als Funktionen in Abhängigkeit von dem Gitterplatz {{kolbe2018hubbard_FO0081||FO}} und dem Zustand(state) definiert. Die abstrakte Methode (copy(x)) wird benutzt, um den ursprünglichen Zustand zu kopieren. In der Kopie wird der Spin, mittels if-Bedingungen, entsprechend geändert von der Funktion zurückgegeben.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "020",
"parent_section": "kolbe2018hubbard_H24"
},
{
"title": "kolbe2018hubbard_PARA_0075",
"text": "\n\nEs können beliebige Kombinationen von Operatoren mit den Operatorfunktionen berechnet werden. Im folgenden ist ein Beispiel für einen Term des Hamilton.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "021",
"parent_section": "kolbe2018hubbard_H24"
},
{
"title": "kolbe2018hubbard_PARA_0076",
"text": "\n\nDie Hamilton Matrix wird mit dem Funkion (HamiltonHeisenberg(N,J,K)) berechnet. Die Funktion berechnet eine {{kolbe2018hubbard_FO0146||FO}}-Matrix. Die Funktion hat die Parameter {{kolbe2018hubbard_FO0012||FO}}, Anzahl der Gitterplätzen, {{kolbe2018hubbard_FO0007||FO}} Kopplungskonstante und {{kolbe2018hubbard_FO0147||FO}}, Kopplungs-Matrix. Dabei wird mit der Gleichung {{kolbe2018hubbard_FO0148||FO}} und über zwei for-Schleifen mit den Laufvariablen {{kolbe2018hubbard_FO0149||FO}} jedes Element der Matrix berechnet. Die Laufvariablen {{kolbe2018hubbard_FO0150||FO}} und {{kolbe2018hubbard_FO0151||FO}} entnehmen dem Array (states), dass mit der Funktion (spin_state_Generator(N)) erzeugt wurde, die Zustände. In der Funktion werden für jeden Zustand {{kolbe2018hubbard_FO0152||FO}}, über zwei weitere for-Schleifen mit den Laufvariablen {{kolbe2018hubbard_FO0070||FO}} alle Spin Wechselwir kungen im Gitter berechnet. Dabei beschreiben {{kolbe2018hubbard_FO0153||FO}} die Position der Spins im Gitter. Das Gitter wird durch ein {{kolbe2018hubbard_FO0154||FO}}-Matrix beschrieben und wird Kopplungs-Matrix genannt. Eine Kopplungs Matrix einer Heisenberg-Kette mit {{kolbe2018hubbard_FO0114||FO}} Gitterplätzen und periodischen Randbedingungen kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "021",
"parent_section": "kolbe2018hubbard_H24"
},
{
"title": "kolbe2018hubbard_PARA_0077",
"text": "\n\nDie Kopplungs-Matrix enthält viele Elemente, die gleich Null sind. Es wird mittels if-Bedingungen im Programm abgefragt, ob der Eintrag {{kolbe2018hubbard_FO0155||FO}} in der Matrix gleich Null ist. Wenn keine Kopplung zwischen den Spins besteht {{kolbe2018hubbard_FO0156||FO}}, überspringt das Programm diesen Rechenschritt und beginnt mit dem nächsten. Der {{kolbe2018hubbard_FO0157||FO}} Operator trägt nur auf der Diagonalen bei, weil er keinen Spin-Flip verursacht. In der Funktion wird mittels if-Bedingung abgefragt, ob {{kolbe2018hubbard_FO0158||FO}} ist und nur dieser Fall weiter berechnet, um die Rechenzeit und Speicherbedarf zu optimieren.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "021",
"parent_section": "kolbe2018hubbard_H24"
},
{
"title": "kolbe2018hubbard_PARA_0078",
"text": "!! 4.1.1 Korrelationsfunktion\n\n \n\nDie Spin-Korrelationsfunktion in Gleichung (2.32), kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "021",
"parent_section": "kolbe2018hubbard_H25"
},
{
"title": "kolbe2018hubbard_PARA_0079",
"text": "\n\nDer Grundzustands-Vektor wird durch Aufruf der Julia Funktion (eig(H)) über die Hamilton Matrix berechnet. Der Vektor hat {{kolbe2018hubbard_FO0140||FO}} Elemente, die jeweils einer reellen Zahlen entsprechen. Ein Element {{kolbe2018hubbard_FO0159||FO}} vom Grundzustands-Vektor kann als Produkt zwischen einer Zahl {{kolbe2018hubbard_FO0160||FO}} und einem Zustand {{kolbe2018hubbard_FO0161||FO}} aufgefasst werden. Der Grundzustand kann geschrieben werden",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "021",
"parent_section": "kolbe2018hubbard_H25"
},
{
"title": "kolbe2018hubbard_PARA_0080",
"text": "\nals:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "022",
"parent_section": "kolbe2018hubbard_H25"
},
{
"title": "kolbe2018hubbard_PARA_0081",
"text": "\n\nDie Spin-Korrelationsfunktion kann, mit mehreren for-Schleifen berechnet werden. Das Programm arbeitet mit einer for-Schleife für {{kolbe2018hubbard_FO0049||FO}} die Gitterplätze, eine for-Schleife für die {{kolbe2018hubbard_FO0161||FO}} Zustände und einer for-Schleife für {{kolbe2018hubbard_FO0150||FO}} die Entartung.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "022",
"parent_section": "kolbe2018hubbard_H25"
},
{
"title": "kolbe2018hubbard_PARA_0082",
"text": "!! 4.2 Das Hubbard-Modell\n\n \n\nDas Hubbard-Modell hat vier Basiszustände und auf einem Gitter mit {{kolbe2018hubbard_FO0012||FO}} Plätzen sind {{kolbe2018hubbard_FO0162||FO}} Zustände möglich. Die Zustände (states) werden mit der Funktion (fermion-state-generator(N)), in Abhängigkeit von der Anzahl {{kolbe2018hubbard_FO0012||FO}} der Gitterplätze, berechnet. Die Funktion berechnet {{kolbe2018hubbard_FO0162||FO}} Arrays mit jeweils {{kolbe2018hubbard_FO0012||FO}} Einträgen. Die Einträge können einen der Werte {{kolbe2018hubbard_FO0163||FO}} haben. Die Einträge in dem Array repräsentieren den Zustand. Dabei beschreibt {{kolbe2018hubbard_FO0164||FO}}, und {{kolbe2018hubbard_FO0165||FO}}.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "022",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0083",
"text": "\n\nDie Erzeugungs- und Vernichtungsoperatoren sind als Funktionen programmiert. An die Funktion wird die Position {{kolbe2018hubbard_FO0081||FO}} und der Zustand (state) übergeben. Die entsprechende Operation wird auf einer Kopie vollzogen und der veränderte (state) zurückgegeben.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "022",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0084",
"text": "\n\nUm einen Besetzungszahloperator {{kolbe2018hubbard_FO0166||FO}} auf einen Zustand wirken zu lassen, setzt man die Opera torfunktionen in einander ein. Wie beim Heisenberg-Modell kann man beliebige Kombinationen von Operatoren mit den Operatorfunktionen berechnen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "023",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0085",
"text": "\n\nDie Hamilton Matrix ist als Funktion der Parametern ( {{kolbe2018hubbard_FO0167||FO}} ) und der Hopping-Matrix implementiert. Die Hopping-Matrix ist eine {{kolbe2018hubbard_FO0168||FO}} Matrix, die das Gitter beschreibt. Die Hopping-Matrix kann beliebig gewählt werden und entsprechend kann man beliebige Gitter Konfi gurationen definieren. Die Hopping-Matrix einer lineare Hubbard-Kette mit {{kolbe2018hubbard_FO0114||FO}} Gitterplätzen kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "023",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0086",
"text": "\n\nDie folgenden Formel zeigt, dass die Reihenfolge der Operatoren beachtet werden muss, weil ein Vorzeichenwechsel stattfindet. Dabei sind die Gleichungen (2.49-2.51) für den Vorzeichenwechsel verantwortlich.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "023",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0087",
"text": "\n\nBei der Gleichung (4.5) handelt es sich um eine Konvention. Durch den Hopping-Term kommt es bei einigen Zuständen zu einem Vorzeichenwechsel. Die Zustände können mittels kurzer Rechnung bestimmt werden. Für ein System aus {{kolbe2018hubbard_FO0169||FO}} Gitterplätzen kann man die Zustände berechnen, bei denen ein Vorzeichenwechsel zu beachten ist. Die folgenden Zustände liefern keine Beiträge. Der Vakuum Zustand kann nicht \"hüpfen\", er entsteht wenn auf dem Gitterplatz kein Fermion ist. Die andern Zuständen können nicht \"hüpfen\", weil das Pauli-Prinzip es verbietet.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "023",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0088",
"text": "\n\nDie nächsten vier Zustände haben ein positives Vorzeichen. Es ist nur eine Elektron vorhanden, dass die Position ändern kann.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "023",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0089",
"text": "\n\nBei den nächsten vier Zuständen wird das Vorzeichen negativ. Wegen dem Pauli-Prinzip kann nur ein Elektron seine Position ändern.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "024",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0090",
"text": "\n\nDie letzten vier Zustände haben positive und negative Vorzeichen. Der Hopping-Term erzeugt zwei Zustände, das Pauli-Prinzip verbietet keinen Zustand. Die Elektronen können die Position in beide Richtungen ändern.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "024",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0091",
"text": "\n\nDer Vorzeichenwechsel im Hopping-Term wird mit mehreren if-Bedingungen berücksichtigt. Der Energie-Term {{kolbe2018hubbard_FO0137||FO}} und der Wechselwirkungs-Term {{kolbe2018hubbard_FO0133||FO}} sind nur auf der Diagonalen ungleich Null. Die Terme können mit dem Besetzungzahloperator geschrieben werden als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "024",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0092",
"text": "\n\nBei diesen Termen tritt kein Vorzeichen-Wechsel auf, weil sie durch den Besetzungzahloperator dargestellt werden können. Durch diesen Operator werden die Teilchen vernichtet und an der selben Position wieder erzeugt. Der Zustand wird nicht verändert. Es wird die Anzahl der Teilchen berechnet, die sich im gleichen Zustand befinden. Mann kann mit einer if-Bedingung die Rechenschritte, die gleich Null sind, überspringen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "024",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0093",
"text": "\n\nEs ergeben sich anstatt {{kolbe2018hubbard_FO0170||FO}} nur die {{kolbe2018hubbard_FO0162||FO}} Einträge auf der Diagonalen. Das verkürzt die Rechenzeit und spart Speicher. Der Hopping-Term {{kolbe2018hubbard_FO0171||FO}} hat die längste Rechenzeit, weil für jedes Matrix Element mehrere if-Bedingungen abgefragt werden müssen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "024",
"parent_section": "kolbe2018hubbard_H26"
},
{
"title": "kolbe2018hubbard_PARA_0094",
"text": "!! 4.2.1 Korrelationsfunktion\n\n \n\nDie Korrelationsfunktion, für die Fermion-Korrelation, wird mit der Gleichung (2.32) berechnet. Die Spin-Operatoren kann man schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "025",
"parent_section": "kolbe2018hubbard_H27"
},
{
"title": "kolbe2018hubbard_PARA_0095",
"text": "\n\nWenn man die Gleichungen (4.12) in (2.32) einsetzt, ergibt sich die Korrelationsfunktion für die Fermion-Korrelation in der folgende Form:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "025",
"parent_section": "kolbe2018hubbard_H27"
},
{
"title": "kolbe2018hubbard_PARA_0096",
"text": "\n\nMan kann, mit dem Besetzungzahloperator, die Gleichung schreiben als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "025",
"parent_section": "kolbe2018hubbard_H27"
},
{
"title": "kolbe2018hubbard_PARA_0097",
"text": "\n\nDer Grundzustands-Vektor wird durch Aufruf der Julia Funktion (eig(H)) über die Hamilton Matrix berechnet. Der Vektor hat {{kolbe2018hubbard_FO0162||FO}} Elemente, die einer reellen Zahlen entsprechen. Ein Element {{kolbe2018hubbard_FO0172||FO}} vom Grundzustands-Vektor kann als Produkt zwischen einer Zahl {{kolbe2018hubbard_FO0160||FO}} und einem Zustand {{kolbe2018hubbard_FO0161||FO}} aufgefasst werden. Der Grundzustand kann geschrieben werden als:",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "025",
"parent_section": "kolbe2018hubbard_H27"
},
{
"title": "kolbe2018hubbard_PARA_0098",
"text": "\n\nDie Fermion-Korrelationsfunktion lässt sich nach dem gleichen Schema wie, die Spin-Korrelationsfunktion programmieren.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229036",
"modified": "20260602105229036",
"page": "025",
"parent_section": "kolbe2018hubbard_H27"
},
{
"title": "kolbe2018hubbard_PARA_0099",
"text": "! 5 Ergebnisse der numerischen Analyse\n\n \n\nIn diesem Abschnitt der Arbeit werden die Ergebnisse für drei Gitter-Konfigurationen vorgestellt und jeweils die Korrelation für den Grundzustand berechnet. Die Korrelationsfunktion wird nach Gleichung (2.32) mit {{kolbe2018hubbard_FO0173||FO}} und {{kolbe2018hubbard_FO0174||FO}} berechnet. Das Ergebnis wird gegen {{kolbe2018hubbard_FO0049||FO}}, die Gitterposition {{kolbe2018hubbard_FO0175||FO}}, aufgetragen. Es wird in diesem Teil der Arbeit ohne Einheiten gerechnet, d.h. es wurde Plancksche Wirkungsquantum auf {{kolbe2018hubbard_FO0176||FO}} gesetzt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "026",
"parent_section": "kolbe2018hubbard_H28"
},
{
"title": "kolbe2018hubbard_PARA_0100",
"text": "!! 5.1 Das Heisenberg-Modell",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "026",
"parent_section": "kolbe2018hubbard_H29"
},
{
"title": "kolbe2018hubbard_PARA_0101",
"text": "!! 5.1.1 Nächste-Nachbar Wechselwirkung\n\n \n\nIn den folgenden Diagrammen wird die Spin-Korrelation für eine linearen Kette dargestellt. Eine schematische Darstellung dieser Kette, ist in der Abbildung(3.1) zu sehen. Die Spin-Korrelation wird für das ferromagnetische und antiferromagnetische Heisenberg-Modell gezeigt. \nIn dem folgenden Diagramm ist die Spin-Korrelation, für ein antiferromagnetische Kopplung {{kolbe2018hubbard_FO0129||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "026",
"parent_section": "kolbe2018hubbard_H30"
},
{
"title": "kolbe2018hubbard_PARA_0102",
"text": "\n\nDer Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem zweiten-, vierten-, sechsten-, achten- und zehnten Gitterplatz antikorreliert. Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem dritten-, fünften-, siebten- und neunten Gitterplatz korreliert.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "026",
"parent_section": "kolbe2018hubbard_H30"
},
{
"title": "kolbe2018hubbard_PARA_0103",
"text": "\n\nDie Korrelation des ersten Spins mit sich selbst hat den Wert {{kolbe2018hubbard_FO0177||FO}} und setzt sich aus den Beiträgen der drei Raumrichtungen zusammen. Die Korrelation zwischen den Spins nimmt mit zunehmen den Abstand ab. Das Diagramm bestätigt für {{kolbe2018hubbard_FO0129||FO}} die antiferromagnetische Anordnung der Spins. \n\nIn dem folgenden Diagramm ist die Spin-Korrelation, mit ferromagnetischer Kopplung {{kolbe2018hubbard_FO0128||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "027",
"parent_section": "kolbe2018hubbard_H30"
},
{
"title": "kolbe2018hubbard_PARA_0104",
"text": "Abbildung 5.2: Eindimensionale Heisenbergkette mit {{kolbe2018hubbard_FO0001||FO}} Gitterplätzen und Nächster- Nachbar Wechselwirkung \n\nIn diesem Diagramm hat die Korrelation des ersten Spin mit sich selbst der Wert {{kolbe2018hubbard_FO0177||FO}} und die darauf folgenden Spins haben alle den gleichen Wert {{kolbe2018hubbard_FO0178||FO}}. Die Werte sind alle positiv und entsprechend korreliert jeder Spin mit dem ersten. Das Diagramm zeigt für {{kolbe2018hubbard_FO0128||FO}} den ferromagnetischen Fall, dabei sind alle Spins parallel ausgerichtet. \n\nIn dem quantenmechanischen Heisenberg-Modell wird die Ausrichtung in alle Raumrichtungen betrachtet. Man kann mit dem klassischen Heisenberg-Modell die genaue Ausrichtung im Raum bestimmen, weil die Operatoren als Vektoren beschrieben werden[2].",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "027",
"parent_section": "kolbe2018hubbard_H30"
},
{
"title": "kolbe2018hubbard_PARA_0105",
"text": "!! 5.1.2 Über-Nächste-Nachbar Wechselwirkung\n\n \n\nIn den folgenden Diagrammen ist die Spin-Korrelation für \"Über-Nächste-Nachbar Wechsel wirkung dargestellt. In der Abbildung Abbildung2.1 ist eine schematische Darstellung einer Gitter-Konfiguration mit Über-Nächster-Nachbar Wechselwirkung.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "028",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0106",
"text": "Abbildung 5.3: Eine Schematische Darstellung einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung. \n\nDie gewählte Gitter-Konfiguration kann man als eindimensionale Kette auffassen. Dabei wird für die Kopplung {{kolbe2018hubbard_FO0179||FO}} eine längere Reichweite zugelassen. Die Abbildung 5.3 zeigt, die eindimensionale Interpretation der Gitter-Konfiguration. \n\nDer Parameter {{kolbe2018hubbard_FO0179||FO}} beschreibt die Kopplung zwischen den Über-Nächsten-Nachbarn. Die lineare Heisenberg-Kette (Abbildung3.1) wird als Referenz Kurve in den Diagrammen dargestellt. \n\nDer Kopplung zwischen den Nächsten-Nachbarn {{kolbe2018hubbard_FO0180||FO}} ist konstant und während {{kolbe2018hubbard_FO0179||FO}} verändert wird. Es wird als Erstes untersucht, wie sich das System bei kleiner Kopplung {{kolbe2018hubbard_FO0179||FO}}, im Vergleich zur linearen Kette verhält. Im nächsten Schritt wird das System für große Kopplungen {{kolbe2018hubbard_FO0179||FO}} untersucht. Es wird gezeigt, dass für die Spin-Korrelation das Verhältnis von {{kolbe2018hubbard_FO0181||FO}} relevant ist \n\nIn den Diagrammen wird die Nächste-Nachbar Wechselwirkung mit \"NN-WWünd die Über- Nachste-Nachbar Wechselwirkung mit \"ÜNN-WW\" gekennzeichnet.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "028",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0107",
"text": "\n\nIn dem folgenden Diagramm ist die Spin-Korrelation für die Über-Nächste-Nachbar Wechselwir kung dargestellt. Die Spin-Korrelation wird zuerst für geringere Kopplung {{kolbe2018hubbard_FO0182||FO}} zwischen den Über-Nächsten Nachbar Gitterplätzen untersucht.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "029",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0108",
"text": "Abbildung 5.4: Eine Heisenberg-Kette mit {{kolbe2018hubbard_FO0001||FO}} Gitterplätzen und Über-Nächste-Nachbar Wechselwirkung. \n\nFür die Kopplungen {{kolbe2018hubbard_FO0183||FO}} und {{kolbe2018hubbard_FO0184||FO}} kann der Verlauf der Spin-Korrelation wie folgt beschrieben werden: Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem zweiten , vierten-, sechsten-, achten- und zehnten Gitterplatz antikorreliert. Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem dritten-, fünften-, siebten- und neunten Gitterplatz korreliert. \n\nFür die Kopplung {{kolbe2018hubbard_FO0185||FO}} kann der Verlauf wie folgt beschrieben werden. Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem zweiten Gitterplatz antikorreliert. Die Korrelation zwischen dem Spin auf dem ersten Gitterplatz und dem Spin auf dem zweiten- und allen weiteren Gitterplätzen verschwindet. \n\nIm Vergleich zur Nächsten-Nachbar-Wechselwirkung fällt auf, dass die Spin-Korrelation, für kleine Kopplung {{kolbe2018hubbard_FO0179||FO}} geringe Abweichungen zeigt. Die Anti- Korrelation am zweiten Gitterplatz nimmt für stärkere antiferromagnetische Kopplung zwischen den Über-Nächsten-Nachbarn zu. Dagegen nimmt die Korrelation an den Gitterplätze {{kolbe2018hubbard_FO0186||FO}} ab. Für den Wert {{kolbe2018hubbard_FO0187||FO}} sind die Abweichungen sehr gering. Für die Kopplung {{kolbe2018hubbard_FO0188||FO}} nimmt die Korrelation zwischen den Spins erkennbar ab. Für die beiden Werte stehen die Spins des Systems antiparallel zu ihren Nächsten Nachbar und parallel zu den Über-Nächsten-Nachbar.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "029",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0109",
"text": "\n\nBei einer Kopplung von {{kolbe2018hubbard_FO0189||FO}} verschwindet die Korrelation zwischen den Spins für die Gitterplätze {{kolbe2018hubbard_FO0186||FO}}. Die beteiligten Spins könne,n wegen konkurrierender Wechselwirkung, nicht den energetisch günstigsten Zustand annehmen. Das heißt, bei dieser Gitter Konfiguration, ist für den Wert {{kolbe2018hubbard_FO0190||FO}} die geometrische Frustration zu beobachten. \n\nIn dem folgenden Diagramm ist die Spin-Korrelation für Über-Nächste-Nachbar Wechselwirkung dargestellt. Die Spin-Korrelation wird für geringere Kopplung {{kolbe2018hubbard_FO0191||FO}} zwischen den Über-Nächsten Gitterplätzen untersucht.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "030",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0110",
"text": "Abbildung 5.5: Eine Heisenberg-Kette mit {{kolbe2018hubbard_FO0001||FO}} Gitterplätzen und Über-Nächster-Nachbar Wechselwirkung. \n\nDer Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem zweiten-, dritten-, sechsten-, siebten- und zehnten Gitterplatz antikorreliert. Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem vierten-, fünften-, achten- und neunten Gitterplatz korreliert. \n\nWenn der Kopplungs-Parameter {{kolbe2018hubbard_FO0179||FO}} erhöht wird nimmt die anti-Korrelation zwischen dem Spin auf dem ersten Gitterplatz und dem Spin auf dem dritten-, fünften-, sechsten- und siebten Gitterplatz zu. Die anti-Korrelation zwischen dem Spin auf dem ersten Gitterplatz und dem Spin auf dem zweiten- und zehnten Gitterplatz nimmt ab. Die Korrelation zwischen dem Spin auf dem ersten Gitterplatz und dem Spin auf dem vierten Gitterplatz nimmt ab. Die Korrelation zwischen dem Spin auf dem ersten Gitterplatz und dem Spin auf dem fünften-, achten und neunten Gitterplatz nimmt zu.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "030",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0111",
"text": "\n\nIm Vergleich zur Nächsten-Nachbar-Wechselwirkung fällt auf, dass sich die Spins für {{kolbe2018hubbard_FO0192||FO}} an den Gitterplätzen {{kolbe2018hubbard_FO0193||FO}} gedreht haben und das für {{kolbe2018hubbard_FO0194||FO}} die Spin-Korrelation hat an den Gitterplätzen {{kolbe2018hubbard_FO0195||FO}} den gleichen Wert. Der Verlauf der Kurven unterscheidet sich deutlich. Die Korrelation nimmt, für die Über-Nächste-Nachbar Wechselwirkung, mit dem Abstand etwas geringer ab. \n\nDer erste Spin steht antiparallel zum zweiten- und dritten Spin. Der zweite- und dritte Spin stehen Parallel zueinander, aber antiparallel zum vierten- und fünften Spin. Diese Ordnung wird beibehalten bis zum neunten Spin, der antiparallel zum letzten Spin steht. Der Erste und letzte Spins haben keinen Nachbar Spin der parallel ist. \n\nEs ist keine Frustration zu erkennen, weil alle Spins korrelieren. Die Spins in dem System bilden eine Struktur im Grundzustand die nicht die energetisch Günstigste ist.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "031",
"parent_section": "kolbe2018hubbard_H31"
},
{
"title": "kolbe2018hubbard_PARA_0112",
"text": "!! 5.1.3 Störstellen",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "031",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0113",
"text": "Abbildung 5.6: Ein Sketch einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung und sechs Plätzen. \n\nIn den folgenden Diagrammen, wird die Spin-Korrelation zwischen einer linearen Kette mit Störstellen an den Enden dargestellt. Die Kopplung der Störstellen an die Heisenberg-Kette wird, durch die Kopplungskonstante {{kolbe2018hubbard_FO0179||FO}} beschrieben. Das System wird mit der antiferromagnetische Kopplung {{kolbe2018hubbard_FO0196||FO}} für das Heisenberg-Modell untersucht. Die Kopplung zwischen linearen Kette hat den Wert {{kolbe2018hubbard_FO0197||FO}} und wird nicht verändert. Eine schematische Darstellung wird in Abbildung 5.6 gezeigt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "031",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0114",
"text": "\n\nIn dem folgenden Diagramm wird die Spin-Korrelation für den Limes der Kopplung {{kolbe2018hubbard_FO0198||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "032",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0115",
"text": "\n\nDer Spin auf der Störstelle auf dem ersten Gitterplatz ist mit dem Spin auf dem zweiten-, vierten-, sechsten- und achten Gitterplatz antikorreliert. Der Spin auf der Störstelle auf dem ersten Gitterplatz ist mit dem Spin auf dem dritten-, fünften-, siebten-, und neunten Gitterplatz korreliert. Der Spin auf der Störstelle auf dem ersten Gitterplatz ist mit dem Spin auf der Störstelle auf dem zehnten Gitterplatz antikorreliert. \n\nDie Spin-Korrelation zwischen der Störstelle und dem Spin am Gitterplatz {{kolbe2018hubbard_FO0199||FO}} nimmt für {{kolbe2018hubbard_FO0198||FO}} ab. Die Störstelle und der Spin stehen parallel zueinander. Die Spin-Korrelation steigt insgesamt an für stärkere Kopplung {{kolbe2018hubbard_FO0179||FO}} zwischen der Störstelle und dem System. Die Spin-Korrelation an den Gitterplätzen {{kolbe2018hubbard_FO0200||FO}} verläuft im Limes {{kolbe2018hubbard_FO0198||FO}} gegen Null. Das bedeutet die Korrelation mit der Kette verschwindet und es sind nur noch die Störstellen antikorreliert. Die Spin-Korrelation zwischen beiden Störstellen hat, für den Wert {{kolbe2018hubbard_FO0201||FO}}, einen Wert von {{kolbe2018hubbard_FO0202||FO}} und verläuft im Limes {{kolbe2018hubbard_FO0198||FO}} gegen {{kolbe2018hubbard_FO0203||FO}}. Die beiden Störstellen sind stark anti-korreliert, obwohl ein großer Abstand zwischen ihnen liegt. Die Anti-Korrelation wird stärker für geringere Kopplung. Es bildet sich für {{kolbe2018hubbard_FO0198||FO}} ein Singulett Zustand zwischen den Störstellen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "032",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0116",
"text": "\n\nIn dem folgenden Diagramm ist die Spin-Korrelation für den Limes der Kopplung {{kolbe2018hubbard_FO0204||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "033",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0117",
"text": "\n\nDer Spin auf der Störstelle auf dem ersten Gitterplatz ist, für {{kolbe2018hubbard_FO0205||FO}} mit dem Spin auf dem zweiten-, vierten-, sechsten-, achten- und zehnten Gitterplatz antikorreliert. Der Spin auf dem ersten Gitterplatz ist mit dem Spin auf dem dritten-, fünften-, siebten- und neunten Gitterplatz korreliert. \n\nIm Vergleich mit dem System ohne Störstelle fällt auf, dass die Spin-Korrelation etwas stärker, mit zunehmenden Abstand abnimmt. Die Spin-Korrelation hat für {{kolbe2018hubbard_FO0205||FO}} ein ähnliches Muster wie das System ohne Störstellen. Die Störstelle ist stark anti-korreliert mit dem Spin am zweiten Gitterplatz. \n\nDie Spin-Korrelation ,für den Limes {{kolbe2018hubbard_FO0206||FO}}, zwischen der Störstellen auf dem ersten Gitterplatz und dem Spins auf den Gitterplätzen {{kolbe2018hubbard_FO0186||FO}} verschwindet. Die Spin-Korrelation zwischen dem Spin auf der Störstellen auf dem ersten Gitterplatz und dem Spin auf der Störstelle auf dem zehnten Gitterplatz verschwindet. Die Spin-Korrelation zwischen der Störstelle auf dem ersten Gitterplatz und dem Spin auf dem zweiten Gitterplatz nimmt den Wert {{kolbe2018hubbard_FO0203||FO}} an. Es bildet sich ein Singulett-Zustand zwischen dem Spin auf der Störstelle und dem Spin auf dem zweiten Gitterplatz.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "033",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0118",
"text": "\n\nIn dem folgenden Diagramm wird die Spin-Korrelation zwischen der ersten Störstelle und dem letzten {{kolbe2018hubbard_FO0207||FO}} gegen {{kolbe2018hubbard_FO0208||FO}} aufgetragen. Die Spin-Korrelation ist in dem Diagramm für die Gitterplatz Anzahl {{kolbe2018hubbard_FO0209||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "034",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0119",
"text": "\n\nDie Kurven haben den gleichen Verlauf im Diagramm. In den Grenzfällen {{kolbe2018hubbard_FO0210||FO}} und {{kolbe2018hubbard_FO0211||FO}} verlaufen die Kurven übereinander. Das Maximum liegt, bei jeder Kurve im Intervall ( {{kolbe2018hubbard_FO0212||FO}} , {{kolbe2018hubbard_FO0194||FO}} ). Das Maximum wird mit zunehmender Gitterplatz Anzahl kleiner und ist bei kleineren Kopplungen {{kolbe2018hubbard_FO0179||FO}}. Das Diagramm bestätigt, dass für {{kolbe2018hubbard_FO0210||FO}} und {{kolbe2018hubbard_FO0211||FO}} die Spin-Korrelation verschwindet.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "034",
"parent_section": "kolbe2018hubbard_H32"
},
{
"title": "kolbe2018hubbard_PARA_0120",
"text": "!! 5.2 Das Hubbard-Modell",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "035",
"parent_section": "kolbe2018hubbard_H33"
},
{
"title": "kolbe2018hubbard_PARA_0121",
"text": "!! 5.2.1 Nächste-Nachbar Hopping\n\n \n\nIn dem folgenden Diagramm ist die Korrelation zwischen Fermionen, für eine lineare Kette dargestellt. In dem Diagramm sind die Graphen mit {{kolbe2018hubbard_FO0213||FO}} konstanten Hopping-Parameter, für unterschiedliche Parameter des Interaction-Parameter {{kolbe2018hubbard_FO0134||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "035",
"parent_section": "kolbe2018hubbard_H34"
},
{
"title": "kolbe2018hubbard_PARA_0122",
"text": "\n\nDas Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem zweiten-, vierten- und sechsten Gitterplatz antikorreliert. Das Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem dritten- und fünften Gitterplatz korreliert. \n\nDie Elektron-Korrelation hat ein ähnliches Muster wie die Spin-Korrelation im Heisenberg Modells. Die Korrelation zwischen den Elektronen wird, mit zunehmenden Parametern des Interaction-Parameters stärker. Das Diagramm zeigt, dass für die Elektron-Korrelation das Verhältnis {{kolbe2018hubbard_FO0214||FO}} relevant ist. Die Fermionen-Korrelation zeigt, dass die Fermionen für große {{kolbe2018hubbard_FO0134||FO}} und kleines Verhältnis {{kolbe2018hubbard_FO0215||FO}}, stärker korrelieren. Die Elektron-Korrelation nimmt mit steigender Gitterposition ab. Für genügend große {{kolbe2018hubbard_FO0134||FO}} verschwindet die doppele Belegung der Gitterposition[2]. Es befindet sich für ein kleines Verhältnis {{kolbe2018hubbard_FO0216||FO}} an jeder Gitterposition genau ein Elektron im Grundzustand. Die Fermionen-Korrelation zeigt, dass sich eine antiparallele Anordnung der Elektronen Zustände bildet. Die Elektronen befinden sich in den Up- und Down Zuständen. Die Elektronen können dann wegen dem Pauli-Prinzip nicht mehr hüpfen. Wenn das Band voll besetzt ist, können sich die Elektronen nicht frei im Gitter bewegen, d.h. das System beschreibt wird zu einem Isolator.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "035",
"parent_section": "kolbe2018hubbard_H34"
},
{
"title": "kolbe2018hubbard_PARA_0123",
"text": "!! 5.2.2 Über-Nächste-Nachbar Hopping\n\n \n\nIn den folgenden Diagrammen wird die Korrelation zwischen Fermionen, für ein System mit Über-Nächste-Nachbar Hopping dargestellt. Es wird für diese Gitter-Konfiguration angenommen, dass die Fermionen einen Gitterplatz weiter hüpfen können, als bei der Nächsten-Nachbarn Konfiguration. Der Sprung zum Über-Nächsten-Nachbarn wird mit dem Parameter {{kolbe2018hubbard_FO0217||FO}} beschrieben. In Abbildung 2.1 ist eine schematische Darstellung einer Gitter-Konfiguration mit Über-Nächster Nachbar Hopping. Die Gitter-Konfiguration kann man als eindimensionale Kette (Abbildung5.3) auffassen werde. In dieser Gitter-Konfiguration ist, für die Elektron-Korrelation das Verhältnis von {{kolbe2018hubbard_FO0218||FO}} und {{kolbe2018hubbard_FO0219||FO}} relevant. Der Hopping-Parameter für den Sprung zum Nächsten-Nachbar {{kolbe2018hubbard_FO0220||FO}} ist für beide Diagramme gleich. \n\nIn dem folgenden Diagramm ist die Elektron-Korrelation für verschiedene Interaction-Parameter {{kolbe2018hubbard_FO0134||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "036",
"parent_section": "kolbe2018hubbard_H35"
},
{
"title": "kolbe2018hubbard_PARA_0124",
"text": "\n\nDas Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem zweiten-, vierten- und sechsten Gitterplatz antikorreliert. Das Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem dritten- und fünften Gitterplatz korreliert. \n\nDie Kurven in dem Diagramm haben ein konstantes Verhältnis {{kolbe2018hubbard_FO0221||FO}}. Das Verhältnis {{kolbe2018hubbard_FO0215||FO}} wird durch die steigenden Interaction-Parameter geändert. Die Fermionen-Korrelation hat das gleiche Muster wie die Nächsten-Nachbar-Hopping. Die Korrelationen nehmen mit zunehmen den Parametern des Interaction-Parameters zu und verändern sich auf die gleiche Weise, wie",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "036",
"parent_section": "kolbe2018hubbard_H35"
},
{
"title": "kolbe2018hubbard_PARA_0125",
"text": "\nbei der Nächsten-Nachbar-Hopping. Die Korrelation ist für die Gitterpositionen {{kolbe2018hubbard_FO0222||FO}} sehr gering. \n\nIn dem folgenden Diagramm ist die Elektron-Korrelation für verschiedene Hopping-Parameter {{kolbe2018hubbard_FO0217||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "037",
"parent_section": "kolbe2018hubbard_H35"
},
{
"title": "kolbe2018hubbard_PARA_0126",
"text": "\n\nDas Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem zweiten-, dritten- und sechsten Gitterplatz antikorreliert. Das Elektron auf dem ersten Gitterplatz ist mit dem Elektron auf dem vierten- und fünften Gitterplatz korreliert. \n\nIm Vergleich zum Nächsten-Nachbar Hopping zeigt das Diagramm, dass für {{kolbe2018hubbard_FO0223||FO}} die Elektron Korrelation an der Gitterplätzen drei und vier umklappt. Die Elektron-Korrelation mit dem zweiten Gitterplatz ist für den Wert {{kolbe2018hubbard_FO0224||FO}} schwächer antikorreliert wie für den Wert {{kolbe2018hubbard_FO0213||FO}}. Am dritten Gitterplatz ist den Wert {{kolbe2018hubbard_FO0225||FO}} schwächer antikorreliert wie für den Wert {{kolbe2018hubbard_FO0226||FO}}. Die Elektron-Korrelation mit dem vierten Gitterplatz ist für den Wert {{kolbe2018hubbard_FO0224||FO}}, die korreliert verschwunden und für den Wert {{kolbe2018hubbard_FO0213||FO}} ist eine geringe Korrelation erkennbar. An dem fünften Gitterplatz ist die Korrelation, für beide Parameter, sehr schwach. Die Elektron-Korrelation mit dem sechsten Gitterplatz ist für den Wert {{kolbe2018hubbard_FO0224||FO}} etwas stärker antikorreliert, wie für den Wert {{kolbe2018hubbard_FO0213||FO}}. Bei dem Verhältnis {{kolbe2018hubbard_FO0227||FO}} ist die Elektron-Korrelationen wieder sehr ähnlich, zu der Nächsten-Nachbar Hopping und wird deshalb nicht extra dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229037",
"modified": "20260602105229037",
"page": "037",
"parent_section": "kolbe2018hubbard_H35"
},
{
"title": "kolbe2018hubbard_PARA_0127",
"text": "!! 5.2.3 Störstellen\n\n \n\nIn den folgenden Diagrammen wird die Korrelation von einem System aus einer linearen Kette mit Störstellen an beiden Enden dargestellt. Dabei charakterisiert {{kolbe2018hubbard_FO0217||FO}} den Hopping-Parameter für den Sprung von der Störstellen auf die lineare Kette. Der Hopping-Parameter {{kolbe2018hubbard_FO0213||FO}} charakterisiert die Sprünge zwischen den Gitterplätzen der linearen Kette und hat in allen Diagrammen einen festen Wert. \n\nIn dem folgenden Diagramm ist die Elektron-Korrelation mit einem festen Wert {{kolbe2018hubbard_FO0005||FO}} für ver schiedene Interaction-Parameter {{kolbe2018hubbard_FO0134||FO}} dargestellt. Die Elektron-Korrelation wird für das Verhältnis der Hopping-Parameter {{kolbe2018hubbard_FO0227||FO}} und {{kolbe2018hubbard_FO0228||FO}} untersucht.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "038",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0128",
"text": "Abbildung 5.13: Hubbard-Kette mit {{kolbe2018hubbard_FO0004||FO}} Gitterplätzen und Über-Nächster-Nachbar Hopping mit {{kolbe2018hubbard_FO0005||FO}} \n\nDas Elektron auf der Störstelle ist mit dem Elektron auf dem zweiten- und vierten Gitterplatz antikorreliert. Das Elektron auf der Störstelle ist mit dem Elektron auf dem dritten- und fünften Gitterplatz korreliert. Die Elektronen auf den Störstellen sind antikorreliert. \n\nDie Korrelation zwischen den Störstellen ist erkennbar stärker, als die Korrelation zwischen der Störstelle und der linearen Kette. Für größere Interaction-Parameter {{kolbe2018hubbard_FO0134||FO}} nimmt die Korrelation an allen Gitterplätzen zu.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "038",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0129",
"text": "\n\nIn dem folgenden Diagramm ist die Elektron-Korrelation mit festen Parameter {{kolbe2018hubbard_FO0229||FO}}, für verschiedene Hopping-Parameter {{kolbe2018hubbard_FO0230||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "039",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0130",
"text": "Abbildung 5.14: Hubbard-Kette mit, Störstellen an beiden Enden, {{kolbe2018hubbard_FO0004||FO}} Gitterplätzen und {{kolbe2018hubbard_FO0006||FO}} \n\nDas Elektron auf der Störstelle auf dem ersten Gitterplatz ist, für die Parameter {{kolbe2018hubbard_FO0231||FO}} und {{kolbe2018hubbard_FO0232||FO}}, mit dem Elektron auf dem zweiten- und vierten Gitterplatz antikorreliert. Das Elektron auf der Störstelle ist mit dem Elektron auf dem dritten- und fünften Gitterplatz korreliert. Die Elektronen auf den Störstellen sind antikorreliert. \n\nDie Kurven der Elektron-Korrelation sind vergleichbar, mit den Ergebnissen für das System mit Störstellen, dass mittels dem Heisenberg-Modell untersucht wurde. Die Spins an den beiden Störstellen sind anti-korreliert und haben eine erkennbar stärkere Korrelation. Die Korrelation nimmt, mit steigendem Abstand, bist zum fünften Gitterplatz ab. Das Elektron auf der Störstelle auf dem letzten Gitterplatz ist, im Vergleich zu den Elektronen an den Gitterplätzen davor, mit dem Elektron auf dem ersten Gitterplatz erkennbar stark antikorreliert. Die Korrelation, für die Parameter {{kolbe2018hubbard_FO0233||FO}} und {{kolbe2018hubbard_FO0234||FO}}, zwischen dem Elektron auf der Störstelle am ersten Gitterplatz und den Elektronen auf den Gitterplätzen der linearen Kette verschwindet. Für die Parameter {{kolbe2018hubbard_FO0231||FO}} und {{kolbe2018hubbard_FO0232||FO}} ist die Anti-Korrelation zwischen den Elektronen auf den Störstellen schwächer als bei dem Wert {{kolbe2018hubbard_FO0233||FO}}, aber die Korrelationen mit den Elektronen auf den Gitterplätzen der linearen Kette sind stärker. Es bildet sich ein Singulett-Zustand zwischen den Elektron auf der Störstelle auf dem ersten Gitterplatz und dem Elektron auf der Störstelle auf dem letzten Gitterplatz.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "039",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0131",
"text": "\n\nIn dem folgenden Diagramm ist die Elektron-Korrelation mit einem festen Wert {{kolbe2018hubbard_FO0006||FO}} für verschiedene Hopping-Parametert' {{kolbe2018hubbard_FO0235||FO}} dargestellt.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "040",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0132",
"text": "Abbildung 5.15: Hubbard-Kette mit, Störstellen an beiden Enden, {{kolbe2018hubbard_FO0004||FO}} Gitterplätzen und {{kolbe2018hubbard_FO0006||FO}} \n\nDas Elektron auf der Störstelle ist, für die Parameter {{kolbe2018hubbard_FO0225||FO}} und {{kolbe2018hubbard_FO0236||FO}}, mit dem Elektron auf dem zweiten-,vierten- und sechsten Gitterplatz antikorreliert. Das Elektron auf der Störstelle ist mit dem Elektron auf dem dritten- und fünften Gitterplatz korreliert. Die Elektronen auf den Störstellen sind antikorreliert. \n\nFür den Parameter {{kolbe2018hubbard_FO0237||FO}} ist das Elektron auf der Störstelle mit dem Elektron am zweitern Gitterplatz antikorreliert. Die Korrelation zwischen dem Elektron auf der Störstelle und dem Elektron auf dem dritten-, vierten-, fünften- und sechsten Gitterplatz verschwindet. \n\nIn dem Diagramm ist zu sehen, dass für den Parameter {{kolbe2018hubbard_FO0237||FO}} die Elektron-Korrelation ab dem dritten Gitterplatz verschwindet. Es bildet sich ein Singulett-Zustand zwischen den Elektron auf der Störstelle und dem Elektron auf dem zweiten Gitterplatz. Für die beiden anderen Parameter ist eine geringe Korrelation, mit allen Gitterplätzen, die dem Verlauf der antiferromagnetische an Ordnung ähnlich ist, zu erkennen.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "040",
"parent_section": "kolbe2018hubbard_H36"
},
{
"title": "kolbe2018hubbard_PARA_0133",
"text": "! 6 Fazit und Ausblick\n\n \n\nIn dieser Arbeit wurden drei verschiedene Gitter-Konfigurationen mit zwei Modellen auf Korre lation untersucht. Die Modelle wurden am Beginn der Arbeit vorgestellt und die wesentlichen Grundlagen, für die Modelle, sowie für die Korrelation, bereit gestellt. Die Umsetzung der Modelle in einen Programmcode wurde teilweise gezeigt und begründet. Bei den Ergebnissen wurde zuerst die einfachste Gitter-Konfiguration vorgestellt, um einen Bezug zu dem Modell herzustellen. \nDas Ziel dieser Arbeit war es, an gleichen Gitter-Konfigurationen, die Korrelation zwischen Spins und die Korrelation zwischen Fermionen zu untersuchen. Dabei sollte für das Heisenberg-Modell ein Beispiel gefunden werden, bei dem das Phänomen der \"magnetischen Frustration\" auftritt. Dafür wurde eine Über-Nächste-Nachbar Wechselwirkung als Gitter-Konfiguration gewählt. Ein weiteres Ziel dieser Arbeit war es, die Bildung eines Singulett-Zustand nachzuweisen. Dafür wurde eine linearen Kette mit Störstellen an beiden Enden als letzte Gitter-Konfiguration betrachtet. Im Heisenberg-Modell konnte erfolgreich, die ferromagnetische und antiferromagnetische Ordnung in der linearen Kette mittels Spin-Korrelation dargestellt werden. Es wurde ein Parameter {{kolbe2018hubbard_FO0238||FO}} gefunden, der in der Gitter-Konfiguration für Über-Nächste-Nachbar die Wechselwirkung beschreibt. Es wurden erfolgreich Singulett-Zustände in dem System mit Störstellen nachgewiesen und graphisch dargestellt. \nMit dem Hubbard-Modell wurden Elektronen-Zustände untersucht, für die lineare Kette konnte eine antiferromagnetische Ordnung mittels der Fermionen-Korrelation berechnet werden. Es wurde gezeigt, dass die Elektronen für genügend großes {{kolbe2018hubbard_FO0134||FO}} eine anti-parallele Ordnung in der linearen Kette aufweisen. Damit konnte gezeigt werden, dass sich an jedem Gitterplatz ein Elektron befindet. Es handelt sich also in diesem Fall um ein voll besetztes Band. Wegen dem Pauli-Prinzip können sich die Elektronen nicht bewegen, daher beschreibt die Konfiguration einen Isolator. Es konnte gezeigt werden, dass sich auch in einer Elektronen Konfiguration mit Störstellen Singulett-Zustände bilden. \nDie beiden Modelle wurden mit der Programmiersprache Julia implementiert. Für die Modelle wurden verschiedene Algorithmen, Funktionen und Methoden entwickelt. Die Implementation in der Programmiersprache Julia erwies sich als sehr elegant und leicht verständlich. Der Pro grammcode ist deutlich kürzer, als entsprechende C- Sourcen. Alle Berechnungen wurden mit den selbst-erstellten Programmen durchgeführt. Die Ausführungsgeschwindigkeit ist vergleichbar mit C-Code, da Julia für die wesentlichen numerischen Routinen auf die gleichen Bibliotheken (LAPACK/BLAS) zugreift. \nDie Architektur der Programme erlaubt die Verwendung für beliebige Gitter-Konfigurationen. Für jeden Operator wurde eine Funktion implementiert, sodass man sie nacheinander ausführen kann, wie man es aus der Quantenmechanik gewohnt ist. Die Algorithmen wurden so modular strukturiert, dass die einzelnen Funktionen für andere Modelle wieder verwendbar sind.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"page": "041",
"parent_section": "kolbe2018hubbard_H37"
},
{
"title": "kolbe2018hubbard_PARA_0134",
"text": "! Literaturverzeichnis\n\n \n[1] Matthias Bartelmann, Björn Feuerbacher, Timm Krüger, Dieter Lüst, Anton Rebhan, and Andreas Wipf. Theoretische Physik. Springer-Verlag, 2014. \n[2] Gerd Czycholl. Theoretische Festkörperphysik: von den klassischen Modellen zu modernen Forschungsthemen. 2004. \n[3] M. G. Gonzalez, F. T. Lisandrini, G. G. Blesio, A. E. Trumper, C. J. Gazza, and L. O. Manuel. Correlated partial disorder in a weakly frustrated quantum antiferromagnet. ArXiv e-prints, April 2018. \n[4] Armen G. Khachaturyan. Theory of Structural Transformations in Solids (Dover Books on Engineering). Dover Publications, 2008. ISBN 0486462803. \n[5] Wolfgang Nolting. Grundkurs Theoretische Physik 7: Viel-Teilchen-Theorie. Springer-Verlag, 2009. \n[6] Wolfgang Nolting. Grundkurs Theoretische Physik 5/2. Springer, 2015. \n[7] Jochen Pade. Quantenmechanik zu Fuß 2: Anwendungen und Erweiterungen. Springer-Verlag, 2012. \n[8] Jan-Markus Schwindt. Tutorium Quantenmechanik: von einem erfahrenen Tutor-für Physik und Mathematikstudenten. Springer-Verlag, 2016. \n[9] M. R. Zirnbauer. Lectures on Advanced Quantum Mechanics. Universität zu Köln, 2010. \n[10] M. R. Zirnbauer. Quantenphysik. Universität zu Köln, 2013.",
"type": "text/vnd.tiddlywiki",
"tags": "paragraph kolbe2018hubbard",
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"modified": "20260602105229038",
"page": "042",
"parent_section": "kolbe2018hubbard_H38"
},
{
"title": "kolbe2018hubbard_H1",
"text": "{{kolbe2018hubbard_PARA_0004||PARA}}\n\n{{kolbe2018hubbard_TOC01||TOC}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "1",
"caption": "Inhaltsverzeichnis",
"page": "002",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H2",
"text": "{{kolbe2018hubbard_PARA_0005||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "2",
"caption": "Abbildungsverzeichnis",
"page": "003",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H3",
"text": "{{kolbe2018hubbard_PARA_0006||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "3",
"caption": "Selbständigkeitserklärung",
"page": "004",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H4",
"text": "{{kolbe2018hubbard_PARA_0007||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "4",
"caption": "Danksagung",
"page": "005",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H5",
"text": "{{kolbe2018hubbard_PARA_0008||PARA}}\n\n{{kolbe2018hubbard_DIA_0002||DIA}}\n\n{{kolbe2018hubbard_PARA_0009||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "5",
"caption": "1 Einleitung",
"page": "006",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H6",
"text": "{{kolbe2018hubbard_PARA_0010||PARA}}\n\n\n\n!! Subsections\n\n* <$link to=\"kolbe2018hubbard_H7\">{{kolbe2018hubbard_H7!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H8\">{{kolbe2018hubbard_H8!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H9\">{{kolbe2018hubbard_H9!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H10\">{{kolbe2018hubbard_H10!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H11\">{{kolbe2018hubbard_H11!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H12\">{{kolbe2018hubbard_H12!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H13\">{{kolbe2018hubbard_H13!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H14\">{{kolbe2018hubbard_H14!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H15\">{{kolbe2018hubbard_H15!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H16\">{{kolbe2018hubbard_H16!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H17\">{{kolbe2018hubbard_H17!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H18\">{{kolbe2018hubbard_H18!!caption}}\n\n* <$link to=\"kolbe2018hubbard_H19\">{{kolbe2018hubbard_H19!!caption}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "1",
"section_number": "6",
"caption": "2 Grundlagen der Quanten-Mechanik",
"page": "007",
"kind": "section",
"parent_section": "kolbe2018hubbard"
},
{
"title": "kolbe2018hubbard_H7",
"text": "{{kolbe2018hubbard_PARA_0011||PARA}}\n\n{{kolbe2018hubbard_EQ0001_p007||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0012||PARA}}\n\n{{kolbe2018hubbard_LI0001||LI}}\n\n{{kolbe2018hubbard_LI0002||LI}}\n\n{{kolbe2018hubbard_PARA_0013||PARA}}\n\n{{kolbe2018hubbard_LI0003||LI}}\n\n{{kolbe2018hubbard_LI0004||LI}}\n\n{{kolbe2018hubbard_LI0005||LI}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.1",
"caption": "2.1 Hilbertraum und Eigenschaften von Operatoren",
"page": "007",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H8",
"text": "{{kolbe2018hubbard_PARA_0014||PARA}}\n\n{{kolbe2018hubbard_EQ0002_p008||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0015||PARA}}\n\n{{kolbe2018hubbard_EQ0003_p008||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0016||PARA}}\n\n{{kolbe2018hubbard_EQ0004_p008||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0017||PARA}}\n\n{{kolbe2018hubbard_EQ0005_p008||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0018||PARA}}\n\n{{kolbe2018hubbard_EQ0006_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0019||PARA}}\n\n{{kolbe2018hubbard_EQ0007_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0020||PARA}}\n\n{{kolbe2018hubbard_EQ0008_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0021||PARA}}\n\n{{kolbe2018hubbard_EQ0009_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0022||PARA}}\n\n{{kolbe2018hubbard_EQ0010_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0023||PARA}}\n\n{{kolbe2018hubbard_EQ0011_p009||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0024||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.2",
"caption": "2.2 Drehimpulsoperator",
"page": "008",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H9",
"text": "{{kolbe2018hubbard_PARA_0025||PARA}}\n\n{{kolbe2018hubbard_EQ0012_p010||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0026||PARA}}\n\n{{kolbe2018hubbard_EQ0013_p010||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0027||PARA}}\n\n{{kolbe2018hubbard_EQ0014_p010||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0028||PARA}}\n\n{{kolbe2018hubbard_EQ0015_p010||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0029||PARA}}\n\n{{kolbe2018hubbard_EQ0016_p011||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0030||PARA}}\n\n{{kolbe2018hubbard_EQ0017_p011||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0031||PARA}}\n\n{{kolbe2018hubbard_EQ0018_p011||EQBLOCK}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.3",
"caption": "2.3 Der Spin",
"page": "010",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H10",
"text": "{{kolbe2018hubbard_PARA_0032||PARA}}\n\n{{kolbe2018hubbard_EQ0019_p011||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0033||PARA}}\n\n{{kolbe2018hubbard_EQ0020_p011||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0034||PARA}}\n\n{{kolbe2018hubbard_EQ0021_p011||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0035||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
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"level": "2",
"section_number": "6.4",
"caption": "2.4 Spin-Korrelation",
"page": "011",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H11",
"text": "{{kolbe2018hubbard_PARA_0036||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.5",
"caption": "2.5 Vielteilchen-Systeme",
"page": "012",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H12",
"text": "{{kolbe2018hubbard_PARA_0037||PARA}}\n\n{{kolbe2018hubbard_EQ0022_p012||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0038||PARA}}\n\n{{kolbe2018hubbard_EQ0023_p012||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0039||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.6",
"caption": "2.5.1 Der Hilbertraum",
"page": "012",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H13",
"text": "{{kolbe2018hubbard_PARA_0040||PARA}}\n\n{{kolbe2018hubbard_EQ0024_p012||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0041||PARA}}\n\n{{kolbe2018hubbard_EQ0025_p012||EQBLOCK}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.7",
"caption": "2.5.2 Operatoren",
"page": "012",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H14",
"text": "{{kolbe2018hubbard_PARA_0042||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.8",
"caption": "2.6 Zweite Quantisierung",
"page": "012",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H15",
"text": "{{kolbe2018hubbard_PARA_0043||PARA}}\n\n{{kolbe2018hubbard_EQ0026_p013||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0044||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.9",
"caption": "2.6.1 Hilbertraum",
"page": "013",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H16",
"text": "{{kolbe2018hubbard_PARA_0045||PARA}}\n\n{{kolbe2018hubbard_EQ0027_p013||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0046||PARA}}\n\n{{kolbe2018hubbard_EQ0028_p013||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0047||PARA}}\n\n{{kolbe2018hubbard_EQ0029_p013||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0048||PARA}}\n\n{{kolbe2018hubbard_EQ0030_p013||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0049||PARA}}",
"type": "text/vnd.tiddlywiki",
"tags": "section kolbe2018hubbard",
"created": "20260602105229038",
"modified": "20260602105229038",
"level": "2",
"section_number": "6.10",
"caption": "2.6.2 Vielteilchenwellenfunktion",
"page": "013",
"kind": "subsection",
"parent_section": "kolbe2018hubbard_H6"
},
{
"title": "kolbe2018hubbard_H17",
"text": "{{kolbe2018hubbard_PARA_0050||PARA}}\n\n{{kolbe2018hubbard_EQ0031_p014||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0051||PARA}}\n\n{{kolbe2018hubbard_EQ0032_p014||EQBLOCK}}\n\n{{kolbe2018hubbard_PARA_0052||PARA}}\n\n{{kolbe2018hubbard_EQ0033_p014||EQBLOCK}}",
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},
{
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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},
{
"title": "kolbe2018hubbard_FO0015",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\mathbb{C}^{n}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0016",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0017",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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},
{
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"latex": "|0\\rangle+|\\phi\\rangle=|\\phi\\rangle",
"displayMode": "false"
},
{
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"tags": "formula kolbe2018hubbard",
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},
{
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},
{
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0022",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
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"tags": "formula kolbe2018hubbard",
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},
{
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0024",
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"tags": "formula kolbe2018hubbard",
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"latex": "\\langle\\psi| \\in \\mathcal{H}^{*}",
"displayMode": "false"
},
{
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"tags": "formula kolbe2018hubbard",
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"latex": "\\langle\\psi|",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0026",
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},
{
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},
{
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"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0029",
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"tags": "formula kolbe2018hubbard",
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"latex": "\\hat{\\mathrm{A}}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0030",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"displayMode": "false"
},
{
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"displayMode": "false"
},
{
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"tags": "formula kolbe2018hubbard",
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},
{
"title": "kolbe2018hubbard_FO0033",
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"tags": "formula kolbe2018hubbard",
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},
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},
{
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},
{
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"latex": "\\vec{p} \\rightarrow \\frac{i}{\\hbar} \\nabla",
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},
{
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"latex": "\\vec{r} \\rightarrow \\hat{r}",
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},
{
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},
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},
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},
{
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},
{
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},
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"tags": "formula kolbe2018hubbard",
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"latex": "\\hat{J}^{2}=\\hat{J}_{x}^{2}+\\hat{J}_{y}^{2}+\\hat{J}_{z}^{2}",
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},
{
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},
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},
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},
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},
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},
{
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},
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},
{
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"tags": "formula kolbe2018hubbard",
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},
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},
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"tags": "formula kolbe2018hubbard",
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},
{
"title": "kolbe2018hubbard_FO0054",
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"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\hat{J}^{+}",
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},
{
"title": "kolbe2018hubbard_FO0055",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\hat{J}^{-}",
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},
{
"title": "kolbe2018hubbard_FO0056",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\mathcal{H}_{s=1 / 2}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0057",
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"tags": "formula kolbe2018hubbard",
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"latex": "|\\uparrow\\rangle",
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},
{
"title": "kolbe2018hubbard_FO0058",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\left\\{|\\uparrow\\rangle=\\binom{1}{0},|\\downarrow\\rangle=\\binom{0}{1}\\right\\}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0059",
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"tags": "formula kolbe2018hubbard",
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"latex": "z",
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},
{
"title": "kolbe2018hubbard_FO0060",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"latex": "\\alpha, \\beta",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0061",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "|\\alpha|^{2}+|\\beta|^{2}=1",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0062",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
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"tags": "formula kolbe2018hubbard",
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},
{
"title": "kolbe2018hubbard_FO0063",
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"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "2 \\times 2",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0064",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "\\sigma_{i}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0065",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "(2.20)",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0066",
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"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "\\{A, B\\}=A B+B A",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0067",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "[-1,1]",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0068",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "\\vec{S}_{i} \\vec{S} j",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0069",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
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"modified": "20260602105229039",
"latex": "T",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0070",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "i, j \\in(1, \\ldots, N)",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0071",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "\\left|\\Psi_{E_{n}, l}\\right\\rangle",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0072",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "E_{n}, \\beta=\\frac{1}{k_{B} T}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0073",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "g_{n}",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0074",
"text": "<$latex text={{!!latex}} displayMode={{!!displayMode}} />",
"type": "text/vnd.tiddlywiki",
"tags": "formula kolbe2018hubbard",
"created": "20260602105229039",
"modified": "20260602105229039",
"latex": "\\left|\\psi_{g}\\right\\rangle",
"displayMode": "false"
},
{
"title": "kolbe2018hubbard_FO0075",
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},
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},
{
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},
{
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},
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},
{
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},
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},
{
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},
{
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},
{
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},
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},
{
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},
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},
{
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},
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},
{
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},
{
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},
{
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},
{
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},
{
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},
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},
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},
{
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},
{
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},
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{
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},
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},
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},
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},
{
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"type": "text/vnd.tiddlywiki",
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},
{
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},
{
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},
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},
{
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},
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},
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},
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"type": "text/vnd.tiddlywiki",
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"latex": "\\mathbf{H}_{U}",
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},
{
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},
{
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"latex": "\\mathrm{H}_{t}",
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},
{
"title": "kolbe2018hubbard_FO0136",
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"latex": "t",
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},
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"height": "200",
"width": "435",
"top_left_x": "781",
"top_left_y": "1155",
"latex_tex": "\\begin{aligned} c(\\left| \\phi \\right>+\\left| \\psi \\right>)=&\\,c\\left| \\phi \\right>+c\\left| \\psi \\right> \\qquad \\text{}\\\\ (c+d)\\left| \\phi \\right>=&\\,c\\left| \\phi \\right>+d\\left| \\phi \\right>\\\\ c(d\\left| \\phi \\right>)=&\\,cd\\left| \\phi \\right> \\end{aligned}",
"score_tex": "0.657"
},
{
"title": "kolbe2018hubbard_EQ0002_p008",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229077",
"modified": "20260602105229077",
"kind": "Equation",
"latex": "\\vec{J}=\\vec{r} \\times \\vec{p}",
"displayMode": "true",
"refnum": "2.4",
"equation_number": "(2.4)",
"page": "008",
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"latex_tex": "\\vec{J}=\\vec{r}\\times\\vec{p}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0003_p008",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229110",
"modified": "20260602105229110",
"kind": "Equation",
"latex": "\\hat{J}=\\frac{\\mathrm{i}}{\\hbar} \\hat{r} \\times \\nabla",
"displayMode": "true",
"refnum": "\\2.5\\",
"equation_number": "(\\2.5\\)",
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"latex_tex": "\\begin{aligned} \\hat{J}= & \\dfrac{\\mathrm{i}}{\\hbar}\\hat{r}\\times\\nabla \\end{aligned}",
"score_tex": "0.986"
},
{
"title": "kolbe2018hubbard_EQ0004_p008",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229140",
"modified": "20260602105229140",
"kind": "Equation",
"latex": "\\hat{J}_{x}=\\frac{\\mathrm{i}}{\\hbar}\\left(y \\frac{\\partial}{\\partial z}-z \\frac{\\partial}{\\partial y}\\right) \\quad ; \\quad \\hat{J}_{y}=\\frac{\\mathrm{i}}{\\hbar}\\left(z \\frac{\\partial}{\\partial x}-x \\frac{\\partial}{\\partial z}\\right) \\quad ; \\quad \\hat{J}_{z}=\\frac{\\mathrm{i}}{\\hbar}\\left(x \\frac{\\partial}{\\partial y}-y \\frac{\\partial}{\\partial x}\\right)",
"displayMode": "true",
"refnum": "\\2.5\\",
"equation_number": "(\\2.5\\)",
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"height": "127",
"width": "1275",
"top_left_x": "395",
"top_left_y": "1923",
"latex_tex": "\\hat{J}_x=\\dfrac{\\mathrm{i}}{\\hbar}\\left(y\\dfrac{\\partial}{\\partial z}-z\\dfrac{\\partial}{\\partial y}\\right)\\,\\,\\,\\, ;\\,\\,\\,\\, \\hat{J}_y= \\dfrac{\\mathrm{i}}{\\hbar}\\left(z\\dfrac{\\partial}{\\partial x}-x\\dfrac{\\partial}{\\partial z}\\right)\\,\\,\\,\\, ;\\,\\,\\,\\,\\hat{J}_z=\\dfrac{\\mathrm{i}}{\\hbar}\\left(x\\dfrac{\\partial}{\\partial y}-y\\dfrac{\\partial}{\\partial x}\\right)",
"score_tex": "0.934"
},
{
"title": "kolbe2018hubbard_EQ0005_p008",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229173",
"modified": "20260602105229173",
"kind": "Equation",
"latex": "\\left[\\hat{J}_{x}, \\hat{J}_{y}\\right]=\\mathrm{i} \\hbar \\hat{J}_{z} \\quad ; \\quad\\left[\\hat{J}_{y}, \\hat{J}_{z}\\right]=\\mathrm{i} \\hbar \\hat{J}_{x} \\quad ; \\quad\\left[\\hat{J}_{z}, \\hat{J}_{x}\\right]=\\mathrm{i} \\hbar \\hat{J}_{y}",
"displayMode": "true",
"refnum": "",
"equation_number": "",
"page": "008",
"canonical_uri": 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OT6AkZlh44tbv4cDxlNayQQi1e4NuzDdlSRtB6HJGAfcdKAOrHPNcf8AC/8A5EO2/wCvu9/9Kpa6LRb9tV0PT9Re3a3a6t45zCxyYyyhtue+M4rnfhf/AMiHbf8AX3e/+lUtAHY1h65qOvWUsS6PoMWpowPmM98tv5Z7cFTmtysPXT4oEsP9gQaPImD5p1CaVCD227FOePWgDJ/t/wAbdvAtvj/sNJ/8bo/t/wAb/wDQi2//AIOk/wDjdG/4kf8APn4U/wDAq4/+N0eZ8SP+fPwn/wCBVx/8boA1tD1DXb6SddY0GLSwoHllb5bjzD3GAoxitztWJoTeJ2ef/hIIdIjTA8k6fNI5J77t6jHbpW32oA8r+MMur6JYWWtaXr+pWplvobZ7aOQCIqQxyABnOQO9enzSxwQyTSsEjjUszHoABk5rzT46kf8ACGabyB/xN7f+T1t/FfWP7G+GmtTq+JZYfsyD1MhCcfgSfwoA434Radqeu2OteIri5lsbTWNQluP3B2zTgHABfkqikuPlwSSeQBhul8Natew/FHxD4XN3Pd6da2sVxCbhzI8LMBlN55YHdn5s4xXQeDtLXw34G0iwlAjNraIZvQORlz/30Wrg/hpesNK13xxcwl7rxBqQjtIc8lA/lxr+DFgfZM9qAPXc461heM9Y/sDwbrGqbtr29q7Rn/bIwn/jxFY+s+O7nTviFpnhSy0Se9NzGstxcq5C26MSAxGDwNpJyR+Nc78c9QlufD+neE9P/falrN2irAvUopzk+g3bPwB9KANH4IaP/ZXwwsZHXEt/JJdvn3O1f/HVU/jXo24ZxVLSrCLSdGstPhz5NpAkKn/ZVQv9K5a48canaX089x4UvI/D0JcNqZuI92FON/kE7tuRwepGDjmgDtsilqhpV5Pf2CXM9nJaGQkpBKfnCZ+UsP4WIwdvbNXx0oAKKKKAOMubXxqfiZbXMN5bL4UWAiWEhdxbafbOd2OQcY/I9nWK/inQ4/E0fh1tRiXV5E8xbUg7mGCeuMZwCcZzjmtodKACiiigArjviH/x56B/2MFh/wCjhXY1x3xD/wCPPQP+xgsP/RwoA7DNGRWP4o15PDPhrUNZkgeZbSPeI06uSQAPzNUvC/iiTV/BsWv6vYtpAMbyyxTPkIik/NkgHBAzyOhoA4K7/wCKl/aUtoD81voFj5jDtvK5B/OVP++a9izXkfwXtLjU77xP4zuoWT+17wi23DBEYJbj2+ZR/wAArqvEXjg6EWnjsBcWMV7FYyyeaVdpXIyIk2nftBBOSOcgZwaAOyJxS1z3iDxLHoGpaJYi2a4n1a8FsiIwXYuMtIfUKMcVc13xHpPhfTP7Q1m8W0td4jDspOWPQAAEk8H8qANWjNQ213BeWkN1bTJLbzIJI5EOVdSMgg+hFYPjfxV/wh/hi41dbOS8kR0ijgQ43OxwMnBwKAOj3D+teO+Gf+Kl/aE8R6v9+30a3+yRH+4/CH9RL+degReKPI8Cr4k1i0fTStp9pmtpW+ZDjhecZJ4AHByQODXHfAzSbu28JXmtX8ZW71q7a53EYLJ/CfzLn6EUAep5H0oLAc9q5zxHr+r6bNFbaH4cuNZumXzJAJ1gjiTOBl24LHnCjnjJxxl2h+JJNdu5Io9MubZbZSt205H7qb5f3alchiBkkg4Hy+uAAUPGX/IyeCv+ws3/AKTy12Ncd4x/5GTwV/2FW/8ASeWuxoAjlZ1jdo13yAHapbGT2Ge31rkf7f8AG3/QjW59/wC2U/8AjddfIH8t/LCl8HaGJAz2z7VyG/4kdrPwnj/r6uP/AI3QAf2/43/6EW3/APB0n/xuj+3vG+f+RGtx6/8AE5T8/wDV0eZ8SP8Anz8J/wDgVcf/ABul3/EjvZ+FP/Aq4/8AjdAHXRFmiQuAHKgsAc4P171FeWzXVpLAlxLbs6kCWEgOvuMgjP4VNHv8tfMCh8DcFORnvilzQB5n8M7zVX8X+NtJ1HV7zUYdNuYIrdrlwWVT5noAMnAzgDpVH4xPdarq/hLwrZRRzz3t/wDaZInOFKxj+LvtIZs/7pq38OD/AMXL+JB9by3/APatM0z/AIqH9oLVrzAe30DT0tEYdBJJyfx+aQfhQBf8eJqHhrwPf+II/EF+dUtAjrKHCxMxcLt8n7hXnHIJ9ya7bR759R0SwvZoxFLc20crx/3SygkfgTXnvxa8zXb3wz4MiYgate+bcleogiwzfzJH+7XZTeIILWz1u4W3c2ujxneY+d5WPeyKPYbR9SR2NAG7uArx3x3/AMVH8cfB/h8fNBYA383oDndg/hEv/fVdt4D8WXfi3w1Jq9/pD6WPNdI0kcsHQAHeCQOOSM+1cV8NkfxP8UPFXjXYzWJP2KylI4cDAyv/AAFFP/A6APYc0bhWTe6ncx6gmn6dapc3Xl+dL5svlxxISQCzBWOWIbAAP3TnFcn/AMLIvZtI1S+s/Dstw+k3BtL2KOVmLzCTZshKod/GGJO3AYdewB6HRTIX8yCOTYyblB2MMFcjoR60+gAppB5xTqQnFAHG+BLXxrbNqv8AwmN5bXG6cfYjCF+Vfm3dAOD8uAeeua7MdKxtC8U6J4lW6bRdQiuxbSeXN5YPyt+IGRxwRwcVsjpQAUUUUAFcf/zWU/8AYvj/ANKK7CuP/wCayn/sXx/6UUAdfmms6qpdiAgGSSelcb8QfHM/gyDTxaaPNql5fTmOKCJiOBjPQEk8jA9z6UfEzxCNC+HOpXLkxXVzB9lt48/N5sg24HqR8zfRTQByXwTU6zqni7xdKCTqF+YoSR91QS5H5Og/4DXsOa434W6BL4c+HWlWNxEY7p4zPMrDBDOS2CPUAhfwqfWvE+uWerNbaR4TvNVtoCPtVytxHCFyN2Iw+PMIB5xxnjOc0AdXuFLWLoOuDxBFNd29rNFY5CwSzfK0pGdxC9l6ANnnntgkk8W6FF4li8OSajEuryJvW2IOSMZ64xnHOM59qANqkzzil6iuI1Hx5cW3xJsvCNpok12siLJc3auQIAwJBxjpx3IoA0fiBrH9heAdb1EPseO1ZI2HZ3+Rfx3MKxfg1o/9j/DDStybZbsNdv77z8p/75CVh/HC7m1Kx0XwdpxaTUdWvEYxoMkRrnlh2G4g5/2Ce1ekmSz8O6CucpZ2VuFUKMnaqhQAO5OAAO5oA0s0ZrjNV8ZX+h32mW2oaKN2qyNDZpBdBnEuBtWQFQFBzywLBfccnT8P69e6vf6tZXulSWj6fKkfmgs0U+4ZOxmVScY9O4oAz5ufjJY/9gCf/wBHxV2NcdNz8Y7E/wDUAn/9HxV2NAFS/kuYLKeWztVubpFJjhaTy959N2Dj8q5j+3/G/wD0Itv/AODpP/jddTfi8FjMdOWBrvYfJW4ZljLdtxUE4+grlvM+JH/Pn4T/APAq4/8AjdAB/b/jf/oRbf8A8HSf/G6kt9d8ZSXMSTeDIIYWcB5BrCvsGeTgJz9Kj8z4kf8APn4T/wDAq4/+N1Lbv8QvtMX2m08MCDePMMd1cFwueduY8ZxmgDrR0FUdV0+TUrCS2iv7qxZyD59qyiRcHsWBH6VeppYDrQB5z8GtS1PVPDOrNql/Nez2+rTW6yzHJ2qkeP6n8ayfG5v9f+NPhnRdM8svpdtJfSPJllhLHAYqDyVKoQOM7gMgE1e+Bx/4prXvfXrn/wBBjpnw4/4nvxD8b+KGAeP7UunWzj+5HwcfULGaAJ/iDd3vgnStM1ew1W/uLx9Rht5IriQOlyrbtylAAq5x1QL0r0vcAK8u8Xq3ib4weF/Do5tNLjbV7r0JBwgI+oX8Hro9e8cR6N4O1LxGlg9zFbTmGCNXx55Egj3AjOBuzzzkDNAHXbhXjukn/hJv2kdUvvv22g2fkRt6PjaR+by/lXfab4oMngePxJrNnJpn+jNcTW8h+aIDPqByRjHHeuM+BmnXR0TWPE1/EUuNcvWnGf4kBJB/Fnf64FAHq+aNwzjvXHax44Om31io09ZtPu9UXSlm84iRpTuViqbTlFZSpJI6NgHjOjq3iZNL8TaFoYtnnuNVaXBVsCJI13M59ewx9aAOhooooAKq6if+Jbd/9cX/APQTVqoriEXFvLCTgSIVyO2RjNAHN/Do/wDFuPDn/YPh/wDQRVqXwrCTcCz1HULCG5dpJYbWRVUsxyxXKkoSeTtIycnqc1W8KeFdQ8MwxWj+Irm/sIIBBBbS28SCMAjBDKAxIAxyT1rqB0560AZWieHdL8O2X2PS7RLeItvcglnkc9WZjyze5qnrXiqw0HXNLsL6N1F8JiLptqwwKihjvdiMZ4AA/HHFdDTHjV/vKrdxmgDy3wbrVlD4n8Y61qsjW13eXca29rMu2eSBI/3RSM/MS4PAA5P0r0yya4msIJLqEQXDxq0kQfeEYjlc98Hj8Kl8oEhiBuHQgYxnripB0oA4zw/4a0TSPGmq3Gi2KWy+SFu3R2IeZ23bcE4G1QDgAAeYK7LrioYbSK2V1gjSNXdpCEXaCzEknjuSck9/rU9AGBL4VhLXAs9S1CwhuXaSWG1kVVLMcsV3KShJ5O0jJyepzVrRPDul+HbL7HpdolvEW3uQSzyOerMx5Zvc1q0UAcd8UPtifDfXm06JnujbbMRrlvLLAPjHopY/hXIeN7/R7nwV4f8ABGhX0U/9pz2lkPs7bikAKks2OnQdeTz713/ii01y4fTJtHunjjt7xZruCMqHuIgD8gLcDJxnpxnms+08NXmpeK7fxBq8cFslijpp9hCd4iZxh5ZGwAXIwMDgDuTzQB1yBI41RVCqowAOgArkfhjx4Dtsjn7Xe8f9vUtbms6dqGo2qR6drM2lSiQM0sUKSllwRtw4IA5B6dqj8L6Avhnw/BpS3Ul0ImkczSKFZi8jOcgcdWNAGzRRRQAUUUUAFFFFAHNa74C8O+Jrgz6zZzXbEghWvJgikDAIQOFBx3A70+88E6Jf6NbaTdW801jb3C3Mcct1LId4PGWZixHJ4ziuiooAaV3Ag4wex5zWFo/g/SdDeL7DDIkUDO1vA07vHblySxRScAklucZG4gYBIO/RQBlX+hQ3t4l8lxPaXyJ5QubZgGKZztIYFWGeQGBwckYyc1tN8JabpuqyasfOu9VlXY19dyeZLt/ur2Rc9lCit6igCrfXtvptlNeXUnlwQjc7YJx9AOST0wOSTgc157c+OtGh1GKbxY19p9znzbDSpLOVuAflf5VIkkzjjOFPTpuPpJjDZz60GJWYMQCQcrx0oAqaXcXF5psFzdWbWcsq7jbM2TGD0B98Yz6HOM9avDpSAYpaACiiigDjdZ8PaNP4+0bU47OP+29zO9wjsGW3RCCSAcH5mjXkZw2O1diM4GetRfZYftTXIiQTMoRpNvzFQSQCfQEkge5qYdKACiiigArjviGf9D8Pj/qYNP8A/Rwrsaw/E/h0+I9NhtVvZLKSC6iu4p40VirxtuXhhg8460AaV7Z2+o2c9pdxLNbTIUkjcZDAjkGsO88E2epwJaanqOqX1gpBFpPc/IQOQGZQHcA4PzMc45zWro9hfWFj5OoarLqc+4nz5YkjOD22oAK0e1AEMFrFa20dvbxJDDGoRI4xtVQOgAHSuB8dpGfHPgdb0rDo8d3cTyyP8sf2hUzCGPQHcWI9TmvRK5O8tvEkHii9vIlGo6ZPbJHbWTSJFHFIDlmckFuvcA9enAoA56HULXxZ8bLV7OYXFj4f013Eq8qZ5jt4PQjZ3HcH0rr/ABXpWhavoM8XiK2jn06E+c6uSuCoOCCpBzyRx1z71B4V8MSaIdRv764S51fVZhPeTRrtTgYSNAeQirwMknqe+BvzWsNwgSeJJEVw4VxkBgcg/UEAj3oAzfC2ntpnhXS7N4vKeK2QNFnPlnAyv0HT8KuajptrqtlJaXkQkhfBwGKkEHIYEcgggEEcgjNXKKAOYu/A9hqnkrrN5farbwkNHa3UqiHI6FlRV3/8D3dTXSBAq7QAABgADGBT6KAOF8SeMLe3ubiGR72z0e1fy77VILd3AfvEpUErjPzOOh4Hzcro+FNe03WoHXQbVl0O2UJDc+W0aTPnkIrDJA7sepPGeTXTGMEEEDB7ULGEQKgAAHAHH/6qAOQ8Y8+JPBXf/iatz/27y12VcnN4PvrvxLaarfeI7q5t7O6a5t7JraJUQlWUDcqhiAGxk5NdZ0oAKKKKACiiigAqteWUV/aS2s5kEUo2t5UrRtj2ZSCPwNWaKAOV0v4deGtF1Q6lp9lPDds+95RfTkyH/by5D/Q5rT0nw3puiXupXlhAY59Sn8+6cuWLv+JwByeB61r0UAZGreG7DWrqyu7oSpd2TM1tcQStHJHuG1gGHYjgirdrpdnZ6eLCCBRbBSvltlg2ck7s5JJJJJPJJJPWrlFAHL3PgizudP8A7NfUNS/srbsFiLnbHs/ubgPM29sbsY4resdOtNMsorOxt47e2hXbHFGuFUfSrVFAHJ3/AI10+w1/UtKe1nF3aW0cysVAFyzZ2RR85ZieBgdc1zHw01KHS/AFrboyXPiC7uZpJ7LdtlEzSEMXGMoFXBYkdMeoz6e0Ss4cqpZc7SRyKPKUOWAG44ycc0ASDpRRRQAU006kIyMdqAON8JeHdF0TxBr76DZpa2j+TFKI3Yq0672fGSQABIgwOAciuz7VDBbR20flwIkaFmbCjHLEsT9SST9SamoAKKKKACuO/wCayng/8i+B0/6eDXY1y2t+EbvUfES63p2v3OlXItPsjeTBFJuTeX/jU45x09KANnVNIttXjiE5dJIH82CeJyskT4I3KfoSMcggkHINZg8GafNqkGp6lNdard2xzbteuGSA+qRqAgPTnGeB6V0MaskSK7l3CgM5GNx9cCnUAMZ1UFmIAHVieBXnWs+NdIll83XZLuw8Nu2yCQ20jJfsOeWUHEeOg/j65K8H0bbkn9DTWiV4yjojIRjaRkH8KAMjw7rKa5p7XlvaSW9gz7bMyqUaWLAw+wgFQTnGeoAPesbxB4b0S68Z6PqK2KHXTMr/AGhWbcsEfzMxAOCM7UyRn5wK7EJjOOuc1GLWIXLXIjQTsgjaTb8zKCSAT6AsfzPrQBMPujnPHWsu/wBCivL4X8Vzc2V6I/K+0WzgMyZJ2srAq2CSRkHGTjGTWrRQBhaT4S0vSdRn1NY3udSnG2S9unMkrL/dBPCr/sqAKXxTr1v4Y8P3GrXVtcXMUDJmO3UF2JYAdSBgZHNblNK7sggEHsaAPLtU1ex1T4u6Bcz3Mcek6bZ3Jhu5WAhkuXADxh/ukqhBxnqCOxr0DS9SOqJPcJCVtfN220pOPPTA+ccdCScHuAD0NXvIQoEKLsH8OOKcUYqQGwexoA5Gb/ksVk3b+wLjn/t4irsa5TR/CF7YeJRrmo+IbnVbhbRrRBNbxRBUZ1c/6sDPKDr611Y6UAFFFFABRRRQAVS1PS7fV7RrW687ymIJ8i4khb/vpGBx7Zq7RQBzWg+A/D3hi5M+jWctozZLKt3MyMSMZKM5Un3IzV7w/wCG9M8L6c1hpMBht2laZgXLEu2Mkk89gPwrXooAxNR8K6ZqeqrqcqzxXogNs09tcPCzxE52MVIyM8+o7Yq7caRY3WlnTZbdPsexUESZQKFxt2kYKkYGCORgY6VeooA5i78EWWqLFFq99f6naRMHS1uph5WR03BQpfB5+ctXRpEsSKkaqqKAoUDAAA4AHp7VJRQB5z4o8mP4reFpNSkjt9Mtre6mgkkIWNrk4GCemQvI/GodDvbfxX8ZdT1OzlWax0TTks4ZF5RpZWLFlPfgEZHBHNbs1v4otfEGrzIialZ3XlfYIZZVjhttq/Nv4LZLEnIB4A/C94T8Mnw7YXBnuftepX1w11e3JXHmSt/dHZQBgCgDoaKKKACiiigAooooAKKKKACiiigAooooAKKKKAEIoAx0wPpS0UAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUmOaWigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigBMc5paKKACiiigD/9k=",
"height": "76",
"width": "862",
"top_left_x": "607",
"top_left_y": "2275",
"latex_tex": "[\\hat{J}_x,\\hat{J}_y]=\\mathrm{i}\\hbar\\hat{J}_z \\,\\,\\,\\, ;\\,\\,\\,\\, [\\hat{J}_y,\\hat{J}_z]=\\mathrm{i}\\hbar\\hat{J}_x \\,\\,\\,\\, ;\\,\\,\\,\\, [\\hat{J}_z,\\hat{J}_x]=\\mathrm{i}\\hbar\\hat{J}_y",
"score_tex": "0.905"
},
{
"title": "kolbe2018hubbard_EQ0006_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229204",
"modified": "20260602105229204",
"kind": "Equation",
"latex": "\\epsilon_{i j k}=\\left\\{\\begin{aligned} +1, & \\text { wenn ijk eine gerade Permutation von } 123 \\text { ist } \\\\ -1, & \\text { wen ijk eine ungerade Permutation von } 123 \\text { ist } \\\\ 0, & \\text { wenn mindestens zwei Indizes gleich sind } \\end{aligned}\\right.",
"displayMode": "true",
"refnum": "2.6",
"equation_number": "(2.6)",
"page": "009",
"canonical_uri": 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"height": "250",
"width": "1077",
"top_left_x": "502",
"top_left_y": "296",
"latex_tex": "\\begin{aligned} \\epsilon_{ijk} = \\begin{cases} +1, & \\text{ wenn ijk eine gerade Permutation von 123 ist} \\\\ -1, & \\text{wen ijk eine ungerade Permutation von 123 ist} \\\\ \\,\\,\\,\\,\\,0, & \\text{wenn mindestens zwei Indizes gleich sind} \\end{cases} \\end{aligned}",
"score_tex": "0.926"
},
{
"title": "kolbe2018hubbard_EQ0007_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229237",
"modified": "20260602105229237",
"kind": "Equation",
"latex": "\\left[\\hat{J}_{i}, \\hat{J}_{j}\\right]=\\mathrm{i} \\hbar \\sum_{k} \\hat{J}_{k} \\epsilon_{i j k}",
"displayMode": "true",
"refnum": "\\2.7\\",
"equation_number": "(\\2.7\\)",
"page": "009",
"canonical_uri": 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"height": "122",
"width": "387",
"top_left_x": "845",
"top_left_y": "651",
"latex_tex": "[\\hat{J}_i,\\hat{J}_j]=\\mathrm{i}\\hbar\\sum_k\\hat{J}_k\\epsilon_{ijk}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0008_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229267",
"modified": "20260602105229267",
"kind": "Equation",
"latex": "\\left[\\hat{J}_{i}, \\hat{J}^{2}\\right]=0 \\quad i=x, y, z",
"displayMode": "true",
"refnum": "\\2.8\\",
"equation_number": "(\\2.8\\)",
"page": "009",
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"height": "88",
"width": "424",
"top_left_x": "826",
"top_left_y": "890",
"latex_tex": "[\\hat{J}_i,\\hat{J}^2]=0 \\,\\,\\,\\,\\,\\,\\,\\, i= x,y,z",
"score_tex": "0.912"
},
{
"title": "kolbe2018hubbard_EQ0009_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229298",
"modified": "20260602105229298",
"kind": "Equation",
"latex": "\\begin{aligned} \\hat{\\mathbf{J}}^{2}|j, m\\rangle & =\\hbar^{2} j(j+1)|j, m\\rangle \\\\ \\hat{J}_{z}|j, m\\rangle & =\\hbar m|j, m\\rangle \\end{aligned}",
"displayMode": "true",
"refnum": "2.10",
"equation_number": "(2.10)",
"page": "009",
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"height": "150",
"width": "464",
"top_left_x": "804",
"top_left_y": "1443",
"latex_tex": "\\begin{aligned} \\hat{\\mathbf{J}}^2\\left| j,m \\right>=&\\,\\hbar^2 j(j+1)\\left| j,m \\right>\\\\ \\hat{J}_z\\left| j,m \\right>=&\\, \\hbar m \\left| j,m \\right> \\end{aligned}",
"score_tex": "0.761"
},
{
"title": "kolbe2018hubbard_EQ0010_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229328",
"modified": "20260602105229328",
"kind": "Equation",
"latex": "\\begin{aligned} \\hat{J}^{+} & =\\left(\\hat{J}_{x}+\\mathrm{i} \\hat{J}_{y}\\right) \\\\ \\hat{J}^{-} & =\\left(\\hat{J}_{x}-\\mathrm{i} \\hat{J}_{y}\\right) \\end{aligned}",
"displayMode": "true",
"refnum": "2.11",
"equation_number": "(2.11)",
"page": "009",
"canonical_uri": 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"height": "186",
"width": "302",
"top_left_x": "884",
"top_left_y": "1765",
"latex_tex": "\\begin{aligned} \\hat{J}^+= & \\left(\\hat{J}_x+\\mathrm{i}\\hat{J}_y\\right) \\\\ \\hat{J}^-= & \\left(\\hat{J}_x-\\mathrm{i}\\hat{J}_y\\right) \\end{aligned}",
"score_tex": "0.963"
},
{
"title": "kolbe2018hubbard_EQ0011_p009",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229357",
"modified": "20260602105229357",
"kind": "Equation",
"latex": "\\left[\\hat{J}_{z}, \\hat{J}^{+}\\right]=\\hbar \\hat{J}^{+} \\quad, \\quad\\left[\\hat{J}_{z}, \\hat{J}^{-}\\right]=-\\hbar \\hat{J}^{-} \\quad, \\quad\\left[\\hat{J}^{+}, \\hat{J}^{-}\\right]=2 \\hbar \\hat{J}_{z}",
"displayMode": "true",
"refnum": "2.13",
"equation_number": "(2.13)",
"page": "009",
"canonical_uri": 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"height": "85",
"width": "944",
"top_left_x": "566",
"top_left_y": "2124",
"latex_tex": "[\\hat{J}_z,\\hat{J}^+]=\\hbar\\hat{J}^+ \\,\\,\\,\\, ,\\,\\,\\,\\, [\\hat{J}_z,\\hat{J}^-]=-\\hbar\\hat{J}^- \\,\\,\\,\\, ,\\,\\,\\,\\, [\\hat{J}^+,\\hat{J}^-]=2\\hbar\\hat{J}_z",
"score_tex": "0.855"
},
{
"title": "kolbe2018hubbard_EQ0012_p010",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229389",
"modified": "20260602105229389",
"kind": "Equation",
"latex": "|s\\rangle=\\alpha|\\uparrow\\rangle+\\beta|\\downarrow\\rangle=\\binom{\\alpha}{\\beta}",
"displayMode": "true",
"refnum": "2.14",
"equation_number": "(2.14)",
"page": "010",
"canonical_uri": 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"height": "122",
"width": "456",
"top_left_x": "808",
"top_left_y": "1135",
"latex_tex": "\\left| s \\right>=\\alpha\\left| \\uparrow \\right>+\\beta\\left| \\downarrow \\right>=\\vector{\\alpha}{\\beta}",
"score_tex": "0.748"
},
{
"title": "kolbe2018hubbard_EQ0013_p010",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229422",
"modified": "20260602105229422",
"kind": "Equation",
"latex": "\\hat{\\sigma}_{x}=\\left(\\begin{array}{ll} 0 & 1 \\\\ 1 & 0 \\end{array}\\right) \\quad ; \\quad \\hat{\\sigma}_{y}=\\left(\\begin{array}{cc} 0 & -\\mathrm{i} \\\\ \\mathrm{i} & 0 \\end{array}\\right) \\quad ; \\quad \\hat{\\sigma}_{z}=\\left(\\begin{array}{cc} 1 & 0 \\\\ 0 & -1 \\end{array}\\right) \\quad ; \\quad \\hat{\\sigma}_{0}=\\left(\\begin{array}{ll} 1 & 0 \\\\ 0 & 1 \\end{array}\\right)",
"displayMode": "true",
"refnum": "\\2.15\\",
"equation_number": "(\\2.15\\)",
"page": "010",
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"height": "175",
"width": "1207",
"top_left_x": "429",
"top_left_y": "1418",
"latex_tex": "\\begin{aligned} \\hat{\\sigma}_x=\\begin{pmatrix} 0 & 1\\\\ 1 & 0 \\end{pmatrix}\\,\\,\\,\\,;\\,\\,\\,\\,\\hat{\\sigma}_y=\\begin{pmatrix} 0 & -\\mathrm{i}\\\\ \\mathrm{i} & 0 \\end{pmatrix}\\,\\,\\,\\,;\\,\\,\\,\\,\\hat{\\sigma}_z=\\begin{pmatrix} 1 & 0\\\\ 0 & -1 \\end{pmatrix}\\,\\,\\,\\,;\\,\\,\\,\\,\\hat{\\sigma}_0=\\begin{pmatrix} 1 & 0\\\\ 0 & 1 \\end{pmatrix} \\end{aligned}",
"score_tex": "0.701"
},
{
"title": "kolbe2018hubbard_EQ0014_p010",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229460",
"modified": "20260602105229460",
"kind": "Equation",
"latex": "\\begin{aligned} \\vec{S} & =\\frac{\\hbar}{2} \\vec{\\sigma} \\\\ \\hat{S}_{i} & =\\frac{\\hbar}{2} \\hat{\\sigma}_{i} \\quad i=x, y, z \\end{aligned}",
"displayMode": "true",
"refnum": "2.16",
"equation_number": "(2.16)",
"page": "010",
"canonical_uri": 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"height": "200",
"width": "366",
"top_left_x": "854",
"top_left_y": "1804",
"latex_tex": "\\begin{aligned} \\vec{S}=&\\,\\dfrac{\\hbar}{2}\\vec{\\sigma}\\\\ \\hat{S_i}=&\\,\\dfrac{\\hbar}{2}\\hat{\\sigma}_i\\,\\,\\,\\,\\,\\, i=x,y,z \\end{aligned}",
"score_tex": "0.949"
},
{
"title": "kolbe2018hubbard_EQ0015_p010",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229494",
"modified": "20260602105229494",
"kind": "Equation",
"latex": "\\begin{aligned} \\mathbf{1}_{2} & =\\hat{\\sigma}_{x}^{2}+\\hat{\\sigma}_{y}^{2}+\\hat{\\sigma}_{z}^{2} \\\\ 2 \\mathrm{i} \\hat{\\sigma}_{z} & =\\left[\\hat{\\sigma}_{x}, \\hat{\\sigma}_{y}\\right] \\quad \\text { und zyklisch } \\\\ \\left\\{\\hat{\\sigma}_{x}, \\hat{\\sigma}_{y}\\right\\} & =\\left\\{\\hat{\\sigma}_{y}, \\hat{\\sigma}_{z}\\right\\}=\\left\\{\\hat{\\sigma}_{z}, \\hat{\\sigma}_{x}\\right\\}=0 \\end{aligned}",
"displayMode": "true",
"refnum": "2.19",
"equation_number": "(2.19)",
"page": "010",
"canonical_uri": 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",
"height": "211",
"width": "597",
"top_left_x": "740",
"top_left_y": "2122",
"latex_tex": "\\begin{aligned} \\mathbf{1}_2=&\\,\\,\\hat{\\sigma}_x^2+\\hat{\\sigma}_y^2+\\hat{\\sigma}_z^2\\\\ 2\\mathrm{i}\\hat{\\sigma}_z=&\\,\\,[\\hat{\\sigma}_x,\\hat{\\sigma}_y] \\,\\,\\,\\, \\text{und zyklisch}\\\\ \\{\\hat{\\sigma}_x,\\hat{\\sigma}_y\\}=&\\,\\,\\{\\hat{\\sigma}_y,\\hat{\\sigma}_z\\}=\\{\\hat{\\sigma}_z,\\hat{\\sigma}_x\\}=0 \\end{aligned}",
"score_tex": "0.987"
},
{
"title": "kolbe2018hubbard_EQ0016_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229528",
"modified": "20260602105229528",
"kind": "Equation",
"latex": "\\begin{aligned} & \\hat{S}_{x}=\\frac{1}{2}\\left(\\hat{S}^{+}+\\hat{S}^{-}\\right) \\\\ & \\hat{S}_{y}=\\frac{1}{2 \\mathrm{i}}\\left(\\hat{S}^{+}-\\hat{S}^{-}\\right) \\end{aligned}",
"displayMode": "true",
"refnum": "2.21",
"equation_number": "(2.21)",
"page": "011",
"canonical_uri": 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"height": "195",
"width": "330",
"top_left_x": "870",
"top_left_y": "367",
"latex_tex": "\\begin{aligned} \\hat{S}_x=&\\,\\,\\dfrac{1}{2}(\\hat{S}^++\\hat{S}^-)\\\\ \\hat{S}_y=&\\,\\,\\dfrac{1}{2\\mathrm{i}}(\\hat{S}^+-\\hat{S}^-) \\end{aligned}",
"score_tex": "0.929"
},
{
"title": "kolbe2018hubbard_EQ0017_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229559",
"modified": "20260602105229559",
"kind": "Equation",
"latex": "\\hat{S}^{+}=\\hbar\\left(\\begin{array}{ll} 0 & 1 \\\\ 0 & 0 \\end{array}\\right) \\quad ; \\quad \\hat{S}^{-}=\\hbar\\left(\\begin{array}{ll} 0 & 0 \\\\ 1 & 0 \\end{array}\\right)",
"displayMode": "true",
"refnum": "2.23",
"equation_number": "(2.23)",
"page": "011",
"canonical_uri": 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"height": "167",
"width": "617",
"top_left_x": "724",
"top_left_y": "667",
"latex_tex": "\\begin{aligned} \\hat{S}^+=\\hbar \\begin{pmatrix} 0 & 1\\\\ 0 & 0 \\end{pmatrix} \\,\\,\\,\\,;\\,\\,\\, \\hat{S}^-=\\hbar \\begin{pmatrix} 0 & 0\\\\ 1 & 0 \\end{pmatrix} \\end{aligned}",
"score_tex": "0.7"
},
{
"title": "kolbe2018hubbard_EQ0018_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229590",
"modified": "20260602105229590",
"kind": "Equation",
"latex": "\\begin{aligned} \\hat{S}^{+}|\\downarrow\\rangle & =\\hbar|\\uparrow\\rangle & \\hat{S}^{+}|\\uparrow\\rangle & =0 \\\\ \\hat{S}^{-}|\\uparrow\\rangle & =\\hbar|\\downarrow\\rangle & \\hat{S}^{-}|\\downarrow\\rangle & =0 \\\\ \\hat{S}_{z}|\\uparrow\\rangle & =\\frac{\\hbar}{2}|\\uparrow\\rangle & \\hat{S}_{z}|\\downarrow\\rangle & =-\\frac{\\hbar}{2}|\\downarrow\\rangle \\end{aligned}",
"displayMode": "true",
"refnum": "2.25",
"equation_number": "(2.25)",
"page": "011",
"canonical_uri": 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"height": "213",
"width": "885",
"top_left_x": "593",
"top_left_y": "950",
"latex_tex": "\\begin{aligned} \\hat{S}^{+}|\\downarrow\\rangle & =\\hbar|\\uparrow\\rangle & \\hat{S}^{+}|\\uparrow\\rangle & =0 \\\\ \\hat{S}^{-}|\\uparrow\\rangle & =\\hbar|\\downarrow\\rangle & \\hat{S}^{-}|\\downarrow\\rangle & =0 \\\\ \\hat{S}_{z}|\\uparrow\\rangle & =\\frac{\\hbar}{2}|\\uparrow\\rangle & \\hat{S}_{z}|\\downarrow\\rangle & =-\\frac{\\hbar}{2}|\\downarrow\\rangle \\end{aligned}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0019_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229628",
"modified": "20260602105229628",
"kind": "Equation",
"latex": "\\begin{aligned} -1 & <\\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}}<0 & & \\text { antikorreliert. } \\\\ 0 & <\\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}}<1 & & \\text { korreliert. } \\\\ 0 & =\\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}} & & \\text { unkorreliert. } \\\\ 1 & =\\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}} & & \\text { maximal korreliert. } \\end{aligned}",
"displayMode": "true",
"refnum": "2.28",
"equation_number": "(2.28)",
"page": "011",
"canonical_uri": 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"height": "279",
"width": "682",
"top_left_x": "696",
"top_left_y": "1528",
"latex_tex": "\\begin{aligned} -1<&\\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}<0\\quad\\text{antikorreliert.}\\\\ 0<&\\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}<1\\quad\\text{korreliert.}\\\\ 0=&\\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}\\quad\\qquad\\text{unkorreliert.}\\\\ 1=&\\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}\\quad\\qquad\\text{maximal korreliert.} \\end{aligned}",
"score_tex": "0.929"
},
{
"title": "kolbe2018hubbard_EQ0020_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229662",
"modified": "20260602105229662",
"kind": "Equation",
"latex": "\\left\\langle\\vec{S}_{i} \\vec{S}_{j}\\right\\rangle_{T}=\\frac{1}{Z} \\sum_{n} e^{\\beta E_{n}} \\sum_{l=1}^{g_{n}}\\left\\langle\\Psi_{E_{n}, l}\\right| \\vec{S}_{i} \\vec{S}_{j}\\left|\\Psi_{E_{n}, l}\\right\\rangle",
"displayMode": "true",
"refnum": "2.31",
"equation_number": "(2.31)",
"page": "011",
"canonical_uri": 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"height": "129",
"width": "734",
"top_left_x": "671",
"top_left_y": "2049",
"latex_tex": "\\langle \\vec{S}_i\\vec{S}_j\\rangle_T=\\dfrac{1}{Z}\\sum_n e^{\\beta E_n}\\sum_{l=1}^{g_n} \\braket{\\Psi_{E_n,l}}{\\vec{S}_i\\vec{S}_j}{\\Psi_{E_n,l}}",
"score_tex": "0.901"
},
{
"title": "kolbe2018hubbard_EQ0021_p011",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229697",
"modified": "20260602105229697",
"kind": "Equation",
"latex": "\\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}}=\\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\hat{S}_{i} \\hat{S}_{j}\\left|\\psi^{0, l}\\right\\rangle",
"displayMode": "true",
"refnum": "2.32",
"equation_number": "(2.32)",
"page": "011",
"canonical_uri": 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"height": "133",
"width": "556",
"top_left_x": "758",
"top_left_y": "2421",
"latex_tex": "\\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}=\\dfrac{1}{g_0}\\sum_{l=0}^{g_0}\\left< \\psi^{0,l} \\right|\\hat{S}_i\\hat{S}_j\\left| \\psi^{0,l} \\right>",
"score_tex": "0.918"
},
{
"title": "kolbe2018hubbard_EQ0022_p012",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229728",
"modified": "20260602105229728",
"kind": "Equation",
"latex": "\\mathcal{H}=\\mathcal{H}_{1} \\otimes \\mathcal{H}_{2} \\otimes \\ldots \\otimes \\mathcal{H}_{N-1} \\otimes \\mathcal{H}_{N}",
"displayMode": "true",
"refnum": "2.33",
"equation_number": "(2.33)",
"page": "012",
"canonical_uri": 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",
"height": "72",
"width": "602",
"top_left_x": "735",
"top_left_y": "1027",
"latex_tex": "\\mathcal{H}=\\mathcal{H}_1\\otimes\\mathcal{H}_2\\otimes\\,....\\,\\otimes\\mathcal{H}_{N-1}\\otimes\\mathcal{H}_N",
"score_tex": "0.945"
},
{
"title": "kolbe2018hubbard_EQ0023_p012",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229760",
"modified": "20260602105229760",
"kind": "Equation",
"latex": "|\\psi\\rangle=|\\psi\\rangle_{1} \\otimes|\\psi\\rangle_{2} \\otimes \\ldots \\otimes|\\psi\\rangle_{N-1} \\otimes|\\psi\\rangle_{N}",
"displayMode": "true",
"refnum": "2.34",
"equation_number": "(2.34)",
"page": "012",
"canonical_uri": 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",
"height": "74",
"width": "712",
"top_left_x": "680",
"top_left_y": "1235",
"latex_tex": "\\mid\\psi\\rangle=\\mid\\psi\\rangle_1\\otimes\\mid\\psi\\rangle_2\\otimes \\,...\\,\\otimes\\mid\\psi\\rangle_{N-1}\\otimes\\mid\\psi\\rangle_N",
"score_tex": "0.85"
},
{
"title": "kolbe2018hubbard_EQ0024_p012",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229797",
"modified": "20260602105229797",
"kind": "Equation",
"latex": "\\hat{\\mathrm{A}}_{i}: \\mathcal{H}_{i} \\rightarrow \\mathcal{H}_{i}",
"displayMode": "true",
"refnum": "2.35",
"equation_number": "(2.35)",
"page": "012",
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"height": "77",
"width": "248",
"top_left_x": "913",
"top_left_y": "1685",
"latex_tex": "\\hat{\\mathrm{A}}_i : \\mathcal{H}_i\\rightarrow\\mathcal{H}_i",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0025_p012",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229829",
"modified": "20260602105229829",
"kind": "Equation",
"latex": "\\overline{\\mathrm{A}}_{1}+\\ldots+\\overline{\\mathrm{A}}_{N}=\\hat{\\mathrm{A}}_{1} \\otimes \\hat{\\mathrm{I}} \\otimes \\ldots \\otimes \\hat{\\mathrm{I}}+\\hat{\\mathrm{I}} \\otimes \\hat{\\mathrm{~A}}_{2} \\otimes \\ldots \\otimes \\hat{\\mathrm{I}}+\\ldots+\\hat{\\mathrm{I}} \\otimes \\ldots \\otimes \\hat{\\mathrm{~A}_{N}}",
"displayMode": "true",
"refnum": "2.36",
"equation_number": "(2.36)",
"page": "012",
"canonical_uri": 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"width": "1168",
"top_left_x": "452",
"top_left_y": "2003",
"latex_tex": "\\overline{\\mathrm{A}}_1+\\,...\\,+ \\overline{\\mathrm{A}}_N= \\hat{\\mathrm{A}}_1\\otimes\\hat{\\mathrm{I}}\\otimes ...\\otimes\\hat{\\mathrm{I}} +\\hat{\\mathrm{I}}\\otimes\\hat{\\mathrm{A}}_2\\otimes ...\\otimes\\hat{\\mathrm{I}} +...+\\hat{\\mathrm{I}}\\otimes ...\\otimes\\hat{\\mathrm{A}_N}",
"score_tex": "0.854"
},
{
"title": "kolbe2018hubbard_EQ0026_p013",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229861",
"modified": "20260602105229861",
"kind": "Equation",
"latex": "\\mathcal{H}=\\mathcal{H}_{1}^{(1)} \\otimes \\mathcal{H}_{1}^{(2)} \\otimes \\ldots \\otimes \\mathcal{H}_{1}^{(N)}",
"displayMode": "true",
"refnum": "2.37",
"equation_number": "(2.37)",
"page": "013",
"canonical_uri": 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",
"height": "90",
"width": "506",
"top_left_x": "781",
"top_left_y": "507",
"latex_tex": "\\mathcal{H}= \\mathcal{H}_1^{(1)}\\otimes\\mathcal{H}_1^{(2)}\\otimes...\\otimes\\mathcal{H}_1^{(N)}",
"score_tex": "0.948"
},
{
"title": "kolbe2018hubbard_EQ0027_p013",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229893",
"modified": "20260602105229893",
"kind": "Equation",
"latex": "\\mathcal{V}\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right)=\\sum_{\\left\\{\\alpha_{i}\\right\\}} a_{\\alpha_{1} \\alpha_{2} \\ldots \\alpha_{N}} \\nu_{\\alpha_{1}}\\left(x_{1}\\right) \\nu_{\\alpha_{2}}\\left(x_{2}\\right) \\ldots \\nu_{\\alpha_{N}}\\left(x_{N}\\right), \\quad a_{\\alpha_{i}} \\in \\mathbb{C}",
"displayMode": "true",
"refnum": "2.38",
"equation_number": "(2.38)",
"page": "013",
"canonical_uri": 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"height": "120",
"width": "1157",
"top_left_x": "459",
"top_left_y": "1082",
"latex_tex": "\\mathcal{V}(x_1,x_2,...,x_N)=\\sum_{\\{\\alpha_i\\}}a_{\\alpha_1\\alpha_2...\\alpha_N}\\nu_{\\alpha_1}(x_1)\\nu_{\\alpha_2}(x_2)...\\nu_{\\alpha_N}(x_N),\\quad a_{\\alpha_i}\\in\\mathbb{C}",
"score_tex": "0.917"
},
{
"title": "kolbe2018hubbard_EQ0028_p013",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229926",
"modified": "20260602105229926",
"kind": "Equation",
"latex": "\\begin{array}{lr} \\Psi\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right)=\\operatorname{sign}(\\pi) \\Psi\\left(x_{\\pi(1)}, x_{\\pi(2)}, \\ldots, x_{\\pi(N)}\\right) & \\text { für Fermionen } \\\\ \\Phi\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right)=\\Phi\\left(x_{\\pi(1)}, x_{\\pi(2)}, \\ldots, x_{\\pi(N)}\\right) & \\text { für Bosonen } \\end{array}",
"displayMode": "true",
"refnum": "2.40",
"equation_number": "(2.40)",
"page": "013",
"canonical_uri": 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"height": "147",
"width": "1235",
"top_left_x": "376",
"top_left_y": "1382",
"latex_tex": "\\begin{aligned} \\Psi(x_1,x_2,...,x_N)=&\\,\\,\\text{sign}(\\pi)\\Psi(x_{\\pi(1)},x_{\\pi(2)},...,x_{\\pi(N)})& \\text{für Fermionen}\\\\ \\Phi(x_1,x_2,...,x_N)=&\\Phi(x_{\\pi(1)},x_{\\pi(2)},...,x_{\\pi(N)})& \\text{für Bosonen} \\end{aligned}",
"score_tex": "0.835"
},
{
"title": "kolbe2018hubbard_EQ0029_p013",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229959",
"modified": "20260602105229959",
"kind": "Equation",
"latex": "\\Psi\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right)=\\sum_{\\left\\{\\alpha_{i}\\right\\}} a_{\\alpha_{1} \\alpha_{2} \\ldots \\alpha_{N}} \\psi_{\\alpha_{1} \\alpha_{2} \\ldots \\alpha_{N}}\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right), \\quad a_{\\alpha_{1} \\alpha_{2} \\ldots \\alpha_{N}} \\in \\mathbb{C}",
"displayMode": "true",
"refnum": "2.41",
"equation_number": "(2.41)",
"page": "013",
"canonical_uri": 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"height": "129",
"width": "1253",
"top_left_x": "413",
"top_left_y": "1932",
"latex_tex": "\\Psi(x_1,x_2,...,x_N)=\\sum_{\\{\\alpha_i\\}}a_{\\alpha_1\\alpha_2...\\alpha_N}\\psi_{\\alpha_1\\alpha_2...\\alpha_N}(x_1,x_2,...,x_N),\\,\\,\\,\\,\\,\\,a_{\\alpha_1\\alpha_2...\\alpha_N}\\in\\mathbb{C}",
"score_tex": "0.858"
},
{
"title": "kolbe2018hubbard_EQ0030_p013",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105229990",
"modified": "20260602105229990",
"kind": "Equation",
"latex": "\\psi_{\\alpha_{1} \\alpha_{2} \\ldots \\alpha_{N}}\\left(x_{1}, x_{2}, \\ldots, x_{N}\\right)=\\frac{1}{\\sqrt{N!}} \\operatorname{det}\\left(\\begin{array}{ccc} \\psi_{\\alpha_{1}}\\left(x_{1}\\right) & \\ldots & \\psi_{\\alpha_{N}}\\left(x_{1}\\right) \\\\ \\vdots & \\ddots & \\vdots \\\\ \\psi_{\\alpha_{1}}\\left(x_{N}\\right) & \\ldots & \\psi_{\\alpha_{N}}\\left(x_{N}\\right) \\end{array}\\right)",
"displayMode": "true",
"refnum": "2.42",
"equation_number": "(2.42)",
"page": "013",
"canonical_uri": 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"height": "248",
"width": "1089",
"top_left_x": "488",
"top_left_y": "2213",
"latex_tex": "\\begin{aligned} \\psi_{\\alpha_1\\alpha_2...\\alpha_N}(x_1,x_2,...,x_N)=\\dfrac{1}{\\sqrt{N!}}det\\begin{pmatrix} \\psi_{\\alpha_1}(x_1) & \\dots & \\psi_{\\alpha_N}(x_1)\\\\ \\vdots & \\ddots & \\vdots \\\\ \\psi_{\\alpha_1}(x_N) & \\dots & \\psi_{\\alpha_N}(x_N)\\end{pmatrix} \\end{aligned}",
"score_tex": "0.781"
},
{
"title": "kolbe2018hubbard_EQ0031_p014",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230023",
"modified": "20260602105230023",
"kind": "Equation",
"latex": "\\left\\langle n_{1 \\sigma}, n_{2 \\sigma}, \\ldots \\mid n_{1 \\sigma}^{\\prime}, n_{2 \\sigma}^{\\prime}, \\ldots\\right\\rangle=\\prod_{i, \\sigma} \\delta_{n_{i \\sigma}, n_{i \\sigma}^{\\prime}}",
"displayMode": "true",
"refnum": "2.43",
"equation_number": "(2.43)",
"page": "014",
"canonical_uri": 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"height": "122",
"width": "677",
"top_left_x": "699",
"top_left_y": "964",
"latex_tex": "\\bracket{n_{1\\sigma},n_{2\\sigma},\\dots}{n_{1\\sigma}',n_{2\\sigma}',\\dots}=\\prod_{i,\\sigma}\\delta_{n_{i\\sigma},n_{i\\sigma}'}",
"score_tex": "0.815"
},
{
"title": "kolbe2018hubbard_EQ0032_p014",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230055",
"modified": "20260602105230055",
"kind": "Equation",
"latex": "|\\Psi\\rangle=\\sum_{n_{1 \\sigma}, n_{2 \\sigma}, \\ldots} a_{n_{1 \\sigma}, n_{2 \\sigma}, \\ldots}\\left|n_{1 \\sigma}, n_{2 \\sigma}, \\ldots\\right\\rangle, \\quad \\text { wobei } 2 N=\\sum_{i, \\sigma} n_{i, \\sigma}",
"displayMode": "true",
"refnum": "2.44",
"equation_number": "(2.44)",
"page": "014",
"canonical_uri": 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90htbGBBl5ZnGFAHU46n6Vn/AAn8Hz+DPBUdneYF7cym5uFH/LNiFAXPsFH45oA3vFtrpE3h28u9YsYby3sYZLnZKueUUnj8q8g8FwXXwy+KlpoN/M5stdsoirOeBPjp9fMDrj/bWvWPGP8ApNlp+lDk6lqEMDAd41PmyfgUjcfjXKfG/wAPS6l4Pj1qyyuoaJKLmJ1+9s434+mFb/gFAHoOq6dp+q6fJa6pbxT2h5dJPu8c5ri/hz4H0PT9GsNcWxLX9yDcxTTOztFHJkoi5PGEZR69anfxOPE/woi1G0YLcatClkNv/LOaVxC2P91mJz6DNdxDBHbwRwxKFjjUIijsB0/lQBJRRWTrd9rFlbxPpGjx6nKzYeN7sQbRjrkqc0Aa1Fcd/wAJB43/AOhGt/8AwdJ/8bo/4SDxv/0I1v8A+DpP/jdAHY0Vz2jat4lvL0xar4Zh0622E+emorP83ptCA/jXQ0AJivKPjR8Oh4o0j+2tNizq1ih3KgybiIdV/wB5eSPXkdxXrFJj3NAHhXwL+Iv2iFPCOqzYliU/YJX/AIl7xfUdR7ZHYV7rn0r5p+M3gOfwrrcfi3Qg0FnPMHkEPH2afOQwx0DEZ9jkdwK9d+GXj2Hxx4bWaUqmqWwWO7iB6ns4/wBlv0II57gHdUUUUARvBHJt8xFfa25dwzg+oqSiigBu45I4z6Uu6vJvGniDWtG0rT/EFnc3Yv73WVt7TT92I3t8sApToS4UNuPILjBFdXqWm3/9gX+o6nrN3BdpbSTAWU3lx22EJwB/HjHV85PZelAHW5J57U6uU+HGuXviTwBpOrakB9snjYSkLt3FXZN2B6hQfxrYvNf0+x1rT9IuJit9qHmG2jCMd4QZbkDA49aANOiiigAooooAKKKKACiiigDjZv8Akstj/wBgC4/9KIq7Bo1kRkcBlYEFSMgg1yEw/wCLyWJ/6gFx/wClENdjQB454u8H3ng7wD4mh0W9ibw/cxNM1hdAh7ViRzE4zkE4+Ujt161F4L8I33jP4a+HbHVL+KDw9Eoka0tc+bdEO2BI5xtXPOAD9eBj0XV/Anh/XpJm1S3u7lZiC8TX9wIjjpiMOFH4Cm6T4C8PaE8LaZb3lssTb0iTULjy8+6F9pHtjFAHQwQRW0EcEKBIo1CIijAUAYAH4Vz/AI41afSPCl21ng6hdFbOyXPLTynYn5Z3fQGukrir3OvfE2yssbrPQIPtk3obmUFIgfdU8xv+BCgDo9C0mLQtBsNKt+YrOBIVJ74GCfx61pUmKWgDnNYk8YLfY0S30J7TaPmvp5kkz34VCMfjVHzfiT/z5+FP/Aq4/wDjddhgUuKAOO834k/8+fhT/wACrj/43W1oj681vIdei02OcPhPsEsjoVx33qCDmtfFIVB5xyO9AC0UUUAFFFFABRRRQAUUVzni/wAXWvhLR/tUsbXF3Mwis7SPl7iU/dUfjjn+ZIBAOc+LN5Z3uhJ4UjshqOtau2yytVPMZHPnMf4VXnnvz23Y2vAHgiz8C+HE06BhJcykPdXHTzZPb0A6Af1zVTwP4TutOkuvEPiF1uPEmo4ad/4bdOqxJ6AcfkPQV22KAFooooAKKge6iSeOB5Y1mkBKRlvmYDG4gd8ZH5ip6ACiiigAooooAK8n+EFnKmu+N7+7yb2XV3hk3dV2lm/L5/yA64r1isS58KaZPqU+oJ9ptbm5VUuXtLl4fPC/d3hSMkDgN1xxnFAHB31xD4m+P+l2kUqS2/h6xluJQDkCZztIz0yN0Z+ox2NdfN4tkfSba6sbFJJrmGe6iSaYon2ePpIzBSRuDRkDH8fsamuPBGgz3ENwlq9rLFbm03WkrQl4SdxjbaRlSeee/wBayfijdDSfhtqUdnCBNPEtjbRooGPNITA9Bgn8hQA/TPHF9r/hga9o+ir9lWAyP9tuTDuZRl0jwjbgMEbjtGR35xv+H9eg8Q+HbLWoEaKC6hEoV+qeoP0wa5Pxukvhb4NT6fYAF47KLT1cHAUMFjZiewwSc/jW94TNtFpMelaeiy6Xp8EVrFdK2VuGVSHI7EA4GQfvbh/DyAaNh4h0nU76aysdRtrq4gQPKkEgfYCSBkjIHTpnNadcJpaKnxl1tVUKq6PahQBgD536Vsa94iurXVLXQ9GtobrV7qNpgJnKxW8SkAySEZOCSAAByfTFAHR0V55Ya548l8ZT6DdP4bUQQR3bSRQTnfEzspxl+GBU8Guq8TeJLXwpoM+sX0NxNbwlQyWyb35OOhIGOetACa7rc+lhIrS2iuLp4pZ9kspjRY4wCzFgrY5ZR0/i9qxNM8cX2v8Ahga9o+ir9lWAyP8Abbkw7mUZdI8I24DBG47Rkd+cQfEjWk/4VZfX1gPNfUrZLe14+ZhOVXjPTg5/CofG6S+Fvg1Pp9gAXjsotPVwcBQwWNmJ7DBJz+NAHV6Br9vr/hqz1uFTDBcwCbbIfuDuCfbnmok8XaJJdQWwvlSS5YLbtKjIk5PQRuQFcnttJrK0zTLHVfCM/hi2d/7HgtEsEvreUBpWCkOUOCOPl55+YsP4ecz4hWT6/o0PgvS99xqUzwPJcu242caMpM0jdmO3A7tk46UAeh0tc3r3iG5sL2x0fSrVLvV70O0SSuVjijX70shAztBKjAGSTgY61z1vrvj1vGbeHp38Nqy2i3vmJbzsGiL7CP8AWcMCOPUenSgD0WisbxN4ktfCmgz6xfQ3E1vCVDJbJvfk46EgY561Hq3izT9I8JHxLIlxPYCGOYC3j3OyvjaQCR/eBOTxQBu0Vhax4ps9E8Kv4iuYLp7NIklMcUWZcORjKkjH3hnPTmn6r4ms9H8LyeILiG5e0jgWcxxxZl2tjA2nHPPOTx3oA2q47wJ/yEPGP/Yfl/8ARMNdPYXyajp1rfQpIsdzEkqLIu1grAEbh2OD0rmPAv8AyEPGP/Yfl/8ARMNAHPfFAf2z4t8E+FRh0ub83lwh/wCecQzg/UGQfhXRfE3XD4e+Hur30XFw8XkQYHO+Q7AR7gHP4VtS+GtLm8TweI5IC2pwW5to5S5wqEk8Dpnk8+9Tazomn+INJn0vU7cT2c4AeMkjODkHI5BBANAHN+CLNfCmhaB4WERa7+xvcXJBH7s5BYn6u+0euCf4TWX8YUWPw5oxRQpOuWpJAxk5bmu503R7XS/NaJppZpiDLNcStJI+OgJPYc4A4GTxya83+MevaQdJ0yxGpWjXcGsW0k0CTK0karuJLKDkAe9AHqu7AyeAOua4S6+Ieo3aT3HhXwpd67Y25ZXvFuEgjkZeoi3ZaTuMgckYGav+Kbz/AISD4fa4PDF7BeztayRo1lMJMtt+6Cp+8R268j1qhZ+JNJ0bwHp9roLR3t8lksNnYQMGlaQJjDKOVw332OMc5oAl8F+Ndd8XJa3r+FBZaRcozpe/2lHL0OANgAbJII9q3td8WaJ4Z+yf2zqMNn9rkMcO8E7jx6ZwBkZJ45qp4E8OSeFPBmnaNNIJJ4EZpXHd2Yu31GWPPtVX4g6Fo2taDu1TT4ry5hytirOynzn+VVGCMgttBHI9eBwAdcDn0rgfjHqzaV8M9TEZPnXu2zjx1beeR/3yGrubaH7PaxQbi3loF3HqcDFZ+t+G9L8RLZLqcBmWzuVuoV3kASLnBOOvU8GgCHRbKDwr4Os7aU4h02yUSlefuJ8ze/IJrgPhhcyWnhu98WXkBlv/ABNqu6OFThipcqo57L+8b/dGa9ZeNJI2jdQyMCGU9CD1rF0fwjpGhGL7DHMEgDLbxyTvIkCsckIrEhfr1xxnFAENj4eurLxnq2uHVZpLW/hiQWJjwsTIANwbPPQ8Y/iNchZxyap+0Bd6jpqn7Fp2mCzv51+685YsEz3YArn02888VZ8d/EzRtC1NfD8mqtZXLruurmKFpHtkOCFUAH94wPGeF6nPAK+CfGvhjUtQs/Dng5S1tDFLPcl4XUhQQM7mwWZmYEk5zzQBuaz4zktdVfR9D0e41vVolDzwQyLEkCkZHmSN8qkjoOT7Vz2k/EjxTq+rXmnReAWSexljju1k1aNTDv5U4KjII5BGc9qd4EvrHw5Za8Nev4bbVW1S4nu/tDhXYEjyyozllKhduOM8DmtLwPpd5JrHiHxTfwSWr61PH5FtKMOkESlELD+FmByR2oA6nVdXstD0y41LUrhLezt1DSyvnCgnA6c9SAPUnFLpOr2WuaZBqWm3CXNncDdHKnQjofxBBB9MYpur6bp+s6VcafqkCT2MyYlSQkKQOc5HTGM5yDxWT4G0200zwxHFYQGCxkmlltosk4iLnYeefmXa3OT81AG9d3kFhZz3l1KkNvBG0ksjnhVUEkn8BVPQvEOmeJdNXUdIu0urRmKiRVZeR1BDAEH2Pt61du7O3v7Oezuollt54zHLG3R1IwQfqKqaH4f0rw1piabo9mlraKxYRqSck9SSSST9TQBfkkWJGd2CooJLHgAD1rK0DxRo3im0lutFvku4IpDE7KrKVbAOMMAehrWeNJEZHUMjDBU8gisnQPC2i+FrSW10SwSzhlk811Qklm9yxJ/DoO1AGxWLpHizQ9ev7+x0vUIrm5sH8u4jQMNh6dSMMMgjIyK2qxtI8J6HoN9fXul6dFbXN+++5dCTvOSehOAMk8DAoA2a474hSvdaTaeHLditzrtwtmdvVYPvTP8AhGrD/gQrsa4rS8698SNU1Q/NaaLENNtj1BnfDzt9QPLT8DQB2MUMcESRRrtRAFUDsBWToPizRPE/2r+xdQivPskgjn8sH5SenUDIODyOODW1XF+FvDmi6L4o1mTQrCO1t9kcc3lsSHnyzMBknG1SmAOBuPAwaAO0ooooAKKKKAPMPjLaT2Ol6T4uskJutBvUmOON0TEBge+MhR9CaqeJ9Lbxf8PtZ8TWW8XjzrqGmPjDrHb5CY/3gJWH/XWvT9S0y11fTbnT72PzLa5iaKVc4ypGDyKfa2NtZWEFjbxBLaCJYo4x0CKMAflQByPgzWIvGV1/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"height": "129",
"width": "1036",
"top_left_x": "520",
"top_left_y": "1253",
"latex_tex": "\\left| \\Psi \\right>=\\sum_{n_{1\\sigma},n_{2\\sigma},\\dots}a_{n_{1\\sigma},n_{2\\sigma},\\dots}\\left| n_{1\\sigma},n_{2\\sigma},\\dots \\right>,\\,\\,\\,\\,\\text{wobei}\\,\\, 2N=\\sum_{i,\\sigma}n_{i,\\sigma}",
"score_tex": "0.922"
},
{
"title": "kolbe2018hubbard_EQ0033_p014",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230086",
"modified": "20260602105230086",
"kind": "Equation",
"latex": "\\left.F^{(2 N)}=\\mathcal{H}^{(+)}=\\{|\\Psi\\rangle \\in \\mathcal{H}|\\hat{\\pi}| \\Psi\\rangle=(-1)^{\\pi}|\\Psi\\rangle, \\forall \\pi \\in S_{n}\\right\\}",
"displayMode": "true",
"refnum": "\\2.45\\",
"equation_number": "(\\2.45\\)",
"page": "014",
"canonical_uri": 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",
"height": "81",
"width": "935",
"top_left_x": "571",
"top_left_y": "1493",
"latex_tex": "F^{(2N)}=\\mathcal{H}^{(+)}=\\{\\left| \\Psi \\right>\\in\\mathcal{H}\\mid \\hat{\\pi}\\left| \\Psi \\right>=(-1)^{\\pi}\\left| \\Psi \\right>,\\forall\\pi\\in S_n\\}",
"score_tex": "0.856"
},
{
"title": "kolbe2018hubbard_EQ0034_p014",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230116",
"modified": "20260602105230116",
"kind": "Equation",
"latex": "c_{i \\sigma}^{\\dagger}\\left|n_{1 \\sigma}, \\ldots, n_{i \\sigma}, \\ldots\\right\\rangle=\\left(1-n_{i \\sigma}(-1)^{\\sum_{\\sigma, j=n_{i\\sigma}(-1)^{\\sum_{\\sigma,j",
"score_tex": "0.882"
},
{
"title": "kolbe2018hubbard_EQ0035_p014",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230148",
"modified": "20260602105230148",
"kind": "Equation",
"latex": "\\left|n_{1 \\uparrow} n_{1 \\downarrow} \\ldots\\right\\rangle=\\prod_{i, \\sigma} \\frac{1}{\\sqrt{n_{i \\sigma!}}}\\left(c_{i, \\sigma}^{\\dagger}\\right)^{n_{i \\sigma}}|0\\rangle",
"displayMode": "true",
"refnum": "2.47",
"equation_number": "(2.47)",
"page": "014",
"canonical_uri": 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"height": "134",
"width": "597",
"top_left_x": "740",
"top_left_y": "2215",
"latex_tex": "\\left| n_{1\\uparrow}n_{1\\downarrow}\\dots \\right>=\\prod_{i,\\sigma}\\dfrac{1}{\\sqrt{n_{i\\sigma!}}}(c\\;\\!\\!^\\dagger_{i,\\sigma})^{n_{i\\sigma}}\\left| 0 \\right>",
"score_tex": "0.864"
},
{
"title": "kolbe2018hubbard_EQ0036_p015",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230178",
"modified": "20260602105230178",
"kind": "Equation",
"latex": "c_{i \\sigma}\\left|n_{1 \\sigma}, \\ldots, n_{i \\sigma}, \\ldots\\right\\rangle=n_{i \\sigma}(-1)^{\\sum_{\\sigma, j=(1-n_{i\\sigma}(-1)^{\\sum_{\\sigma,j",
"score_tex": "0.885"
},
{
"title": "kolbe2018hubbard_EQ0037_p015",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230211",
"modified": "20260602105230211",
"kind": "Equation",
"latex": "\\begin{aligned} {\\left[c_{i \\sigma}, c_{j \\sigma^{\\prime}}^{\\dagger}\\right] } & =\\delta_{i j} \\delta_{\\sigma \\sigma^{\\prime}} \\\\ {\\left[c_{i \\sigma}, c_{j \\sigma^{\\prime}}\\right] } & =0 \\\\ {\\left[c_{i \\sigma}^{\\dagger}, c_{j \\sigma^{\\prime}}^{\\dagger}\\right] } & =0 \\end{aligned}",
"displayMode": "true",
"refnum": "2.50",
"equation_number": "(2.50)",
"page": "015",
"canonical_uri": 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"height": "218",
"width": "316",
"top_left_x": "879",
"top_left_y": "584",
"latex_tex": "\\begin{aligned} [c_{i\\sigma},c\\;\\!\\!^\\dagger_{j\\sigma'}]=&\\,\\,\\delta_{ij}\\delta_{\\sigma\\sigma'}\\\\ [c_{i\\sigma},c_{j\\sigma'}]=&\\,\\,0\\\\ [c\\;\\!\\!^\\dagger_{i\\sigma},c\\;\\!\\!^\\dagger_{j\\sigma'}]=&\\,\\,0 \\end{aligned}",
"score_tex": "0.758"
},
{
"title": "kolbe2018hubbard_EQ0038_p015",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230244",
"modified": "20260602105230244",
"kind": "Equation",
"latex": "\\hat{n}_{i \\sigma}=c_{i \\sigma}^{\\dagger} c_{i \\sigma}",
"displayMode": "true",
"refnum": "2.52",
"equation_number": "(2.52)",
"page": "015",
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"height": "72",
"width": "208",
"top_left_x": "932",
"top_left_y": "986",
"latex_tex": "\\hat{n}_{i\\sigma}=c\\;\\!\\!^\\dagger_{i\\sigma}c_{i\\sigma}",
"score_tex": "0.826"
},
{
"title": "kolbe2018hubbard_EQ0039_p015",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230275",
"modified": "20260602105230275",
"kind": "Equation",
"latex": "\\hat{n}_{i \\sigma}\\left|n_{1 \\sigma}, \\ldots, n_{i \\sigma}, \\ldots\\right\\rangle=n_{i \\sigma}\\left|n_{1 \\sigma}, \\ldots, n_{i \\sigma}, \\ldots\\right\\rangle",
"displayMode": "true",
"refnum": "2.53",
"equation_number": "(2.53)",
"page": "015",
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",
"height": "63",
"width": "748",
"top_left_x": "662",
"top_left_y": "1256",
"latex_tex": "\\hat{n}_{i\\sigma}\\left| n_{1\\sigma},\\dots,n_{i\\sigma},\\dots \\right>=n_{i\\sigma}\\left| n_{1\\sigma},\\dots,n_{i\\sigma},\\dots \\right>",
"score_tex": "0.908"
},
{
"title": "kolbe2018hubbard_EQ0040_p017",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230307",
"modified": "20260602105230307",
"kind": "Equation",
"latex": "\\mathbf{H}_{\\mathrm{Heis}}=-J \\sum_{\\langle i, j\\rangle} \\vec{S}_{i} \\cdot \\vec{S}_{j}",
"displayMode": "true",
"refnum": "3.1",
"equation_number": "(3.1)",
"page": "017",
"canonical_uri": 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"height": "113",
"width": "380",
"top_left_x": "847",
"top_left_y": "1836",
"latex_tex": "\\displaystyle \\mathbf{H}_{\\text{Heis}}=-J\\sum_{\\langle i,j\\rangle }\\vec{S_{i}}\\cdot \\vec{S_{j}}",
"score_tex": "0.889"
},
{
"title": "kolbe2018hubbard_EQ0041_p017",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230338",
"modified": "20260602105230338",
"kind": "Equation",
"latex": "\\vec{S}_{i} \\cdot \\vec{S}_{j}=S_{i}^{x} S_{j}^{x}+S_{i}^{y} S_{j}^{y}+S_{i}^{z} S_{j}^{z}",
"displayMode": "true",
"refnum": "3.2",
"equation_number": "(3.2)",
"page": "017",
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",
"height": "72",
"width": "518",
"top_left_x": "778",
"top_left_y": "2078",
"latex_tex": "\\displaystyle \\vec{S_{i}}\\cdot\\vec{S_{j}} = S^x_i S^x_j+ S^y_iS^y_j+S^z_iS^z_j",
"score_tex": "0.632"
},
{
"title": "kolbe2018hubbard_EQ0042_p017",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230373",
"modified": "20260602105230373",
"kind": "Equation",
"latex": "\\mathbf{H}_{\\mathrm{Heis}}=-J \\sum_{\\langle i, j\\rangle} \\frac{\\hat{S}_{i}^{+} \\hat{S}_{j}^{-}}{2}+\\frac{\\hat{S}_{i}^{-} \\hat{S}_{j}^{+}}{2}+\\hat{S}_{i}^{z} \\hat{S}_{j}^{z}",
"displayMode": "true",
"refnum": "3.3",
"equation_number": "(3.3)",
"page": "017",
"canonical_uri": 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"height": "128",
"width": "638",
"top_left_x": "717",
"top_left_y": "2330",
"latex_tex": "\\displaystyle \\mathbf{H}_{\\text{Heis}}=-J\\sum_{\\langle i, j\\rangle}\\tfrac{\\hat{S}^+_i\\hat{S}^-_j}{2}+\\tfrac{\\hat{S}^-_i\\hat{S}^+_j}{2}+\\hat{S}^z_i\\hat{S}^z_j",
"score_tex": "0.798"
},
{
"title": "kolbe2018hubbard_EQ0043_p019",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230410",
"modified": "20260602105230410",
"kind": "Equation",
"latex": "\\mathbf{H}_{\\mathrm{Hub}}=\\mathbf{H}_{U}+\\mathbf{H}_{\\epsilon}+\\mathbf{H}_{t}",
"displayMode": "true",
"refnum": "3.4",
"equation_number": "(3.4)",
"page": "019",
"canonical_uri": 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"height": "44",
"width": "394",
"top_left_x": "840",
"top_left_y": "1174",
"latex_tex": "\\mathbf{H}_{\\text{Hub}}=\\mathbf{H}_U+\\mathbf{H}_{\\epsilon}+\\mathbf{H}_t",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0044_p019",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230441",
"modified": "20260602105230441",
"kind": "Equation",
"latex": "\\mathbf{H}_{\\mathrm{Hub}}=U \\sum_{i=1}^{N} \\hat{c}_{i, \\uparrow}^{\\dagger} \\hat{c}_{i, \\uparrow} \\hat{c}_{i, \\downarrow}^{\\dagger} \\hat{c}_{i, \\downarrow}+\\sum_{\\sigma}\\left(\\sum_{i=1}^{N} \\epsilon_{i} \\hat{c}_{i, \\sigma}^{\\dagger} \\hat{c}_{i, \\sigma}-t \\sum_{\\langle i, j\\rangle}\\left(\\hat{c}_{i, \\sigma}^{\\dagger} \\hat{c}_{j, \\sigma}+\\hat{c}_{j, \\sigma}^{\\dagger} \\hat{c}_{i, \\sigma}\\right)\\right)",
"displayMode": "true",
"refnum": "3.5",
"equation_number": "(3.5)",
"page": "019",
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"height": "150",
"width": "1233",
"top_left_x": "415",
"top_left_y": "2224",
"latex_tex": "\\displaystyle \\mathbf{H}_{\\text{Hub}}=U\\sum_{i=1}^N\\hat{c}^{\\dagger}_{i,\\uparrow}\\hat{c}_{i,\\uparrow}\\hat{c}^{\\dagger}_{i,\\downarrow}\\hat{c}_{i,\\downarrow} +\\sum_{\\sigma}\\left( \\sum_{i=1}^{N}\\epsilon_i \\hat{c}^{\\dagger}_{i,\\sigma}\\hat{c}_{i,\\sigma}-t\\sum_{\\langle i,j\\rangle}( \\hat{c}^{\\dagger}_{i,\\sigma}\\hat{c}_{j,\\sigma}+\\hat{c}^{\\dagger}_{j,\\sigma}\\hat{c}_{i,\\sigma})\\right)",
"score_tex": "0.724"
},
{
"title": "kolbe2018hubbard_EQ0045_p021",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230476",
"modified": "20260602105230476",
"kind": "Equation",
"latex": "\\hat{S}_{i}^{+} \\hat{S}_{j}^{-}|Z u s t a n d\\rangle \\equiv \\operatorname{SpinPlus}(i, \\operatorname{SpinMinus}(j, Z u s t a n d))",
"displayMode": "true",
"refnum": "4.1",
"equation_number": "(4.1)",
"page": "021",
"canonical_uri": 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",
"height": "72",
"width": "958",
"top_left_x": "557",
"top_left_y": "589",
"latex_tex": "\\hat{S}^+_i\\hat{S}^-_j\\left| Zustand \\right>\\equiv SpinPlus(i,SpinMinus(j,Zustand))",
"score_tex": "0.857"
},
{
"title": "kolbe2018hubbard_EQ0046_p021",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230512",
"modified": "20260602105230512",
"kind": "Equation",
"latex": "\\left(\\begin{array}{lll} 0 & \\mathrm{~J} & 0 \\\\ 0 & 0 & \\mathrm{~J} \\\\ \\mathrm{~J} & 0 & 0 \\end{array}\\right)",
"displayMode": "true",
"refnum": "",
"equation_number": "",
"page": "021",
"canonical_uri": 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"height": "227",
"width": "254",
"top_left_x": "909",
"top_left_y": "1302",
"latex_tex": "\\left( \\begin{tabular}{ccc} 0 & J & 0 \\\\ 0 & 0 & J \\\\ J & 0 & 0 \\end{tabular} \\right)",
"score_tex": "0.694"
},
{
"title": "kolbe2018hubbard_EQ0047_p021",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230546",
"modified": "20260602105230546",
"kind": "Equation",
"latex": "\\left\\langle\\hat{S}_{1} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}}=\\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{\\hat{S}_{1}^{+} \\hat{S}_{j}^{-}}{2}+\\frac{\\hat{S}_{1}^{-} \\hat{S}_{j}^{+}}{2}+\\hat{S}_{1}^{z} \\hat{S}_{j}^{z}\\left|\\psi^{0, l}\\right\\rangle",
"displayMode": "true",
"refnum": "4.2",
"equation_number": "(4.2)",
"page": "021",
"canonical_uri": 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"height": "129",
"width": "840",
"top_left_x": "616",
"top_left_y": "2106",
"latex_tex": "\\langle \\hat{S}_1\\hat{S}_j\\rangle_{\\psi_g}=\\dfrac{1}{g_0}\\sum_{l=0}^{g_0}\\left< \\psi^{0,l} \\right|\\tfrac{\\hat{S}^+_1\\hat{S}^-_j}{2}+\\tfrac{\\hat{S}^-_1\\hat{S}^+_j}{2}+\\hat{S}^z_1\\hat{S}^z_j\\left| \\psi^{0,l} \\right>",
"score_tex": "0.847"
},
{
"title": "kolbe2018hubbard_EQ0048_p022",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230580",
"modified": "20260602105230580",
"kind": "Equation",
"latex": "\\left|\\psi_{g}\\right\\rangle=\\sum_{k=1}^{2^{N}} \\alpha_{k}|k\\rangle \\quad \\text { Heisenberg-Modell }",
"displayMode": "true",
"refnum": "4.3",
"equation_number": "(4.3)",
"page": "022",
"canonical_uri": 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"height": "145",
"width": "664",
"top_left_x": "705",
"top_left_y": "306",
"latex_tex": "\\begin{aligned} \\displaystyle \\mid\\psi_g\\rangle=&\\sum_{k=1}^{2^N}\\alpha_k \\mid k\\rangle\\quad\\text{Heisenberg-Modell} \\end{aligned}",
"score_tex": "0.855"
},
{
"title": "kolbe2018hubbard_EQ0049_p023",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230615",
"modified": "20260602105230615",
"kind": "Equation",
"latex": "\\hat{n}_{\\uparrow}|Z u s t a n d\\rangle=\\hat{c}_{i \\uparrow}^{\\dagger} \\hat{c}_{j \\uparrow}|Z u s t a n d\\rangle \\Leftrightarrow \\operatorname{CupDagger}(i, \\operatorname{Cup}(j, \\text { Zustand }))",
"displayMode": "true",
"refnum": "4.4",
"equation_number": "(4.4)",
"page": "023",
"canonical_uri": 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"height": "72",
"width": "1150",
"top_left_x": "461",
"top_left_y": "566",
"latex_tex": "\\hat{n}_{\\uparrow}\\left| Zustand \\right>=\\hat{c}_{i\\uparrow}\\;\\!\\!^\\dagger\\hat{c}_{j\\uparrow}\\left| Zustand \\right> \\Leftrightarrow CupDagger(i,Cup(j,Zustand))",
"score_tex": "0.935"
},
{
"title": "kolbe2018hubbard_EQ0050_p023",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230651",
"modified": "20260602105230651",
"kind": "Equation",
"latex": "\\left(\\begin{array}{lll} 0 & \\mathrm{t} & 0 \\\\ 0 & 0 & \\mathrm{t} \\\\ 0 & 0 & 0 \\end{array}\\right)",
"displayMode": "true",
"refnum": "",
"equation_number": "",
"page": "023",
"canonical_uri": 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"height": "231",
"width": "260",
"top_left_x": "906",
"top_left_y": "932",
"latex_tex": "\\left( \\begin{tabular}{ccc} 0 & t & 0 \\\\ 0 & 0 & t \\\\ 0 & 0 & 0 \\end{tabular} \\right)",
"score_tex": "0.694"
},
{
"title": "kolbe2018hubbard_EQ0051_p023",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230688",
"modified": "20260602105230688",
"kind": "Equation",
"latex": "\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}^{\\dagger}|0\\rangle_{j}=|\\uparrow \\downarrow\\rangle_{j} \\quad \\quad \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}^{\\dagger}|0\\rangle_{j}=-\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}^{\\dagger}|0\\rangle_{j}=-|\\uparrow \\downarrow\\rangle_{j}",
"displayMode": "true",
"refnum": "4.5",
"equation_number": "(4.5)",
"page": "023",
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"height": "85",
"width": "1224",
"top_left_x": "424",
"top_left_y": "1375",
"latex_tex": "\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}^{\\dagger}|0\\rangle_{j}=|\\uparrow \\downarrow\\rangle_{j} \\quad \\quad \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}^{\\dagger}|0\\rangle_{j}=-\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}^{\\dagger}|0\\rangle_{j}=-|\\uparrow \\downarrow\\rangle_{j}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0052_p023",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230718",
"modified": "20260602105230718",
"kind": "Equation",
"latex": "|0,0\\rangle=[0,0] \\quad|\\downarrow, \\downarrow\\rangle=[1,1] \\quad|\\uparrow, \\uparrow\\rangle=[2,2] \\quad|\\uparrow \\downarrow, \\uparrow \\downarrow\\rangle=[3,3]",
"displayMode": "true",
"refnum": "4.6",
"equation_number": "(4.6)",
"page": "023",
"canonical_uri": 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",
"height": "72",
"width": "1024",
"top_left_x": "525",
"top_left_y": "1873",
"latex_tex": "\\left| 0,0 \\right>=[0,0]\\quad\\left| \\downarrow,\\downarrow \\right>=[1,1]\\quad\\left| \\uparrow,\\uparrow \\right>=[2,2]\\quad\\left| \\uparrow \\downarrow,\\uparrow\\downarrow \\right>=[3,3]",
"score_tex": "0.883"
},
{
"title": "kolbe2018hubbard_EQ0053_p023",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230747",
"modified": "20260602105230747",
"kind": "Equation",
"latex": "\\begin{array}{rll} |0, \\downarrow\\rangle=[0,1] & \\rightarrow & |\\downarrow, 0\\rangle=[1,0] \\\\ |\\downarrow, 0\\rangle=[1,0] & \\rightarrow & |0, \\downarrow\\rangle=[0,1] \\\\ |0, \\uparrow\\rangle=[0,2] & \\rightarrow & |\\uparrow, 0\\rangle=[2,0] \\\\ |\\uparrow, 0\\rangle=[2,0] & \\rightarrow & |0, \\uparrow\\rangle=[0,2] \\end{array}",
"displayMode": "true",
"refnum": "4.7",
"equation_number": "(4.7)",
"page": "023",
"canonical_uri": 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"height": "268",
"width": "584",
"top_left_x": "744",
"top_left_y": "2140",
"latex_tex": "\\begin{array}{rll} |0, \\downarrow\\rangle=[0,1] & \\rightarrow & |\\downarrow, 0\\rangle=[1,0] \\\\ |\\downarrow, 0\\rangle=[1,0] & \\rightarrow & |0, \\downarrow\\rangle=[0,1] \\\\ |0, \\uparrow\\rangle=[0,2] & \\rightarrow & |\\uparrow, 0\\rangle=[2,0] \\\\ |\\uparrow, 0\\rangle=[2,0] & \\rightarrow & |0, \\uparrow\\rangle=[0,2] \\end{array}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0054_p024",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230781",
"modified": "20260602105230781",
"kind": "Equation",
"latex": "\\begin{array}{lll} |\\uparrow, \\uparrow \\downarrow\\rangle=[1,3] & \\rightarrow & |\\uparrow \\downarrow, \\uparrow\\rangle=[3,1] \\\\ |\\downarrow, \\downarrow \\uparrow\\rangle=[1,3] & \\rightarrow & |\\uparrow \\downarrow, \\downarrow\\rangle=[3,2] \\\\ |\\uparrow \\downarrow, \\uparrow\\rangle=[3,1] & \\rightarrow & |\\uparrow, \\uparrow \\downarrow\\rangle=[1,3] \\\\ |\\uparrow \\downarrow, \\downarrow\\rangle=[3,2] & \\rightarrow & |\\downarrow, \\uparrow \\downarrow\\rangle=[2,3] \\end{array}",
"displayMode": "true",
"refnum": "4.8",
"equation_number": "(4.8)",
"page": "024",
"canonical_uri": 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",
"height": "275",
"width": "624",
"top_left_x": "724",
"top_left_y": "379",
"latex_tex": "\\begin{array}{lll} |\\uparrow, \\uparrow \\downarrow\\rangle=[1,3] & \\rightarrow & |\\uparrow \\downarrow, \\uparrow\\rangle=[3,1] \\\\ |\\downarrow, \\downarrow \\uparrow\\rangle=[1,3] & \\rightarrow & |\\uparrow \\downarrow, \\downarrow\\rangle=[3,2] \\\\ |\\uparrow \\downarrow, \\uparrow\\rangle=[3,1] & \\rightarrow & |\\uparrow, \\uparrow \\downarrow\\rangle=[1,3] \\\\ |\\uparrow \\downarrow, \\downarrow\\rangle=[3,2] & \\rightarrow & |\\downarrow, \\uparrow \\downarrow\\rangle=[2,3] \\end{array}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0055_p024",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230813",
"modified": "20260602105230813",
"kind": "Equation",
"latex": "\\begin{aligned} |\\uparrow, \\downarrow\\rangle=[1,2] & \\rightarrow & |\\uparrow \\downarrow, 0\\rangle+|0, \\uparrow \\downarrow\\rangle=[3,0]+[0,3] \\\\ |\\downarrow, \\uparrow\\rangle=[2,1] & \\rightarrow & -|\\uparrow \\downarrow, 0\\rangle-|0, \\uparrow \\downarrow\\rangle=-[3,0]-[0,3] \\\\ |\\uparrow \\downarrow, 0\\rangle=[3,0] & \\rightarrow & |\\uparrow, \\downarrow\\rangle-|\\downarrow, \\uparrow\\rangle=[2,1]-[1,2] \\\\ |0, \\uparrow \\downarrow\\rangle=[0,3] & \\rightarrow & |\\uparrow, \\downarrow\\rangle-|\\downarrow, \\uparrow\\rangle=[1,2]-[2,1] \\end{aligned}",
"displayMode": "true",
"refnum": "4.9",
"equation_number": "(4.9)",
"page": "024",
"canonical_uri": 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"top_left_x": "555",
"top_left_y": "904",
"latex_tex": "\\begin{aligned} |\\uparrow, \\downarrow\\rangle=[1,2] & \\rightarrow & |\\uparrow \\downarrow, 0\\rangle+|0, \\uparrow \\downarrow\\rangle=[3,0]+[0,3] \\\\ |\\downarrow, \\uparrow\\rangle=[2,1] & \\rightarrow & -|\\uparrow \\downarrow, 0\\rangle-|0, \\uparrow \\downarrow\\rangle=-[3,0]-[0,3] \\\\ |\\uparrow \\downarrow, 0\\rangle=[3,0] & \\rightarrow & |\\uparrow, \\downarrow\\rangle-|\\downarrow, \\uparrow\\rangle=[2,1]-[1,2] \\\\ |0, \\uparrow \\downarrow\\rangle=[0,3] & \\rightarrow & |\\uparrow, \\downarrow\\rangle-|\\downarrow, \\uparrow\\rangle=[1,2]-[2,1] \\end{aligned}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0056_p024",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230847",
"modified": "20260602105230847",
"kind": "Equation",
"latex": "\\mathbf{H}_{\\epsilon}+\\mathbf{H}_{U}=\\sum_{i=1}^{N}\\left(\\epsilon_{i} \\cdot\\left(\\hat{n}_{i, \\uparrow}+\\hat{n}_{i, \\downarrow}\\right)+U_{i} \\cdot \\hat{n}_{i, \\uparrow} \\hat{n}_{i, \\downarrow}\\right)",
"displayMode": "true",
"refnum": "4.10",
"equation_number": "(4.10)",
"page": "024",
"canonical_uri": 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"height": "142",
"width": "794",
"top_left_x": "639",
"top_left_y": "1414",
"latex_tex": "\\mathbf{H}_{\\epsilon}+\\mathbf{H}_{U}=\\sum_{i=1}^N\\left(\\epsilon_i\\cdot(\\hat{n}_{i,\\uparrow}+\\hat{n}_{i,\\downarrow})+U_i\\cdot\\hat{n}_{i,\\uparrow}\\hat{n}_{i,\\downarrow}\\right)",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0057_p024",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230891",
"modified": "20260602105230891",
"kind": "Equation",
"latex": "\\langle l| \\mathbf{H}_{\\epsilon}+\\mathbf{H}_{U}|m\\rangle= \\begin{cases}\\epsilon_{l m}+U_{l m} & \\text { wenn } l=m \\text { ist. } \\\\ 0 & \\text { wenn } l \\neq m \\text { ist. }\\end{cases}",
"displayMode": "true",
"refnum": "4.11",
"equation_number": "(4.11)",
"page": "024",
"canonical_uri": 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"height": "170",
"width": "866",
"top_left_x": "603",
"top_left_y": "1889",
"latex_tex": "\\begin{aligned} \\left< l \\right|\\,\\mathbf{H}_{\\epsilon}+\\mathbf{H}_U\\,\\left| m \\right>= \\begin{cases} \\epsilon_{lm}+U_{lm} & \\quad \\text{wenn $l=m$ ist.}\\\\ 0 & \\quad \\text{wenn $l\\ne m$ ist.} \\end{cases} \\end{aligned}",
"score_tex": "0.838"
},
{
"title": "kolbe2018hubbard_EQ0058_p025",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230921",
"modified": "20260602105230921",
"kind": "Equation",
"latex": "\\hat{S}_{i}^{+}=\\hat{c}_{i, \\uparrow}^{\\dagger} \\hat{c}_{i, \\downarrow} \\quad ; \\quad \\hat{S}_{i}^{-}=\\hat{c}_{i, \\downarrow}^{\\dagger} \\hat{c}_{i, \\uparrow} \\quad ; \\quad \\hat{S}_{i}^{z}=\\frac{1}{2}\\left(\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)",
"displayMode": "true",
"refnum": "4.12",
"equation_number": "(4.12)",
"page": "025",
"canonical_uri": 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",
"height": "92",
"width": "981",
"top_left_x": "543",
"top_left_y": "452",
"latex_tex": "\\hat{S}_{i}^{+}=\\hat{c}_{i, \\uparrow}^{\\dagger} \\hat{c}_{i, \\downarrow} \\quad ; \\quad \\hat{S}_{i}^{-}=\\hat{c}_{i, \\downarrow}^{\\dagger} \\hat{c}_{i, \\uparrow} \\quad ; \\quad \\hat{S}_{i}^{z}=\\frac{1}{2}\\left(\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0059_p025",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230953",
"modified": "20260602105230953",
"kind": "Equation",
"latex": "\\begin{aligned} C_{1 j}= & \\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{1}{2}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right) \\\\ & +\\frac{1}{4}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow}-\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow}\\right)\\left(\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)\\left|\\psi^{0, l}\\right\\rangle \\\\ = & \\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{1}{2}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right) \\\\ & +\\frac{1}{4}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\cdot \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\cdot \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}-\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\cdot \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\cdot \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)\\left|\\psi^{0, l}\\right\\rangle \\end{aligned}",
"displayMode": "true",
"refnum": "4.12",
"equation_number": "(4.12)",
"page": "025",
"canonical_uri": 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"height": "432",
"width": "1458",
"top_left_x": "306",
"top_left_y": "715",
"latex_tex": "\\begin{aligned} C_{1 j}= & \\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{1}{2}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right) \\\\ & +\\frac{1}{4}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow}-\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow}\\right)\\left(\\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)\\left|\\psi^{0, l}\\right\\rangle \\\\ = & \\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{1}{2}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right) \\\\ & +\\frac{1}{4}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\cdot \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}-\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\cdot \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}-\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\cdot \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\cdot \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right)\\left|\\psi^{0, l}\\right\\rangle \\end{aligned}",
"score_tex": "1.0"
},
{
"title": "kolbe2018hubbard_EQ0060_p025",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105230994",
"modified": "20260602105230994",
"kind": "Equation",
"latex": "\\begin{aligned} \\left\\langle\\hat{S}_{i} \\hat{S}_{j}\\right\\rangle_{\\psi_{g}}= & \\frac{1}{g_{0}} \\sum_{l=0}^{g_{0}}\\left\\langle\\psi^{0, l}\\right| \\frac{1}{2}\\left(\\hat{c}_{1, \\uparrow}^{\\dagger} \\hat{c}_{1, \\downarrow} \\hat{c}_{j, \\downarrow}^{\\dagger} \\hat{c}_{j, \\uparrow}+\\hat{c}_{1, \\downarrow}^{\\dagger} \\hat{c}_{1, \\uparrow} \\hat{c}_{j, \\uparrow}^{\\dagger} \\hat{c}_{j, \\downarrow}\\right) \\\\ & +\\frac{1}{4}\\left(\\hat{n}_{1, \\uparrow} \\hat{n}_{j, \\uparrow}-\\hat{n}_{1, \\uparrow} \\hat{n}_{j, \\downarrow}-\\hat{n}_{1, \\downarrow} \\hat{n}_{j, \\uparrow}+\\hat{n}_{1, \\downarrow} \\hat{n}_{j, \\downarrow}\\right)\\left|\\psi^{0, l}\\right\\rangle \\end{aligned}",
"displayMode": "true",
"refnum": "4.13",
"equation_number": "(4.13)",
"page": "025",
"canonical_uri": 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"height": "211",
"width": "1029",
"top_left_x": "520",
"top_left_y": "1256",
"latex_tex": "\\begin{aligned} \\langle \\hat{S}_i\\hat{S}_j\\rangle_{\\psi_g}=&\\,\\dfrac{1}{g_0}\\sum_{l=0}^{g_0}\\left< \\psi^{0,l} \\right| \\tfrac{1}{2}\\left(\\hat{c}^{\\dagger}_{1,\\uparrow}\\hat{c}_{1,\\downarrow}\\hat{c}^{\\dagger}_{j,\\downarrow}\\hat{c}_{j,\\uparrow}+\\hat{c}^{\\dagger}_{1,\\downarrow}\\hat{c}_{1,\\uparrow}\\hat{c}^{\\dagger}_{j,\\uparrow}\\hat{c}_{j,\\downarrow}\\right)\\\\ &\\,+\\tfrac14\\left(\\hat{n}_{1,\\uparrow}\\hat{n}_{j,\\uparrow}-\\hat{n}_{1,\\uparrow}\\hat{n}_{j,\\downarrow}-\\hat{n}_{1,\\downarrow}\\hat{n}_{j,\\uparrow}+\\hat{n}_{1,\\downarrow}\\hat{n}_{j,\\downarrow} \\right)\\left| \\psi^{0,l} \\right> \\end{aligned}",
"score_tex": "0.676"
},
{
"title": "kolbe2018hubbard_EQ0061_p025",
"text": "<$latex text={{!!latex}} displayMode=true />",
"type": "text/vnd.tiddlywiki",
"tags": "equation kolbe2018hubbard",
"created": "20260602105231026",
"modified": "20260602105231026",
"kind": "Equation",
"latex": "\\left|\\psi_{g}\\right\\rangle=\\sum_{k=1}^{4^{N}} \\alpha_{k}|k\\rangle \\quad \\text { Hubbard-Modell }",
"displayMode": "true",
"refnum": "4.14",
"equation_number": "(4.14)",
"page": "025",
"canonical_uri": 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"height": "147",
"width": "634",
"top_left_x": "721",
"top_left_y": "1761",
"latex_tex": "\\begin{aligned} \\displaystyle \\mid\\psi_g\\rangle=&\\sum_{k=1}^{4^N}\\alpha_k \\mid k\\rangle\\quad\\text{Hubbard-Modell} \\end{aligned}",
"score_tex": "0.85"
},
{
"title": "kolbe2018hubbard_PIC_0001",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105231057",
"modified": "20260602105231057",
"canonical_uri": 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"page": "026",
"caption": "Eindimensionale Heisenbergkette mit Nächster-Nachbar Wechselwirkung",
"kind": "Abbildung",
"refnum": "5.1",
"height": "782",
"width": "1408",
"top_left_x": "333",
"top_left_y": "1345"
},
{
"title": "kolbe2018hubbard_PIC_0002",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105232095",
"modified": "20260602105232095",
"canonical_uri": 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"page": "027",
"caption": "Eindimensionale Heisenbergkette mit \\(N=10\\) Gitterplätzen und NächsterNachbar Wechselwirkung",
"kind": "Abbildung",
"refnum": "5.2",
"height": "800",
"width": "1415",
"top_left_x": "331",
"top_left_y": "774"
},
{
"title": "kolbe2018hubbard_PIC_0003",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105232961",
"modified": "20260602105232961",
"canonical_uri": 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"page": "029",
"caption": "Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächste-Nachbar Wechselwirkung.",
"kind": "Abbildung",
"refnum": "5.4",
"height": "755",
"width": "1413",
"top_left_x": "333",
"top_left_y": "486"
},
{
"title": "kolbe2018hubbard_PIC_0004",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105233985",
"modified": "20260602105233985",
"canonical_uri": 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"page": "030",
"caption": "Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächster-Nachbar Wechselwirkung.",
"kind": "Abbildung",
"refnum": "5.5",
"height": "767",
"width": "1410",
"top_left_x": "333",
"top_left_y": "849"
},
{
"title": "kolbe2018hubbard_PIC_0005",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105235036",
"modified": "20260602105235036",
"canonical_uri": 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"page": "032",
"caption": "Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\)",
"kind": "Abbildung",
"refnum": "5.7",
"height": "783",
"width": "1404",
"top_left_x": "335",
"top_left_y": "431"
},
{
"title": "kolbe2018hubbard_PIC_0006",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105236026",
"modified": "20260602105236026",
"canonical_uri": 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"page": "033",
"caption": "Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\)",
"kind": "Abbildung",
"refnum": "5.8",
"height": "778",
"width": "1408",
"top_left_x": "333",
"top_left_y": "431"
},
{
"title": "kolbe2018hubbard_PIC_0007",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105237072",
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"page": "034",
"caption": "Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1, N)\\).",
"kind": "Abbildung",
"refnum": "5.9",
"height": "862",
"width": "1410",
"top_left_x": "333",
"top_left_y": "484"
},
{
"title": "kolbe2018hubbard_PIC_0008",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105238074",
"modified": "20260602105238074",
"canonical_uri": 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"page": "035",
"caption": "Eindimensionale Hubbard-kette mit \\(N=6\\) Gitterplätzen",
"kind": "Abbildung",
"refnum": "5.10",
"height": "787",
"width": "1410",
"top_left_x": "333",
"top_left_y": "616"
},
{
"title": "kolbe2018hubbard_PIC_0009",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105239144",
"modified": "20260602105239144",
"canonical_uri": 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"page": "036",
"caption": "Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\)",
"kind": "Abbildung",
"refnum": "5.11",
"height": "771",
"width": "1410",
"top_left_x": "333",
"top_left_y": "1162"
},
{
"title": "kolbe2018hubbard_PIC_0010",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105239914",
"modified": "20260602105239914",
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"page": "037",
"caption": "Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\)",
"kind": "Abbildung",
"refnum": "5.12",
"height": "762",
"width": "1410",
"top_left_x": "333",
"top_left_y": "605"
},
{
"title": "kolbe2018hubbard_PIC_0011",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105240951",
"modified": "20260602105240951",
"canonical_uri": 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"page": "038",
"caption": "Hubbard-Kette mit \\(N=6\\) Gitterplätzen und Über-Nächster-Nachbar Hopping mit \\(t^{\\prime}=0.5\\)",
"kind": "Abbildung",
"refnum": "5.13",
"height": "807",
"width": "1408",
"top_left_x": "333",
"top_left_y": "916"
},
{
"title": "kolbe2018hubbard_PIC_0012",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105241625",
"modified": "20260602105241625",
"canonical_uri": 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"page": "039",
"caption": "Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\)",
"kind": "Abbildung",
"refnum": "5.14",
"height": "798",
"width": "1410",
"top_left_x": "333",
"top_left_y": "429"
},
{
"title": "kolbe2018hubbard_PIC_0013",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "picture kolbe2018hubbard",
"created": "20260602105242688",
"modified": "20260602105242688",
"canonical_uri": 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"page": "040",
"caption": "Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\)",
"kind": "Abbildung",
"refnum": "5.15",
"height": "796",
"width": "1413",
"top_left_x": "333",
"top_left_y": "486"
},
{
"title": "kolbe2018hubbard_DIA_0001",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105243696",
"modified": "20260602105243696",
"page": "001",
"latex_code": "",
"canonical_uri": 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jGS3nJJK4XIijDAsx9h/gK+2q8o+BN1o134NlbTrOG3v0uHF4FA3nJLJzjJXBwPTBr1egAqG4t4bq3kgnjSWGRSro65VgexFTUUAeQeL/gHoWskT6BINIuQPmjCl4ZPwzlT9OPauAtNI+KPwqvwbOG5vdPjwzx2+6e2kBPI24yp98A17H8UPHb+BPDqXVtFFLfXUvlW6Sn5RxlmIHJAH6kfj4hp3x68aWtyj3UtneQhvnjktwmRnoCuMHHA/rQB654Y+OHhbXRHBfyto983DR3Z/d59pOmP97bXpUckc0ayROrxsMqynII9Qa8q1v4e+H/ixoVl4lst+m3t3D5glVAd5PaQcZIIxkfrXm8t38QvgpqFvFPcC60uTKxI7tLbOByQoODG3Pt+IoA+oSARgjIryTxz8GbfWtQ/trwzdJpGqJhvLjTZHI4Od2V5RvcA9Omcmt7wR8VvD/jeZbK3MlpqfleY1rOOuOoRujY/A45xwcd7QB4roXxV1jwlexeH/AIj2EtvKAFi1FBuEg9XwcH/eX8R3r2Cw1Gy1W0W7sLuC6t3+7LBIHU/iKg1jRdO1/TpLDVLOK7tpB80cg/UEcg+4rx/Vvh34o+Hl3LrfgDUJZrFP3k+lTMz7vXC9H4+jemaAPcaK8/8Ah/8AFDTPGkQtbjbp+tx/LLZu2N5HUpnqOvHUfqfQKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooADRQaKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAoorH8QeJNJ8L6ab/WbxLaDIUEgszE9lUZJP0oA05po4InlldY40BZmc4Cj1J7V5F4g+KGo+JNTk8M/Du1e8vOVm1IgeVEvQsp6Y/wBo8egPFZM8fij43Xm1HOleC4p8o5XElxjIzj+I5Hsoz3Ir1nwv4S0jwhpCafpNt5aAZkkbBklb+8zdz+g7YoA47wX8H7LR7o6z4kmGs67K/mtLKSyRv3Iz98/7TD6AV6hRXBfED4naV4Gs3QGK81c42WKy4Zc87nxnaMc+/wCtAHXatrGnaHYSX2p3sVpbR/eklbAz6D1PsOa8Q8a/tBBkay8Iwtlsq19cx4x6GNc/q35VxF5eeM/jT4iWOODdFEABFGWW2thz8zE5+Y888k9uBivYvh98GdN8IXMep6hONQ1RfunZiKHI/hB5J/2j+QoA8t8JfCPxL42v31TxG91YWrsHkmuVJnn552q3I+pGORgGvoDwp4F0HwbaiHSLJVkK7ZLqXDTSj/abHTgcDA9q6WigAr4z+I3hfVvD/jDVJLy0mW1mu5JIbkoRHIGJYYbpnB6ZzX2ZWF4ykWLwRr0zQxS+Vp9xIEmQMjFY2IyD1HFAHyp8N/AN5471wQozQWFuQ11cgfdHZV9WP6da+yK8m/Z9LH4by7rdYwNQkCuqkeaNqfMfU5yuR/dHpXrNABXMeN/GFn4H8OyateRtN84jhgVwrSuegyfoSevA6Vo+IdfsPDOiXOrajMIreBc+7t2VR3JPFfG/ivxVqHi3XLrUb24maOSZnhgeQssCE8Ko6DAwOnOKADxX4s1XxlrUmp6pIGkI2xxqMJEmeFUf16mtHT/hf401TThf2nh+4a2YAqzMiFgehCsQSPcCsXw3JZQeJtMm1EZs0uo2m6fdDDOcg8evFfcoYMoZSCCMgjvQB8YeGvFPiD4deIJHt0eCZP3dzY3KsFf2deCCOoPUfSvq3wd4z0rxrpCX+mTAyKq/aLct88DHPDD8Dg98V8s/FiaO4+KOvvFIHUXAQkHPzKqqR+BBH4Vn+C/F2oeCvEEOqWLEqPlngLYWZO6n+h7GgD7aormfBnjbS/G2ji/099kg4mtndTJC3uAeh7HvXTUAFeBftBsIfEvhSZ/liQuWbHAw6Gvfa8O/aH117PT9I0lLaNnmmN2lyWO6Jo8AbQOOdx65+meaAK37SMLz6f4avohut1edC+e7iMrx15CN+VfPdfR37QTtJ4A0B3JLNdKST3PlNXzjQB2/w/8AiLq/gS6mTT7eG7t7tlEltIDlmHQqRyG5x3HPSvra31GQeH4tTvrWS2l+yi4nt/vNE2zcye5HI/CvmH4F6RZat8Ro2vgGNnbNdQI2MNKrKBweuNxb6rntX0zrXiLTPDwszqdx5P2y4W2gwhbdI3QcCgD5Y+JvxKl8f3dosVo1nYWm7y4mk3M7N1ZsADOAOOcc8816Z8KNOt/h/wDDTUfGWqq6PeRiRI+5iHEYA9WYk/QivO9T8K22rfHafQLZc2UupfvQmRtjzukAJzyBuGema9U8dOnjLxnpHw605S1jZOl3q2xsBYlwAmRznDfmy/gAReB7lfDHg3WfiV4lfffaqfORc5by84jjU8/eOPoAM9DXzvrOrXOu6zeardlTc3crSybBgAk9APSvYfjz4otYlsvBWlKscFjtkuVUcKdo8tB9AST9R715N4f8N6t4o1EWGj2Ul1MeW2DCoM43Mx4Uc9TQBj19GfAfxemsaFc+DtUdHMEZ+zKx5lhbO9P+A5/JvauH1j4C+LtK0iS+jey1CSPlrazd2kK46qGUbj7Dn0zXA6Lq2oeGPEFtqVmzQXtnLkBwRg9GVh6EZBHoTQB7z8PxceH9a1r4V+JPNe0uYpWsHZiFlhcEMqHsGBJ44DBx1ry/VvBWneGfitD4e1q5kj0Zp0YXMmFLQt0JI9/lJ46E8dvZPiXYxa34W0n4haGZBfaWI72Fto+eHIYhhz069x97rnNZvxS0aP4j+ANL8WaEokmtozK6k4byiMuv+8rDp9eemQDutW+GPhS+0G50630DTbeR4mWKeO3VZEbHB3gbuvvVH4PaDf8Ah3wKljqemixvFuZS4JUtKM8MSPy+gFc78GfiLrvi15NK1GySWGxt13agmQc5wocdCSAeRj7prt/iDdeJbPwpcS+FLZZ9SDAHOCyR4O5kU8Mw449z16UAfOXxrs7Sy+JuoJaQxwo6RyusYwC7Lljj1J5NVPg/eR2XxV0KWUMVaR4htHOXjZB+GWFcdey3U99PLfPK90zkytLneWzznPOa6P4Zf8lM8O/9fqfzoA9C+Pkrt8R9BgijhWRbSNllKnJLTOAG9VG3IHua+jI94iQSEGTaNxXoT3xXz3+0YFtfEXh6/iQC5EMn7zHUI4Kg/Qsfzr6As5GmsbeRz87xqzfUigCxRRRQAV8v/Gz4gr4l1dNC0ybfpli26SRCCs83TIPdV6D1OfavQvjJ8TW8N2Q0TRZo/wC1LlSJpRybePpx/tHke2D3xXy/QB0ngrxXdeDfE1rq9uC6odk8WcebEfvL9fQ9iBX2F4d8Q6d4r0WDVtLl821mH8QwyMOqsOxB/wARkEGvhmvQvhb8RLjwPrXkztv0a7kUXceCTH2Ei+hGefUDHXBAB9eUVDDPFcwrNDIksUihkdGDKwPQgjqKmoA8j+O/g/UvEmgadfaVbzXU+nSOGt4V3O6SbQSFAySCq8DsTXzXDpl9NqsWlpbSi9klWBYHUq28nAGD0OTX3hXh2p6nbj9qPT4o4Q7pbLbSFhjaxiZww9flZaAPT/BGhzeG/Bml6PcyrJPawhZGUcbiSSB6gE4z3xWxf6fZ6pZSWd/axXNvKMPFKoZT+Bq1RQB4L4x+AYiP9o+DJ3jlQlzZTTYxjkeW/UHOOGP/AAIVm+EfjDrfg2c6J45sr+VE+7LKh+0x5PfdjevXnOfrX0ZXK+MfAOieOLKODVInWWI5juYSFlT2yQcj2NAGpoPiPSfE2nre6Rfw3cJA3eW3zIT2Zeqn2Na1fLOt+EfGPwd1NtY0i7aTTdwBuoh8rDPCyoenPHpzwc16v4A+MukeLjHYahs03VjwI3f91Mf9hj3/ANk8+hNAEvxA+Eth4unOqadMNN1xBlZ0GElYcjfjkH/aHP1xXOeGfidrnhTWP+Ec+I0LQ4JWHU2jOH54yQMMv+0OnevbaxfE/hfTPF2jSaXqsTPCxDKyHDxsOjKexoA1YZoriFZoZEkicZV0YFWHqCOtS14IzeJfgZeCJVOr+D7ibdvYEPbk9sj7rcemG9iePadG1rT9f0uHUtMu47m1lGVdD09iOxHcHkUAaVFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAAaKDRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUV578TPiJH4NsUsdPQ3OvXi4tIFXft5A3MOvrgdyPrQBqeO/Hem+BNGa6uiJbuTi2tFYBpW9T6L6n+Z4rz7wp4A1L4g3sfjDx7LK6yEPZ6aPlTyuq5HZOeB1PUnmrPgH4W3N/enxX488y91aY7o7S5AKx46M46E+i9B9enswAAwBgUARxxxwxrHEipGowqqMAD0AolljghaWV1SNRlnc4AHuayvEfiPTPCujy6pqtx5VtGQpwPmYk4AUdSfp2BPavmvxn8QfEPxN1v+wtEjnGmzShbeyjUB5sdGkP64ztHXtmgDs/iR8c0jWXSPCEoeXJSXUR90dsRev8AvdPTPWuf8AfBvVPFVz/bXio3NtZSMJQkh/fXWTkkk8qPc8nPHrXonw4+DmneFo7XVNWjW71sKHw/Mds2OigcMRn7xzyOMda9WoAoaTo+naHYR2OmWUNpbR/djiXAz6n1Pueav0UUAFFFFABWD44/5EDxJ/2C7r/0U1b1ZXiWy/tLwvq9iJPL+02U0O/Gdu5CM479aAPN/wBnZ3k+Hd2rOzKmpyKoJztHlxHA9OST+NenatqtlommXGpahOsFrbrvkkc4A7AfUnAA7kivKP2fr63tPhxqstxKscVvqEssrtwqJ5UZJJ6fwmvN/iv8UJfGV8dP0uSSLQ7dsKpJBuW/vsPT0B+vXoAYfi3xZrnxN8UQhYXbc3lWVhD8wQHsOBknqSf0AAGdrvgfxN4atludY0ee1t3baJWwy59CVJAP1rqfgZqdjpfxKgF8ADdQPbW7txslYqR+JAK/8Cr3L4r6Br/irwpHo2hW0EhnuFa4eaUJsReRj1ycfgOnNAHzZ4H8Car461V7TT9kUMIDXFzIDsiB6DjqTg4HfBr6r8E+F7jwj4Wj0mTVZ7+RGZllmXhM4wqjOdox0J7np0HlvgqwuvglrLr4ruLVdL1lAq3dqHkSOWPJUP8AICMh2xx/I49c0bxf4f8AET3CaRqtvdm3UPN5ZOEB6EkjHY0AfLPjj4eeK/D13fapqti0to87M19E29G3Nwx5LLkkfexycVwtfTHxi8feGrv4f3Wkafqlvf3l80aqtrIJNgWQOWYjgfcxjryOMVynhT4B69Hq2m32tvposVkWS4tDK7SFRztIC7c/8CoA878L33iTwle2/iTS7S6WFTtMrW7GGVerIxxgg47HIxkYIr6n8A+ObDx1oK3sBWG8j+S6td2Wib19Sp7H6jqDW9qmo2ei6TcXl7JHDaW8RZixCqAB0/HoBXxho3inUfDniI6xo0xtpd7P5ecqyE52MOhH+Rg0Afb9fP8A+0hGguPD8zRzHiVGYcIRlTjP97ivUvA3jzSvHeki5s38q8jUfabQn54j/VT2P8jXFftFWSzeB9PuxGzSW9+q7gDhUZHzn8VXn/GgCh8eN154X8L6XaQTz3lzMZIYY0LswWMA9ByfnWvBdS0LV9GZBqml3tjv+79pt2j3fTcBmvqcTTS/Fjw3bS7TBBoc00PQkOxRWPTjhQOp/U1a+Jngy88a2Ok21lLbx/ZL5biXz84KAEEDAOTz0oA+XPB3ii58HeJbbWbSOOaSHKmKToysMMM9jjvXo1z8Sbv4m+OPCunmwi0+zg1COUJu84u+RyThegzgD15zxXd/Hiw0WL4emV7a0ivVuIxasFCvnPzBcckbc5HToewrxP4XaFc698QdKjgikeK2mW4ndG27EU5zn64HvQB9P+IP+Ed8JR6l4yurK3S/WDDXBUeZKQuFQH1OAOPx4FefeC76Lwp4K174ja9EsOoa1cSXEMWT8ytkxxqDzyxY9T8oB7Gk+JEV549+JOl+CLPf9gsdtzqTopwm7B+Y5/u4x7v+XS+NfCvhhrrSdS8S6tHaaDpcQht9LfCQu4zj3b5QBtA/h+oIB414L+G2tfE7U7nXdSnezsJpWkkuCpZpmJOVjyeQOmSePevWNQ8a+B/hLpUWi6bELi6QYNtaFWctj70z9ifxPoMVnRavrvxQ87SfCqHw/wCE4B5T33lgSTj+7GoxtHB6Hp1Iziuk0vwv4E+Glo1zcS2kVyvzte38ivOx9VzyPoo/OgDmdM+PJVkl8R+GL/TLKUnyrtAzoT2GCq578gn6VH8Sfh7p/j7Rk8WeEZILi9KbmW3xi8XP6SDnrzxg81qaR8YvB/jDUbvQ9St/s1pMfLga+wY7kHjBHRD6Z/PPFMvfh7qvg7UTr3w8uD5HMlxos0pMU4wOIz6n3P0PagDl/gh4nJ+2/D/Xoj5bLJ5ENwpHX/WQkHpnLHH+961vfD55fA3xA1bwDesRp11uvNKMzZ3KTjaPqAfTlD61ny6xY/FGVbzRrX+xfHejOLiGC4PMqoeULYG4c4wQMfQmr3xT8P6/r/hPRfFltaS2WuaSnnT2isGaMHBYqQTnaVBx6E9xggC6V4W1P4f/AAx8cBibaR3nms5I5QziILhGJHQ/rXR/Bi/Oo/DPT5HmkkkjeSJzJMZGBDHuenGCB2Bqlqmsjx/8B9Q1GFZEnmsmMsUDZZZY2yy8Z4JXp12t7181eH/7fub8afoEl99ouTjybSRlL/XBHA9TwKAOn+NFvaW/xP1P7IVIkCSSbSDiQqN3TvmsT4fNcJ8QdBa0QPML2Pap6HnnuO2e9OuvAfjCPU/sc3h7U2u5Du4hZw2ec7hkHvzmrmleHdY8K+PfD8euadeWRe9hKEHbv+dfutyD1GcUAeh/tK/8hPw9/wBcZv8A0JK9+03/AJBlp/1xT/0EV4J+0o0X2rw+nlHztkx8zd/DleMfXvXvem/8gy0/64p/6CKALNeffFD4h2vgfQmiicPrF2hFrDz8oOQZG9APzJ/HGr498aWngfwzNqUrRvdH5LW2ZsGZ8j8cDOSfT3Ir5D8Q6/qHibWrjVdTnMtxM2ep2ovZVB6KOwoAzpppJ5XlldpJHYszMcliepJ9a9a+BXg/QvFGparPrMCXTWSxeTbu3yNu3ZYr3xtA9Pm+leQV6j8J/DfjmTUBr3hjyLe3B8l5rxsRSjPK7Ry2Pbp60Aez/ED4f+F5vAmryxaHZWklnaTXMMtpAkTK6IWHKjkHaAQa+R6+x/iRo3ijX/Cf9meH7m1hmnOy83uULxkYZVODgHPOe3FfKfiTwrq/hPURY6zZm3lZd6HcGV19VYcGgD0j4OfFFtAu4vD2tTs2kzsFt5XOfszk9PZCT+B59a+mwQRkHIr4Br6M+DHxTOpC28K63Jm7RdtldMf9aAPuNn+IDoe4GOvUA9yr548YrDB+0voskaXMLyzWhkeLIMjH5c8/w4Cq2Owavoevnz4hSeX+0Z4YO0E77MckjrKR2Pv/AI5FAH0HRRRQAUUVTudV06xO27v7W3b0mmVP5mgCS6tLa+tJLW7t4riCQbXilQOjD0IPBrxL4g/AuCSKfVvCatFOo3nTh91/Xyz/AAn25z2xXrejeKNF8Rvdpo+pQXps3CTGI5CkjI56EHB5GRwfStqgD5w+Hnxov9EvRoXjF5pbdZPK+1zZ821I42uMZYAjnPI569K+iYZ4rmFZoZElikUMjowZWB6EEdRXI+NvhvoXjazm+026QakVxFfRrh1I6bv7w9j26YrxfRta8XfBPWP7N1q0a40a4kH3WJjYDq0LHgHnkEc98daAPpS7tLe/tZLW7gjnt5VKyRSKGVh6EGvDvEHgnV/hTq//AAlvgwyXOlqT9s09yW2J392X36r15Ga9f8N+KNJ8WaWuoaRcrNEeGU8PG3oy9jW1QBy3gzxzpPjfTFu9OmCTKP31pIw82E5xyB2PY9PxyB1NeOeMfhhf6JqB8U/DyRrG/jGZtPh4SZeOEXp9VPB7YPXf+HPxPtPGMLWF+iWGvQfLNasceYR1ZAeeucr1Hv1oA9EooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigANFBooAKKKKACiiigAooooAKKKKACiiigAoorzT4qfEdfCNh/ZWkyCTxDdKPKjCbzErZG8jpnjgc/TFAFj4jfEq38IQf2ZYIbzxDcqBbWygsELHCs3rz0XqfpzWf8ADz4c3Vrev4r8Yn7b4luX8weawcWwxgYxxuxjpwoAAxR8Nvhq2mSR+KfErzXviK5XeftLB/s+fTr8+O+eOgr1OgArjfH3j/TvA2iyTyyxTai6/wCi2Rf5pCTjJHUKOefbHWsz4qfEhPAumRwWapLrN0CYI3BKxp0Lt/IDufpXjXhXwD4n+KOujX9baVdOnl3T3kvymUD+GNfTsCBtHPpigDJeXxh8ZPFIXAmkUcAApb2qep64HHuSfWvoT4d/DLS/AdmZAftWqzLia7ZcYH91B2X9T37AdTomhaZ4e06PT9Kso7W2T+GMfePqT1J9zWnQBBc3UFlbS3NzKkMESl5JHOFVR1JNefah8cvAtireXqM946/w21s5z9CwUfrXY+KESTwnrCOoZTZTZDDIPyGvk3wj8MPE3jO1a90u3t0s1cp9onlCqWGMgAZJ6+mKAPXdG+NM/ij4l6RpOkWrW+kT745hdIDI7bWIIwTtxgcZPevbK8c8AfA7/hFdes9b1HWBc3dsCy29vFtRXII+8TlhgnsK6Xxb8XPDPg7VpNKv/tk95Gqs8drErbNwyMlmAzjB/EUAd9RXDeDPin4e8c389jpy3dvcRx+YI7tEQyDvt2sc47/Wu5oAKral/wAgy7/64v8A+gmrNQXYQ2c4kDFDG24L1IxzigDwr9n6XyPCnimUWr3flsrfZ0ALS4RjsAPBJ6fjXk2tfD7xX4f0wanqmiz21o2MyEq2zJ43AElfxxXsn7PUlva6X4mkLiG2jukO6VgNqgN1PSvRPHnhN/HGhQaUL5bW2a5jmnYJuZ4xnhTnAPPUgigD5l+FOhQeIfiHptpcu6xRE3J8s4LeWNwGRyMkDkc19j15j4g+H+j+E9Fl8S+FbZdN1XR4XuVcOxWeNFJeOQEnIZQfQ5xyKzfhv8XdV8c+KG0ufR7WGBLZpnlhlO5MFRnB6glgMDnn2NAHF/H7xna6tqlt4csm3pp0jSXMgwQZSAAo/wB0E59zjtWl+zjDZzR+IlYk3DrEjJzgxnd/XPeqt98H9Z8U/FHWZbmBtO0Nrp5PtWFy6nkCNc8knv0HPfg+zeEvAug+CbeSLRrRkeYDzp5XLySYzjJ6DqeAAKAPjzxDYwaX4n1WwtXEkFreSwxODnKq5AP5CvsLwL4rh8Z+FLTWY08uR8xzxYOElX7wHqO49iO+a8i+J3wTlSSfXPCsUs4ldpLjT+CyknOYsdR/s8n0z0F/WvE+sfDT4R+EY9KsFtbidR9oM8f3GxuZWU85Ykn2wenFAHafGXw9N4h+HN6sNx5LWB+3sD0kWNGyp/Ak/UCvkKvc2+Lfiz4gaXdeGtH8NQveXdq0c8kLlgsbDa7AHAUHdjJJxkdTXJ6d8Itfi8Y6NpHiCzayttRkIM8cqsMKhdlDDcA+FOAep9uaAOP8PeINQ8L61b6tpkojuYCcbhlWBGCrDuCK95+NOqS6t8GPD+pMvlNf3FrPJGpOBvgd9vuAf5VlfEv4OeHvDPgm81zSpr2OezMZ2SuHWQM6pjoCCN2c/wCRc8epDq37N3h+7ilO2zjs2Hy/eZUMLD82P5UAWviR4gvvCOr+ANdt7SKXUPs80E8EbNiZSkQKAjBIBYlcjrg47V7LaTPPZwTSQtC8kau0TdUJGSp9x0ry/XJhdfF/4d2E0UbQw2VxcLkc7zEf5GNSPet74keMb7wba6LcWcMMq3WoJbzrIDkxkEkKexOOuD9KAPCvjL4+Pi7xAunWsEkFjpjPGBMu15Jc4ZiOw4AA69c9cDuPhTpY8BfDfVvHGpQYmuIPMgjkbYTEPuDn++xGPUbcdecz4n+E4db+O2j6bGGVdUghluiOMKGdXIwOuyPv3rR+PmvWNto+meENPfNwkiSSW8aghI1XCKe4JyMAdvwoAu+GNesPhz4OuPE3iZ5G13xDKbw2qnMrrzsGD0A3E5PTd+FN0jwvrvxT16PxH41tnsdDg/489LbKlx1yehx3LHk9BgVd8DfD261WePxl8QJGvdVdEe3gn+VYEUcF1wBnvjoOp5PHJfFn4wLqi3Hhzw5KPsHMdzeIf9eO6J/s+/f6dQDqPHfxp03wwj6H4XhiuL2EeUZcYgt8dgP4yPQce56V8861repeINUm1HVbtrq6lxukfA4HQADgD2FZtFABXp/w9+MOreEZoLDU5Jb7RFXb5OAZIR28skjjpwTjHTFeYUUAfWXiPwtYePNOsvF3g+8t7TXEZZrfUE48zAx5cmO/Qcg4xjpVb4ffFE6hdTeHPF80Vp4htrhofmUIkxBxgY4DA8Y78EV88+FPGWseDNUF5pFyVUkebA/McwHZl/qOR2Ne/wAtn4T+OvhyG4jmFnrNsq+YyAGW3YjlSDjehPQ+3Y5FAFTwhaaj8OviJ/wiV3HbXGl+IDLdQSxIUWJ1ViUAOcjAC491rI8CaHb/AA3+N99pN9eRpBeWDCxkk+XzA0iFVye/yMPcrXLeOde8XaFpmkeHdf08x6jpVx5tjrKuxMqr02nGG4Kg9+BkZrofiQv/AAnfwm0DxdGY31C3dYLhY8gZc7WAHrvC/maAPoavGPjNrlvJr/g/RbaSKS8XVI7iQB8mLDKqhgPUsf8Avn3rsdJ8R6BoU2k+BbrUZBqws4owsm8Fjs6F+zHBwM+gHYV438Q/h1D8O9c0rxHp73Nzpf21HlSUhnicMGxu7g4OM+nJNAG5+0pZ/L4fvt/QzQ7Mf7pzmvcbJ1j0m2d2CosClmY4AG0cmvEv2k43+yaDJsj8vzJV3c784Xj0xWz8Zb+8Hwk0+bTbhRZ3TQCd0Y/vI2TKgEdQTj8KAPFPiV4wfxl4xur5HY2UZ8q0XkARg9cHuTk/jVn4Z/D1viBq11bve/ZLW0QPM6ruc7iQAo6djzXCV6H8J/GV94U8U+VaWDX8V/thnhjB34B4ZcZ6ZPtj060Aa/xN+EVr4G0SHVbHVZLmN5xCYZ0UNyCQQR16enevVfhL4v8ADMvgfSNJg1G2try2i8uW1nkCOXzliATyCxJ49e3SvQ73TbHUDAb20guTbyCWEzRh/LcdGGeh96+dvjNd6d4u8caVonh+BLnUIi0VxNbJuLsxXC8D5toBJOf4j0waAPofUNVsNKtDeajewWlsD/rZ5Ai5xnGT34PFfMnxw8T6R4n8VWR0e7W6itbbypJY/uFixOFPfjv0r1n4teHXf4OtZW8Ml3JpiQSK5O5gsY2s5Pf5N2fqTXI/s5R6L5GqySNb/wBtGULGHI8zydv8IPbOc49s9qAOQ+H/AMG9Q8baW+qXV8NNsSxSE+SZHlI7gZHy89c84/Gue8ceD7z4deKIbH7eJ5PLW6t7mJSjY3EAkZO0gqe5r7Or41+J9x4gn8e6gPEfF3G2yJFPyJDklAn+zg59eTnnNAH0F8KviPa+MdEhs726Qa7AmJ4j8pmA6OvrxjOOh+ormviuir8Yfh+wUAtdxZIHJ/fpXjPw2Xf8SPD67nAa9QEoxU4z6jmvZ/ix/wAlg+Hn/X3F/wCj0oA9sooooAK+S/jjpMumfEq6lknaZb6FLqPcclVOV2/QFDj2r60rk/FHw58NeMdQgvtZs3muIUEaskzJlASdpwemSfzoA8f/AGbtUhg1nXNMfia6himjOe0ZYEf+RB+VfRlYmh+E9A8Nl20fSbWzkkXa7xJ8zDOcFjyRmtugArG8SeHNP8VaHPpOpwmS3mA5BwyMOQynsQf8OhNbNFAHy3qWg+KfgZrkGsWF3FeWFwTF5m0hJR12SJng8ZBBPsete6eB/iJo3jqw32Mnk3sYHn2ch+dPcf3l9x+OK6PUdOtNX0+axv7aO4tplKSRSDIYf0+vUV83+M/h/rnwx8RJ4j8Li4fTYW8xZl+YwZJykgHJTHGTwQcHmgD6dryP4ifDK5m1JPF3gwfZNft5POkijIUTnklh23noR0bJzz13Phv8S7Dx5pvlTNHbazEP39qDgMMnDR5OSMde4P4E+gUAee/D34l2Pi6JNNvCbXxDAm25tZF272Xhinr0yR1H4V6FXl3xL+Go1qH/AISDw5ELPxJaN5ytB8huSCOpH8Q5IPU9D14k+FfxM/4TGyfT9WaGHXbbIeMDb5yj+ML6juB9eBQB6bRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUABooNFABRRRQAUUUUAFFFFABRRRQAUUVy3jjxtpvgbRDqF9l5ZCUt4F+9K+M49h6mgCj8SvH1v4E0ESoqzancZS0t2PBPdm77R+pwO+Ry3wu+G17aag/i7xaWuNbuD5kMcxJaHI5Zsj7/AGx2Hv0j8AeEdT8Ua4vj/wAZqr3MoDafZY+SJcfK+3Jx7DrnLHnmvZKACvP/AInfEa38CaOUh2y6vdKfssJGQvYu3sPTufxxZ+IHxI0vwHYgzA3GpToWtrVf4u25j2XP544ryPwB4W1L4r+KZvFfisvLp8LABSu1JyOka+iL3x6+pJoApeBfAOs/E/XpPEfiiW5OnOxZ52wrXLDHyIOy+4GBjA9vpm2t4bK2htbeJYoIUWOONBgIoGAB7ACvL/Fvxg0rwFrDeHY9AuGNqihVjZIogpUFQoGeO3QVqfDT4ky/EA6kX0hrFbVl2ssnmKQc8E4HzcelAHodFeDfFb4n+LfCXjSTS9NmsorPykli/c73IYYO4txncGxjtitD4N/ELxD401/UINa1K2aKC2DR26QojMxYfMMckAAg/wC8KAPS/Gc1xB4M1mS1tpLqf7HIqQxjLMSpHH55/Cvmb4Z/FC+8D3QsJ1Fzo00uZYWOGhJ4LofyyDwcdutfW9eG/F/4SS6q58QeGrOP7UAzXttHhfNxzvUdN3XI6n3PUA9thmjuIY5onDxyKGRgeGBGQRXzr8YvCmr+J/ic0WhWX26WOwiadYSAY+WxuJwASMY56Vw3hrVPiHqUS6T4cvtblihXYIraVwsQz0znCj8RXsfwZ8FeKtB1bVNY8Ro0TXkQjCzT+ZK7Bs7mwT79TmgD59hl1bwj4ijm2T2Op2MobZIpRlI7EehH5g19Z/Dzx/ZePdFa5jRbe+gIW5tt+Sp7MPVT2+hFcD+0P4atpdJsvEaNFHdwuLaQMcGZDyMDHJBz+BNb/wACfDMGj+Bk1U7Wu9UYyswHKxgkKv6E/jQB6nQQCMEZBoooA+dfh5Ck3w/+Jscio0YSYhSucERyEH8CAR7ivVvhZpF5o3w80u2vrh55Xj84K5z5SvyEByeAD+tecfD7SNRXSvilo0CxTtuuLWNUyHebbKoAzxg8VDf/ABwtLXw34atNFlmjuoXhXUFaAErEgAZVJ4JbHb8xQBnfGDx/4raS98L32lxabYyynZKpYvcRKcghs4KnjOB1GOxFdJ8BPAt7o8MvijUAIjfWojtYs/N5RYMXYe+1ce31rp/FHwxXxZ8RbDXtTuLd9KtbdYjZ+W26QqzMAxzgjLf0x3PHfFH4wx6f53hrwq6CRB5U96n3YscGOMdMj+90HQeoAL3xW+McmgXMmg+HHiN+APPvAwcQH+6owQW9c9PTPT5+m8Qaxcan/ac2q3r3/a5M7eYPo2cis0nJyaSgD3TwD8eLm2a30vxWDNBwg1BSfMT3kH8Q6cjB+tek/Fnw/deLvh3NFpCrczo8d1CkeGMyjqFPfIOR6496+Qq9a+Fvxbn8LzRaRrUzzaIxwjtlntf93/Y9Rj6d8gGr+z7rVjpfiDU9EvYzDqN2B5TvxkpnMZHY8k/gfx+ingilZGkjRzG25Cyg7T6j0NeOfE74dy+Jp9N8V+DbaCe9Zlkl8mRYxOn3lkzkZPbIOSCPSuysPH0bePpvB1/YvaXUdussM7SgrOdoLBR19ccknBoA8r+MnxQnv4dR8Gx6RPZBJlW4luWG6RVIYYUA4BIVgc8jHrVzWnV/2WLDac7fKU+x86rn7SC2f9iaMzCH7cblgh43+XtO73xnb+NVdT/0j9lm03DyBGsePN/jxN/DjPXtnFAGj8ZLyfQdK8IeJdOcw6lZTeXHIBwUaPLK3qDtxj0J9a8b8YfEXxB41uLSTUpYokteYYrVSiq3GW5JO7j147Yr2H4t37XfwP0GfZJILsWkjS7QNuYt2WA6Zz2rxfwF4cu/FPjGw060IXDiWWRukcakFmx39h3JFAH1Tr+qaR4c8OxeK9Tt1nuLK1CRTFd0hLhflBPTccc15r8H/CEviLV7v4ha7GHkubh5LKNuRuLHc+PY8L6EZ7Cr/wAQPtHjr4p6P4JgbfpdiFvtRCjOCCcgn/dKge8lHxh+JH/CL2n/AAimgf6PfPCvmTR4UW0XZUx0YgfgDxyRgA5f4yfFaXULq48NaDc4sEzHd3Mf/Ldu6Kf7o6H1I9OviNFFABRRRQAUV64vwS1C5+G1t4isZ5Z9TmhF19gWMHdERkBSDkttwcd84xmvI6ACtvw14l1PwnrMWp6VOYp0+Vl52yLkEqw7g4HHsKxKKAPrWOfRPjb8PJo0VraTdtIcbmtZxyCDxuGD+IPY1wHwn1rUPBnjW5+H2twQrBcTuVOM4nwuCG6FWVPTrjpyK828B+N77wN4hjv7dme0chbu2z8syf8AxQzkH19ia94+I/hmDx14cs/F3haZJNVsQJ7eaLrNGvzbP94EZHvkd6AOV8X6lpmhftI2GparNH9jSKMyHaT5LGNlUtkdm2tkZwPfitr40eL/AAzqXhC0sbbV7a9aW9ikdLKdJHWMZ3Hg8HHTPesnxrpFj8S/hpD4302Ff7csogt8kfBYpjzFYeq53Dvtx7CvAV++PrQB9C/tJRy/YdBk87EPmyr5W0fewvzZ69OMVZ+J9wl78GPC1pZWjRvqRs1tbdSCEzFkJk49QM1H+0p/yBtA/wCviX/0Fa2fHepRWXgnwT4mWLybaxu7S5NuU5CNH0wOhAPT2oA8Y8R/CPxT4X8OvreoxWv2aPb5yRTbni3EAZ4weSBwT1rsvg/o974J8aJeeKIF0u31HTGFnLdOqq7F4yFzn5WwD8pwfbmvd9J1zRvFOmm70u7hv7QttJAyARzgqRkH6ivJfj94u0v+xV8KwiO41EzJNJgZFsozjnsxzjHoT6igDqrrxkPGer6x4T8MS28yLpkvmairhkSVvlVV7MOeSKoeDvCHh/4ReHn1vXryJdSljCz3DnITPPlxADJ98ZJxngVF8JPB8HgLwlc+I9blW2ubuBZZTKNv2eEchT7ngkdeg614X8Q/GMnjXxXc6kpnWzGEtYJW/wBWgAHQcAkgk/WgD6A8I/F/QfHGpXOiXVn9iebMcCXDh1ulIwV6DDH+7zkd681+Ifwi1Lwvq0OreFRcTWMs6qqxt+9tZGYBRkY+UkgA9uh9T46CVIIJBHIIr3j4X/Gt4Wg0PxXOGiwEg1Fzyvosh7j/AGu2Oc9QAeia/wDE/QPBfiG08Pau17u+zo7XrIHUA5ALbfmJO3nArwv4teIrbx54vGoaDDcXVlZWSwPMsLYOGdi2MZUfN39K7H9oPw5qFzd2HiG3tBLp0UHkzTRclDkkFv8AZ54PTtxkZ6P4MeOfDP8Awien+H/tUNnqkW4PDL8nnMWJ3Kx4YnI4znigDx/4Z+EfEmseJtO1PSbN/s9ldxvLdOQqKAckAnqcZ4Geo6V6j8avN07x14I1ryhJBBdL8u7BZlkRse3HevW9b1vTvDWi3OranKYbK3wZHVCxG5go4AzyWH51438adXtLvUfBd5ps0zPJMLmC6iYhChZdpHPDZ56ZoA94rnvEfjbw74SaFdb1OO1eYExoUZ2IHfCgnHvXQ14N+0Z4fD2ml+IIlOY2NrPgcYPzIc/UMPxHpQB6DoPxS8MeJfE39haTPcT3BR3SbySsTbeSATz69scfTPcV8c/Cy31k+PtKvdI0+a7FvcKZ9qnasbfKxZuAOCcZPXHWvsagArO1rVLfRNFvdVumAgtIWmfnGcDOB7noPc1o18qfGjxH4j1DxTLYanbXWn6dCf8ARbVz8kqgkebkcNn8cdKAEt/jz4xt9YuLxpLWe2lcsLOWL5Ix2CkYbj3Jr0i3+PUVvptrfa14U1azt7n/AFdxEoeKXHXYzbc9q4r4QfClPEi2/iTWGjbS45WEVp1M7Kerei5yMdTj06+qfGxIB8JdVDrHlTB5IYDhvNQfL77d3TtmgDQ8H/E7w/431K4sNK+1Ca3iExE8QQMuQCRgnoSOuOtdhLDHNE8UqK8bqVZGGQwPUEdxXzf+zpc+X4s1S3+1Iiy2QIgI5kZXGGBx/CC3Ged3fHH0rQB80fEb4XX/AIH1FPEnhE3QsISZG8piZLNh3z1Ke/OOc16X8L/ilbeM7FbHUZILfXIuDEDgTqB99M9+uR+PSvSHjSWNo5FV0YEMrDIIPYivnb4l/DK68GXy+L/CLSR2sEnnSwxn5rVs/eXH/LPsR2+nQA+ja8j+InwqN1cP4o8JF7LX4W89o4DtE7AdV/uvx2+9k55Oa1vhl8T7fx1ZNa3Sx2usQLmSFW+WVf76Z7eo5xXo1AHB/DX4gxeONJdLhFt9YsyEurc8E9PnA7AnIx2I+me8rxj4keBNS0fxDH4/8Iq5voJBNe2qcCQDlnwCCQQMMvfOfWu68B+OdO8daKt5aN5d3Hhbq1LZaFv6qccH+uaAOtooooAKKKKACiiigAooooAKKKKACiiigAooooADRQaKACiiigAooooAKKKKACiiigCrf39tpmn3F/eSrDb26GSV26KoGTXhPhvSdQ+L/jybxPras3hmxmZbKCRcLIA3yoB37Fj3PHTgR+KtY1D4vePY/CGiTSQ6FZuTczqNwcqfmkPsDwoJ5PPfA9z0bSLTQdIttMsIhHbW0YjRR7dz6k9SaANGsDxZ4p0/wj4fudVv5FAjUiGItgzSYO1F9z+g5q7res2Ph7SLrVdRmEVrbIXc9z6AepJ4A9TXzaJtZ+O/j+KF/wDQtNtUJIQ5EEWeTz952JA/+sKAIvDfh3XfjJ42m1rVCU01Zf8ASJuioo5EMfrxx7Dk89fqCysrXTbKGzsoI4LaFQkcUa4VQOwFVdD0Sy8O6LaaTp8ey3towi+rerH1JPJrToA+UPGOhX3jj426xpelTRSztKVVpZMIgjQBhnnoQRj1r1v4P+ANf8DHVE1a5tWguShjigO7LDPzEkAjg4xXjHxE0fxD4P8AiJqOsBZ7T7TfS3NneQkhSHdmADD+LB5Fel/Dj43w34t9G8UOIrxiI4tQ4EcnHHmc/K2e44Oe3WgCP4wfDjxV4v8AF9re6Ta289mtqItxlSMxsCSd2cE5yMYz+FeO6lpHiT4deJLb7VE9jqEJE8LowYMAeCCDgjjkfnX2tXGeP/h/p/j3SFguGMF/b7ja3SjlCR0Yd1PGR7cUAR/Dz4iad480hSrLDqsCj7Vak8g/3l9VP6Zwfft6+Jr6y1v4eeMPLdntdSsZN8cinhx2YHurD+ZBr6G0v48+DrvSFudQuZrG8x89qYXkOf8AZZRgj6kUAdH4w1u3+Hng681fTtJtiFmVmgiAhV3dgCx2jk+/evDfEPx+8SaxaG1062g0pW+9LG5eXr2Y4A/KvYPF2t6V4p+DWsapDJPFY3Fk7RtJEVYsp+UY9CwAz0561y3gL4KeGZvDml6vrCz6hcXlvHcmIyFIlDruAwuCcAjOTyR0oA+e73UNS1q7WW9u7q+uGwqtNI0jn2GSTX2/otnFp2h2FlBF5UVvbxxrHz8oCgY55/OorDw3oWlbTp+jWFsU+60NsikfiBmsTxv8RdE8DWQe+k869kB8mziPzv7n+6vufwzQB0uo6lZ6TYy3t/cx29rENzyyNgAV4X47+Psclu9j4P3hm3JJfTxbcDHBjGc592H4VxOueLPFnxf1uDSrS3K27SAxWUGSif7cjd8epwB2FekeGfgToeg2n9p+Lr2K8aFTJJGrlLaMDnJY4LDA74HsaAIf2b5vM07xDvcNM1xE7ZOWOQ3J/GvHF0ufxl8RLix0giVtQvpWhcggbCzNuOeQAuT+FfQfwpm8MXOv+K5/C8EcVmZYAgCbT907toPIXdnHasH4TWGj6HpXifx2yRrbG4nW1O3b5duhJwoOMbiVH/AQOOaAOt+L3jODwt4Nu7eK4VNVvozDbxq+HAbhnGORgZ545xXyLXQ+L/FmoeM/EE+r6gQHYBIol+7FGM4UfmT9STXPUAFFFFABRRRQB6x8H/ia3hW/TRtVdm0i6kAV2b/j2c8bv909x+NdP8cPAGpXeot4x0tmuIFhUXMan54go4dcdVxjPcfy8Ar3v4LfEyWeaz8F6wiSwujR2k7tzwMiJgeCMAgfgKAPCpria4ffPNJK+MbnYscfjXvV5qZP7LMJtXK4C20mVHP77DD/AOvXBfFjwFL4N8SyTQRY0e9cvaOvRD1aM+hBJx7Y98eg6ZHaS/ss3XlxltqSMfNAOJBNyV9PbvQBY+JP/Jufhz/rhYf+iap/CeDTfBPw31PxzqcZSebckJZDlkHCqnrufv7c8AmtC+03VPG3we8EaXawMIbiWCG5ljjL+TFGrIHPp90Z7c1Y8UWD+PPiBaeBrExWvhzQUjuL5YVHLYG2MDp0IA7DLE5wBQA/wK8Hgz4e6l4919idQ1Vmu2Lg72Vv9XGCeu4859CPTNfOus6rda5rF1ql5IXuLqUyOSc9T0+g6Aegr1j4+eLkv9Xt/ClnuW200h5+MAylflAHoqnr/tH058WoAKKvaVb2t3q9lbX1z9ltJZ0SafGfKQsAzY74GTXvcv7OujXFpHLYeJbkCRQySPEkiPnkEYI4I96APnar+kaXPrOsWWmWw/f3cyQpnoCxAyfbmvWb/wDZy8QxYNhq+m3IxkiUPEc+gwGH6ipPhn4HuvCnxat7XxNB5E62skunurbo55eBwwHOFLnHB4H4gHrNzrsfhTxh4W8Ll0j0+6sXt41xjbLHsEeDgnkZXGe4/H5j+IPh4+FfHOp6UFCwpL5kGAceW43Lj6A4+oNey/tD+ZZweG9XtQ8d1bXT7LhMgoQFZeexyuR9KXxd4XT4z+F9H8TeHZLVNRRDFcJM5XjuhxnBVskZ6hvpQB84UV7FZfs6+J52H2zUtLtkzg7XeRvrjaB69+1dHpn7OumR3v8AxMvEz3CRqGlgggWJhn1Ys2Bwe1AHz1XsvwJ8dNo+sr4YvXH2HUJc27MceXORjH/AsAY9cetcL4907w3pnieS18K3rXenpGoaRn3gSZIYBsDI4HIyOetc7Z3dxp97b3trKYrm3kWWJ16qynIP4EUAfR2iR3PgP4w3Xh0wA+H/ABEzTwNNgIj7WJUHucgptPOCvXjPj3xK8GP4L8Xy2iqPsVwfOsyGz+7J+6c85HSvd7m3Hxc+EdreQsI9XRRLFIg2mO6j4YAn7oYj14yOeK5TxlPbfET4GWviZ9x1TSCBKFUk7typID7EbXz7ducAGh+0fFM3hjRplRTAl2yO5AyGKEqB35Ct04457VX+Jdo1/wDADw3eussstvBZSNJknG6IKWY/UgZPc1X+Lupy6t8FPCt9ORczXMlvLNcqVx5hgfcMDoS27gDA2kccVe8dxG+/Zt0ae3eN47a1sWkIbPRVjIGO4ZgCPY0Ad5bHTfhx8MhcRwQiCxtFlkWJwBNIQMkN3LMQAe+RXN6j8O7fx74v0HxpM4t9Payt55bMr+9kfJcBj0xhlU9/l/GvANNv/Ffi2ax8LR6rqFzDO6xR2r3DGMAYPIJxhQM89MV9IfFTxRceCvh4ptJFF9cFLOJxj5MqdzgH0Cn8SKAPL/jh8RI9bvE8N6TcyfYrSRlvWXGyeQEYA9QuD7ZPsDXi1OJLEkkknkk02gAooooA+g/hL8TdOvtGj8HeKHViymK3muSGjmjP/LJyeh5wM8EcccZn0L4OQaV8T9Qvb2zMvh+zj+1Wan5g7k5CEd9uG4P+z1Br51r6k+DfjqXxb4am0S+ucatYR7Fkz88kONqv7lTgE/Q9TQB1Fp4l8I+P/DF2klxBNp7/ALu6guj5TIQc/MCQR0BBB7cHIrgPjro2nab4J8P3+mwpE1jcpb2pjwVERRmA5znlFxz3PWvG/G3hPU/B/iabT9Uk895P3sdyMkTqx+9z3znIPf8AOvePjlp9hH4H0CzlcWtmmq29uZsFjDF5cgJ9TgAH3xQBP8P/AI06V4mFtpur4sNYYBcn/UzN/sn+En0P4E16Ze2FpqFsbe8tYLmAkExTxh1JByDg8cHmvBvEH7PsM2mx33hHWGuiyhlivGUiQY6rIoA9MAjHvWP4a+Jvib4a6u3h7xXb3F3aW5CNHI+ZYV7GNjwy46DOMdCKAPpaKGK3iWKGNI41GFRFAA+gFcb8QtP8bX1lanwbqUNrLG5M0bqA0gxxhmBHHpgdevFdJomt6f4i0mDU9LuVuLSYEpIAR0OCCDyCD2NadAHz3pn7QWq6VP8A2f4m0NJp4H8m4lgk8t1IOGJQggn2BA+ldL8bPDGpeMfDej3+gWZvjDIXKx/6xo3UEMAeo4HHXkcdcedfH7QV0zxxHqMNskUOpQhy6ggPKpwxPbONuceuTya9K+BHjB9e8KS6VeTM95pZChmHWAj5MnuQQw+gFAHF+AfF2v8Awu8N3Ntr3g/V/wCzWuTMLkxNH5RIVSDuGMEgY5HJPXNa1raaX8eda1K9e/1fT7TTo4I0s8qVJbeS/UjJ2kYx2HJzgT/Fn4t6Q2k6j4Y0lVv7iZGgnnx+6i5wcH+JvQjgH16Vz37Oi6iviTUnjt5Dpr222abkIsgYFR6E4LfhQB12nfAo+HvEFhq/h/xNcW8ltIGdbi3D7l/iGVK8EcYI/GvZKKKACo5IkmjaORFdGBVlYZBB6giuB1j40eCdHvJLV9Se6mjOG+yRGRc+zfdP4Guu0HXdP8SaLbatpswltbhcqcYIPQqR2IPBoA8I+J3gS58Ca3a+MfCcU0NskpknWIAJatwBgDB2Nkgjp2zyK9W+HXxCs/H2kyzxR/Z722Krc25bO3PRge4OD9MV11zawXttLbXMSTQSqUkjcZVlPUEV81+OvDeqfCPxlB4j8NM8WlzP+7G7Kqf4onHdT2z/ADGaAPpuvDfGeiXHwq8Ur478OweZpty5j1GwyQil+4PO1S3I/utgDg4HpPgbxpY+N/DyanZgxSK3lXMDHJikwCRnuOeD3+uRXQXtlbalYz2d5Cs1tOhjljfoynqDQBBo2rWmuaPaapYyeZbXMYkjbvg9j7g8H3FaFeALfXXwU+IqaY807eDtRIkjEhDmIkAFgcDBVuoHVSCcmve4pUmiSWNg6OoZWHQg9DQBJRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAAaKDRQAUUUUAFFFFABRRRQAV5V8XvG91plvD4U8Pq82var8m2MEtFG3HH+03IHoATxxXZ+MvFtj4L8Oy6vfKXVWEcUSnDSuc4UfgCfoDXmvwp8LX/iPXpPiT4illNzPI5sYSeApBXd/ugEhR7Z9KAO5+HHgW08DeH0tlAfULgLJdzHBJfH3R/sjnH412dFeJfHP4gnS7I+FtMlYX1yoa6kRsGKM/wcd2/l9RgA5L4peL7z4heLoPCfh/99Zwz+XHsbAuJuhYnptXnH4mvb/APgu08CeG002FzNO7+bczkY8yQgDj0AAAA/qTXJfBv4bx+GNJj1vUYT/bN5HkK4INvGf4cep4J/L6+sUAFZGt+JdF8OrE+salb2YmbbH5rYLH2H9a8c8afHbWdF17U9GsdDt4JbS4eFZrl2csAcB9oC4BHI5PUda8R13X9T8SavLquq3LXF1JjLkAAAdAAOAB6UAfbuoadZ6rZPZ39rFc20gw8UyBlP4Gvl/4p/CmbwdKdV0syz6NK/ORlrYk8BiP4ecA1618MPizaeMLVNO1SSK21xONv3UuR/eT/a9V/L29KuraC9tZbW5iSWCVCkkbjIZTwQaAPnj4Z/Gt9NWPR/FlxJLZgBLe927ni9pO7L6HBI9+30Rb3EN3bx3FvKksMihkdDkMD0INfN3xU+Dkuhyf2t4YtJptNI/f2qAyPAR/EOpKn9Pp05/4cfFbUvBE62VyDeaM75kt2PzRZ6tGf/Zeh9utAHsXx30bTLv4fXGp3UaC/snjFpLkBiWdQye42knH+zn1r5p0nQtV124NvpWn3N7MOSsEZbHfn06Gvs2Cbw/468OJKq22qaXcjO103DI7EHkMPzFalhp1lpdolpYWkNrboMLHCgVR+AoA4jwL4Wu3+FFv4b8VWpy6PHJBkArGWJUZXoRwfWu20+xg0vTbWwtUK29rCkESk5IRQFAz34AqWeeK2gknmkVIolLu7HAVQMkn8K8E+Ifx1gurCTS/CUkyvIWSa+dNuF6fuweefUgED36AHT/Er4y2nhVpdK0Ty7zVxlZHPMdscd/7ze3bv6V5B4O8BeIPifrb6leTS/YTLm71CY5LHOSqerYP0H5A9H8OvgndeIYbfWvEkklvYSMJI7XnzbhfVj/AD+ZHpwa7Tx98WtJ8F2DeHvC8dvNfRRmJTDjybPHGOOrDnjsevpQBs3V74M+C3h1oraOP7U4ysAcG5uW5wWPUL74wK8F8Z/FPxH41Rra7mjtdPLZFpbAqp9NxJy348Z7CuOvr+71O8lvL64kuLmVt0ksrFmY+5plvbz3dwlvbQyTTSHakcalmY+gA60Ae8/s1va48QR7D9r/csWx/B83H50/406np3hPwTYeBdHTykmxI8Y52xKxbknnJfn8D+N74D+ENf8N3Or3Os6ZNZR3MUSxeaQCxBbPy5yOo6ivG/iVrFxrfxC1m6uFdSlw0CI38KJ8oH6Z/GgDkqKKKACiiigAooooAKmgmltp45oZGjljYOjqcFSOQQexqGigD6fsZR8avg9JBOY11mFtrSMuFWdOQwx2ZTg+m4+grmfDs8rfs1eJbOZFVrG5lt/lOc/NG5/VyPwrmPgf4tm0DxpHpUjqLDViI5Qw+7IA2xh+Jwfr7V7d8SNJS2+GHiOHR9MQPcKZ5kt0ClmLKXkIHU4XJ78UAYXhLxYvhv4AW+sSQPG9pA8cKTDHnSFyEI9QSfyBqlpd1P8MvhXe+JtVcXHiLWXEx8wZYyuD5asepCgliOnJA9Tw3w5j1r4iyaX4Wvnj/AOEc0RvtMyqmDJydqMc85Jb8MnnAqr8cfF7694zk0q3mLafpn7pVB+Vpf42/D7v4H1oA82vr641K/nvruVprm4cySyN1Zick1VoooAK9o+G2vQeNdDfwBr8ziVV83SLveQ0EiA4AOc5GePbI9K8Xqe2uZrS6hureRo54XEkbr1Vgcgj8aAPadP8Aib4q+GniGTw54u36pbwEfvN2ZdhAKsrn7wx2PPUZGK9S1iLTPib4Thu/D2qqL61dbyxuImG+CdQcK46jOcEH2POK4W/07UPjH8KYtZbSFi160kK20ilVF2oID4J6D73B43L715Vp3hf4geHdVS80/Qddt7qIgh4LSQj1wSowR6igD0X4za//AG34C0FZbqOLU4rnZf6cf9Yk4jIYlewBzg9w4Ir0z4UeG38K/D6zgu4Bb30+65ug3BVmPAbgYIUKCOxzXzXdeK9ftPiFH4i1uzV9XtZkke3u7fywCowAU4Ix1B7HBr0jXdE+K3xMtLaa4hs7DSplEsNulwqpgrwzYLM2R2PT0FAG74t+LN7rWsL4V+H0YvL+YmN78fdXg58vPHHXeeOOM8GuO8ea7D4I0STwRpcrXGq3SrLrWqO+6SV2GTHnr6dTwD6kmux8L/DfxF4B8D6zd6ctjceKJ0xAyLuMUY6qjEcseuOmQOtfOd89zJfTvemRrtpGMxlzv35+bdnvnNAFaiiigD2H4EeNZNI8RL4bnI+xalIShJP7uYLxjnHzYA6dcV3kVvF4M+L95pN5EreHvFkZdI5EBj+0AfMpz6kn/vtc+tfNNtcy2t1FcwuUmhcSRuOqsDkH86+lby7f4ufCAahYgJr9hIJlSEkFLiM5IXv8y8jHcjnigBv7QFpDY/DLTLW1hSG3h1KJI40GFVRFKAAKxNdZF/Zc03fA8hIiCspIEZ80/McdRjI57sKxviN8RtM8ZfC7RbQ3OdcW6jkvIBGw2lY3VmzgDksCAPXHatvXLz7L+yzp0Owv9qWKHOcbf3xfPv8Acx+NAEf7OvhpC+o+JJ4zuQi1tWOQOmZD0wf4AOf71cf8bvFH/CQ+PJrSCUmz0xfsygN8pkBJdvrn5f8AgIr1bUJm+F/wGighl8rUWgCRl02uZpW3NxjqoZuv9wCvl9mZ2LMSzE5JJySaAGUUUUAFFFFABWroOuXvhzWrXVtOlMdzbvuU9mHdSO4I4rKooA+lPHk9h8Tfg2viSyiDXunkTeWoy0TZAlTntt+b32ipPj7dC++F2k3ao0Ynv4JAj9V3QynB9+a4b4D+NINB8Q3Gh384jtNTK+U7NhUmGQO+BuBx9Qteg/tGf8k8sf8AsKR/+ipaAPIPh98U9V8CzmBg1/pL/etXkI2H+8h52n26H9a92mXwT8Z/D6oJY5LhELJhttzasevHpn6qcV8kVpaNrN/4f1SDUtNuXt7qFsq6n8wfUHoRQB6PLD4x+BniEtE63Ol3LABsEw3ABBwR/A+Bj19MivffBvjfSvHOki+0x3R4yFnt5Bh4m9D6j0I6/mK5bwp8Q/DvxR0efQdWhjtb+5jaOWydsiQY+9GxHUdfUEd8ZrzHxR4N134M67a+JNCuxPYGTy1d15XOT5cg7ggHkenbigD234jeBU8f6BFp5vDZywTCaKXZvGcEEEZHY+tePT/s8eJbSEtp+uWEkjIRIhMkWR3UEA57dcV6x8PPiTpvj3T2RV+zapAoNxak8Y/vIe6/qPyJ7ugD5K0T4L+LdQ8Sf2bfWMljbRt++vJBmPaP7hH3iccY/HFfTnhrw3p3hTRIdL0yLZDGPmY/ekbuzHuTWzRQAVFNDHcwSQzIHikUo6MMhgRgg02S6ginSKSeNJHOERnALfQd+hqegD4g1Xw5fReJdT02w0+9mW1uZEVEhZ2CBiFJwO4xzX1D8H9JvtE+HFhaajay21yXkkMUowyhmJGR247Hmu+ooAKztY0iz17SbrTL+IS2tzGY3XPOD3HoR1BrRooA+XUOr/Ar4hsNslzo91gFmXAuIc+vQOv+eDX0npOq2WuaZbanp1wtxaXCB45EPBHp7EHII6ggg1l+M/Cdn4z8N3Wk3aqHcbreYjJhlA+Vh/X1BIrw74ceK9Q+F/iu48I+Jo/Jsp5hmR+FgfoJFJxmNuMn2yO+QD3bxZ4YsvFvhu60e9XCSjMcgGTFIPuuPp/LIrzn4XeJ9Q0PWpfhz4m+S7s8iwnPSZByFHr8vKn0BHUCvYgwZQykEEZBHevPfir4Fm8T6XBqekYj17TGEttIOGkA52Z9c8j3+tAHolFcT8NvHKeNNBzcqItYsz5V/BjbtfkBgPQ4/A5Hau2oAKKKKACiiigAooooAKKKKACiiigANFBooAKKKKACiiigAppYKpZiAAMkntTq8k+M3xFPh2w/4R3SXJ1e9TDunWCJuOP9pug9OvpQByN7I/xn+LaWcXm/8I5pIIkIJCuqsct14Lngd9o6cGvoK2tYLK2itraJIYIlCRxoMKqjoAK4b4T+Bj4K8KgXRzqV9tnuR2j44jH0ycn1J7YrvJHWJGd2CooJZmOAB6mgDnPHnimPwd4SvdXYoZ1Hl20cjYEkrfdHv3OPQHp1rwz4OeF5vG3jK98Ta8jXVvbv5heU5EtwSCB7hRk47fLVLxtrV/8AFv4jw6Toe+bT4WENrtQ7QvG+Z/bOeeOAO/X6T0LR7Xw9odlpNkoWC2hWIEKFLkDBY443E8k9yaANSuM8S/E/wv4T1NtN1W9kW8VBI0ccDPgHpyBjOOfwrs6+e/2jtEVLvSNeQHdIjWkmF4+UllOfX5m/L2oAdb2WhfG34qXV79nuYtHsLFEZ02xvcSBztLdTggsPXCDpXsR8H6AfC03huPToYtKlQo0CDHfO7PXcDg5POQK+SvCXi3WfAesrqOn/ACedGBJDOh2Tx5z/ADHBHP5mvpLwD8WtI8bubRk/s7UwBi2llDebwSfLPG7GORjNAHhPxK+HFz8O9VtrmxubifTpm3W9yV2vC4OQjMON2ACCMZ54GK9L+Gvxut9SW10TxO4gvf8AVx6gzARy4HHmZ+63v0J9K9mu7O2v7WS2vLeK4gkGHilQMrD3B4NfN3xf+FMXhlX8QaKAulO4WW25PkMx6g/3ScD2oA978ReLdF8J2Ud5q16kMMjqiAfMzk9wB26kn2rzT4o/CPT9X0u48QeHLUQ6gq+dJBCvy3QPUhc4Vsc8Dn6186Wdld6jcrb2dtPdTt92OGMux/Ac1912CldOtVZSpWJAQRgg4FAHzD8BZdQHxGjtoLySG0EEslzb7jtlAXaAR0yGZTn2NfU5IAyTgV5nf/Cq3svGll4q8MXMWl3EUxe6hcExSI2d+B/CSCeOn0rhPi38XLi4vJfDnhe7xb48u5u4DlpWP8CEdB2JHJ6dOoBV+MHxUOuTP4b8PzubFWKXU8ZP+kNnGweqg/8AfX0663wu+Cnl/Z9d8VQHzFO+DTpF4Ho0n89v5+lXvhX8KLTQrCPxN4ogUXyqZY7e4A2WqjkO3+1gZ56fWuY+LXxfOtF9C8NXTDTsbbm5QFWnOfuqf7n8/p1ANr4p/Ge4sryXQ/C11bsBGRPfxPvIJH3YyOAR/eBPXsRXz+7tI7O7FnYksxOST61HRQAV9P8Awz0rS/Cnwjm8V2MMV3qT2E93LMw5JQMfKB6gArg46nJ9K+YK9c+Gvxei8L6RH4d1yyafSdzgSxnLxq/JBU8FcknjB5PWgDV8E/HHXr3xjaWfiCW0bTb2URErEI/ILcKQfTOM7s8E81i/HzRYdL8erewYX+0oBNIgGAHHyk/jgH65Peuls5PgLaOLwF5pQ29YZo7lsHPTbjafoc1wvxa8c2PjrxFbXWmwzJbW0Hkh5gFZzkknAJwOaAPPaKKKACiiigAooooAKKKKAOt+Gmjpr3xF0WwkbbG0/msQccRqZMf+O17j8Wvirq/gfxFp+maVbWr+Zbi5ma4UsGBdlCjBGPuHn3r500DWbrw9rtpq9kwW4tZBImeh9QfYjI/Gvbrn4nfDTxxBE3jDQpobqIbQ+1mwOuBJGQ2M54IoA7i+8UaRofwxufG+lWFna3Wo20cuIo1UyTt8oDdN21mbPsGNfJk88lxNJNM7SSyMXd2OSzE5JJ7mvXfiZ8Q/Cmt+DbPw14as7hILaVWRinlxoqgjAGcsTnPP16145QAUUUUAFavh3RZvEXiGw0i3JEl5OsW7GdgJ5Y+wGT+FZVe+/s8+GoVj1HxTPJAXQNaQKxBMfAZnPpkYA743djQB7dpWnWfh3QLXToWEdpZQiMM5wAoHJJP515H4t+P9vaXT2HhWxGoTBtgup8+Ux/2VGGb65H41N4p8N6h4ovf+K28e6NpmlI37qysZgiuM8FjIR83A67u+MVpeCfh98M/7Qiv9Au01W7sZFkVjeeYY2B4YquO4yCRjI4oA4b4p+E2sPh/p3iLXGkn8T317GL2d2+4rRufKVR8oC7QOB1zzUWtDXPhZHpOs+DdWv7zwxdwrMFucSQhj1DKMBc5HIAPuSK7L9ot5R4G06MRkxNqSlpNw+UiOTAx1Ocn/AL596y/g5NJa/CzWrzxNbpdeHLdjLbwzQiXIUEyYVuCM4x77qANvwl8ePD+sxxQa4BpN6xCliS0LHHXdj5R9enrSfEz4UWXjO0bXvD3kJqhXeTGQUvBjjkHAb/a7964qbx/8JNQYi88BzRK2ctbRRof/AB11/wDrVpaN4h+H1jdQN4b8Za1oD5GLa5V5rbGeVZGBA+u4Y55oA8IuLea1ne3uInimjYq8bqVZSOoIPQ1BX0f8QfDXw88ZRy61ZeK9I0/UcfvJluUZJv8AfTOd2AcEcn3r5wPBoAK9b+AnimTSPGf9iPs+y6sNpZ2xskRWK4+vK47kivJK0NG1B9J1uw1FAxa1uEm2q20ttYHGe2cYoA+hPG3wQh1/xRfa2mvw2Ed2Q5ilgBHmY553Dg4J9c5+tdS3w4S7+Hmh+GJtRSWKwnhmeXycpOqsWK4zwCGIzmuR+M/hbVvGmnaP4g8OifUbJbfd9nizko43LIsZwSSDg9+nHBqX4F+H/EXh3TtWvNdW40/TmCmK2uxswVyWkIblAB7DOc9hQBw3x+8Q3Go+OjozfLa6XGoVf7zyIrlvyKj8PevJKtX15cahfT3l3M01xM5eSRjksxPJqrQAUUUUAFFFFABRRRQBseH9A1fxDqa2mi2M13cLh8R8bBkckngDPc19VfE7wXqHjzwjBplrPbW15FcpcnzWYxkhHUruC5/j647dBXnH7N15YR3Gu2TOFv5lhkQM33413A7RjsWGeecjjg15tro8W+H/AB/Obm91Aa4lwUjuQ53y5Py7TnkEEcdMHFAGd4o8Ha34Ov1tNaszCZMmKVWDRygHGVYfyOCMjIFc9X0F+0Q8x0Lw0sw+fc7OSfm3bVzxXz7QBLHI8EiyROySIQyspwQfUGvov4ZfE7TvFGkHw14yltHusLFE90Bsu1PAVs8bxx9c+ua+b6XODkUAexfET4d6h8N9Vj8VeF7iSLT0mBTaSXtGPGCT95Ccjn1wc9T6T8MPi1beMwdN1XyrXWxkqiZEc6gDlck4brlc9sjvjj/hl8WYdXhXwp408i4hmUQwXU67hJzwkueD2w3tz61lfFH4WS+D54vEnhYXa2ccm+RIyS1o4OQ6sOQvv2I68igD6Xrzn42X97p/w2u5bC9a0ZpokdkfYzITyqnrk8dOwPbNZ/wn+KUXi2yXStZuI49ciGFLEL9qXGdyjj5hzkD0z9O78TeGNN8XaO2l6tHI9szhx5blWVh0II+p60AfFGm3RstUtLve4MEySbkPzDDA8e9fd0MqzwRzKCFkUMM9cEZrgNP+CvgTT2jk/sqSeWNgyvPcyE5Bz0BAP5V6GAAMAYFABRRXl3xR+LNr4Ohl0vTCtxrjpnsUtgejN6t3C/ieOCAc/wDHLxhrnhjWdIXRNcktTLBJ5tvGAcYYYY5B65IH+6fWsf4bfE/x34p8ZWOlS3llPb/fuDLbqpMa43EFcfNjp2zXkM0+seK9dMjm41HU7yTGAC7u3oAO3sOAK96+D/wp1nwvrB17W3igkMJiitY33sN3UuRwOAMYJ69qAPba8x+MHw7Xxjoh1GwRjrVjGTCq/wDLdM5KH36lffjvx6dRQB4v8CfHi6tpP/CMahcf6dZLm13nmWHuAfVfTrg8cA49or51+L3gi68J67F448PYt4DOjSRwKVMEv9/jgK2OenJx3r2HwH4wsvHHhqPVbVGjkVvKuIW6xygAkZ7jkEH39c0AedePdHu/hv4th+IGhM/2S5mEeq22Ny4YjLD2P4YbGODgevaPq9lrulW+p6fOJ7S4TdHIp69iPqCCCOxBqTU9NtdY0u5069jEltcxmORT3BrxfwNq1z8NviDP8PtUmMunXMgbT5yMYZ8FRz2P3T/tDjrQB7pRRRQAUUUUAFFFFABRRRQAUUUUABooNFABRRRQAUUUUAVNS1C20rTLrULt9lvbRNLI3ooGTXgHw60Sb4l/Ei/8camiLZ2tyHSHrvkAHlr9FUKSfXHXJxvfHTWL2+uNI8E6S5e51GQPcRKRlhuAjU+2cnn+6K9S8LeHrbwt4cstHtFUJbxgMw/jc8sx+pzQBtV5F8d/Gh0Pw0mh2UpW+1LIkKn5o4R976bun0zXpet6xaaBo15q165W3tYjK+MZbA+6MkAk9AM9TXzN4M0jUPi58SpdU1jdNZQsJrs5O1U58uJfQEjGPQMaAPT/AIF+Cf7C8ONr15Ft1DUl+QMOY4M8D23Ebvpt9K9M1XWdO0Sya91O+gs7ZTgyTOFBPoM9TweBzVyNFiRURQqKAFVRgAegrn/G/hO08ZeF7nSboAOf3lvITjy5QDtbP4kH2JoAZYfETwfqTbbbxJppYnAWScRk/QNgmr91LoGthbG7k06+G5ZBbyMknOflbac+v618peG/hT4p8V6INV0u2ha2aQxr5soQvjqRntnj8Kg1L4WeN9JjaS68PXXlopZmhKzAAdT8hNAH1X4p8H6N4u0p7DVLNHG0iKZQBJCfVG7duOh718seM/h/r/w81JJZwXtfMza39uSASOR7o3sfQ4JxmvoL4JXl7e/DKxkvrgzMssqRszEsEVsAEn05/DFd5qGn2eq2M1lf28dxazLtkikGVYUAfPvgj4/TaZZfY/FUN1qG3/V3UAUyY9GBIB+uc+teneHvE+g/F3wzqtn9iuUtM+RcRThQcHlWUgnngH2I/Gvn74q+ELfwt46k07SrOWOzuI0ltkLF854IU9T8wIwcmvTPgX4W8X+H728n1Kzay0m6iBMVwcSPIPukL1HBOc4oA9V8M+E9H8I6WLHR7QQxk5dycvIfVm7/ANO1b1FeNfGT4n/8I/ayeHdFmH9qzJtuZlzm3Rh0B/vkd+3XrjABz3xn+KKXLN4b8P3z+WrMt/NESu4g48tW7jrnsePfN/4RfCKGC3tvEviOB/tG4S2lo+VEQGcO47k8EDt3znjN+C3wyGoSR+K9chWW2B3WUEg3eY2TmRh6Ajjrk89ubXxw+JE0Mv8Awi+h36oNp/tCWBzuyekWR04zux1zg45BAMv4zfFBtYuJvDWiXKnTY+LqeI/69wfug90HHTqfavFKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigApwYgYBIFNooAK9C+D/i8eE/G8AuHC2F/i2uCTgLk/K5+h/QmvPaKAPqD9or5vh5YYPXVYsH/tlLXI/FO5XwT8OdB8AWtwkkjxmW9ZCegbd0PZpCx9tnTmu28L2Q+JXgvwfqVzqEiHRrpZJ4VUMLiSL5V3ZPB4ByR0Y8DNeC/E++OofErXp/OWUC6MauuMbUAQDj0CgfhQByNFFFABRRRQAUUUUAeheEvi/4n8Jaeun28ltd2MalYoLqMkR554KkHr2Jxyal8RfGrxd4j0+WwkktLK2mXZItpEVLL3G5iSPwIrziigAooooAKKKKACiiigAooooA0dG1e+0DVrfVNNnMN3btujkX8iD6ggkEdwa9ci/aIvpIbf7d4Z0+5uIuRKJSoDeqgg7e3evEqKAOx8e/EDUPH2pQ3V7bw28NspSCCPnaCckljyScD246Vx1FFABRRRQAV9A/CT4rDUFTwr4plEzTAxWt1MciQEY8p8+vQHv0r5+pwJUggkEcgigD1f4n/Da88B6umveH2uP7LLiRZVPzWcm7hcj+Hpg/gfU+x/C/4kWvjjSVguHWLWrZB9ph6eZ28xfY9x2J+lcV8Jfifb61Zx+D/FDLNJIvkW00w3LOmP8AVvnv2BPXgdevHfEfwZf/AAx8WW+ueHTNbae7hrSZW3GCTHzRknOR1xnqDjnBoA+qK4rxL8UvC/hTWo9J1W5nS5Kq7+XCXWMHoWI/PjNR/C7xwPHHhVbqfYuo2zeTdIp6tjhwOwb+YNY/xr8GW/iHwjPqtvaGTVtNTfE0Y+Z4tw3qfUAbmHpg46mgDnPH/wAeLBdMax8HzPNdyjDXxiZFiX/YDYJb6jA968W8P+HNa8b6/wDZbCF7m6lbfPK54QE8u7Htz9T2yaxrMQNewLdMy2xkUSsg5CZ5I98Zr7X8K+HtG8N6JBaaHbrFauivv6vMSPvM3cn/APVgUAYXgD4X6P4GgE6KLvVXXEl5IvK8chB/CP1Peun1/WbXQdDvNSvLhIIoImbe3rjgAdyT0Heo/EviXTPCejS6nqs/lQpwqjBeRuyqO5r5U+IfxL1Lx7eqkqLb6ZA5a3tVOSD03Me7Y/Adu+QC2fjh4+8kp/bMe7dneLOHOPT7uMfhn3r6p0Rrt9CsG1CRJL1reM3DoMK0m0biOBxnPavjjw14O8Qa7La3lhod3eWQnVWkWL92cEZGTx9a+04gFjVVXYAAAvHy+3FAFTVdMttZ0u602+iEttcxtFIh7gj9D3B7GvnTwnqU/wAH/ipdaDqlyTpNwwjeRlKqVPMc2O2Oh69W64Br6ary740+A5fFnhxNQ08BtS04M6pjmaPqy/UYyPxHegD01JEmjWSNldGAKspyCD3Brzz4v+D5fEnhb7Zp0Uf9raY/2mF8fOyKCWQH8iB6qPWsf4GeOjrugvoOoXIbULAfud5+eWHsfcqePpivXyARg8igDj/hr4uPjTwbbalKFW7jJguVU/8ALRQOfbIIOPeuwrw/UzB8JvizbXsJNv4c18H7VHt+SGTJyQAOACQcDsWHQCvbI3WVFdGDIwBVlOQR6igCSiiigAooooAKKKKACiiigANFBooAKKKKACsvxDrdr4d0C91a7YCG1iaQjPLEDhR7k4H41qV4h8bdZvda1bTPh/o0Ylub1kmnww9TsU+mMFjnttoAh+C2j3XiXxDqfxC1kiS4klaK29mIw59gFIUexP4+61j+F9Dh8NeGdP0e3+5axBM+rdWPQdWJPTvTvEWu2fhnQLvWL4n7PbJuKr95j0Cj3JwKAPFf2h/FbmSy8K2svykC5u1U9T0RT+rY/wB016J8KvBK+CfCUcVxEq6pd4mvG4yD/CmfRQfzJ9a8i+FGkTeOvilfeK76L/RrW4a8IOSPOZiY1BOfu9evG0V9M0AFFYut+LNA8OQs+r6vaWhRd3lvIPMI9kHzH8BS+HPE2leLNLXUdIufOtyxRgRtZGHUMDyDQB8u2Xi/X/hd4w1LTdPmc2dveOj2M7b42UNx9GIxyK9x8PfG7wjrVlLLeXJ0ueEFmguiPnH+ww4b6cH2rpvEvgbw54sRhq+lQTSkbRcKNkq+mHHP4HivA/G3wJ1jQ2kvNAMmq2ABbygv79B6YH3/AKj8qAPbvhfYmz8Aae53f6WZLxQwAIWVy6/oQfxrM+LnjmfwV4cgbTbmGPVbmYCJJEDkoPvHH5DJ9a8Y8MfGXxJ4N0dtFms4rsQfLB9r3K8A4+UgYJUdgcEZ644rkLqfxD8QvFEk3lT6hqdzyI4UJCqOwH8Kj8hQB9i6PeQ63oul6y1oiS3NrHcIpw5i8xQxUNgevtnFa1cT8MPDuteF/BcOma5d+fcrIzIituEEZAxGD3xgn0+bHaul1zWLLw/o11q2oy+VaWqF5GHX0AHqSSAB6kUAcd8VfiGngbQdlq0bavd/LbRtzsHeRh6Dt6n6GvFPhn4HvfiN4qm1rWfOk02OYy3Vwcf6RNkHy/xzk4HA9MisR11/4tePpXhQvcXLZAY5S2hB4BPYAH8T9a+g9Z1XTPg98Nba2h2PPFF5FsmMGecjJcj0zlifoO4oA5/4v/Em28NaSfDPh+4SPUnAjkaDAFpEAPlGOAxGAB2GenFfM5OTk1a1HULrVtRuL+9laW6uHMkkh6sxqpQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAbel+Kdd0XTrjT9M1W7s7a5OZEhkK7j0zkcjjjjrWKTk5NJRQAUVYtLS5v7qO1s7eW4nlO2OKFC7sfQAcmi7tLmwupLW8t5beeI7ZIpkKOp9CDyKAK9FFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFT28Et1OkEETyyyMESNFLMzHgAAdTQBBRXs/g74A6rq0K3niKdtLgZQUt0Aac/7wPCfqfYV6Tpfwr+G2j6gmnSQwXepMNyw3l5vlYDnPlggEcZ+7QB8n0V9qH4a+Cjj/AIpjTODniAVl6p8G/A2pRMP7FW1c5xJayNGVz6DO38xQB8f0V7T4w+AGpabE934bujqECKS1tLhZx1Py44bjtwfQGvHbiCW1neCeJ4pY2KPG6lWVhwQQehoAgooooAertG4dGKspyCDyDX0t8PfF9j8VfDN34V8TxRyX0cQyRwZ0HAkX0dTjP1B9QPmatHSdY1DQ9Rh1DTbuS1uojlZIzg+49we4PBoA7y5h174IePVeCQyWcp+ViPluoMjII7MP0NfT2h61YeItHttU02dZrWddysOoPcH0IPBFefAaD8cvACsxWDU4BgkfetZ9vPGcmM/qPcceV/DrxhqPw28ZSaBrhkj055vJuYZGO2B88SqPTpk9xg9hQB2Oo/s4Ws9zcT2HiEwRuzGOB7TcEyeF3b84HTpmsBfi5r/w+tbrwc0VjqU+mFrSC+DthQvABU9dvTHGMY7V9KBgyhlIIIyCO9fF/wARtHm0T4ga1azo6K93JNEWLHdG7FlOW5PBwTzyDyaAKPiPxZrXi2/W71q/e5dciNDhUjB7Ko4Hb645r2f4a/BCEWqar4wtC0zENDp7MQEHrJg8k8fL27+gufAzwb4eu/CUevXWnwXWom4dd86hxHtPG0HgHnrXttAEMEEVtAkMESRRINqRooVVHoAOleZfFL4m6t4A1bTIrTTrS6tbqJnkMzMG3BgMDB44I6g9farnj34v6L4ML2VuBqOrDg20b4WLr99sHB/2ev0r5n8UeLNX8X6u2oavciWXBWNAAEiTOQqgdv1PfNAH1R8M/G91478PT6ldaeLJorhol2MSjgAHIJ9M4NdvXlfwNudLg+H9pZQapaz30kkk81ukg8yIlsAFevRRzjvxkc16pQB80/EjT7v4Z/FO08UaPCEtbtjMqKuE3YxLGe3IJP8AwL2r6F0PVrbXtEstWsyTb3cSypu6gHsfcdKwfiV4Ubxj4JvNNg/4/FxNbcgAyL0BJ7HkfjXm3wG8XS27XPgrVS0E9uWktUm+Ug5+ePBGc5JbH1oA9K+Ing6Pxr4RudMURreL+9tZHA+WQds44B6HHrXP/BfxLJqfhaTQr0ldT0R/s0yt1KZO08ccYK/8ByetenV4j43d/hj8ULHxlbo76ZqwaDUIUOPmAHPpk8MPUq3TNAHt1FQ288VzbRXELh4pUDow/iUjIP5VNQAUUUUAFFFFABRRRQAGig0UAFFFFAFa8uorGynvJ2VIYI2ldmIACqMkknpwK8T+DltdeLPGmuePtQGd0jW9uBwFYgEgAdlTaOc/e7nmt347+KJNI8Jw6LaqHudYcxY5yI1xuxjuSVH4mu18C+HYvCvg7TtJUfvI4g0zYxukblj+Zx+FAHR188/tDeIp59U0/wAMWsz+WqC4uIk/5aOxwgPrjBIH+19K9/urmCytZbq5lSKCJC8kjnAVRySa+X/hzpd98RvivJrmohnitphfXL7cpkH93Hnp2GB3VT6UAe8/DfwuPCfgmxsHgSK8dPOuimctK3XOe4GB+FddRRQB8ofGrwZdeHvF8+qmQzWOqSNLHIzZZX6sh+nb2IrhdG8Qax4enM+k6ldWTtjd5MhUPj+8OjD2Nfa+oWek60Dp+oQWt55TLMbeZVfaf4WKn8f1qS60nTb21Frd6faXFuBgRSwq6Y9MEYoA8j+HfxytNUhTTvFk8VrfA4S8ICQyj/a7K35D6V7QGDKGUggjII714T44+AIu7t7/AMJywwbzl7GYlUB/6Ztg4Hsfz7V5laeLfHnw9E+jJd3WnqGI8ieJXCnoSm4HH1XigD2T41fDq+8Tiw1LQtOjnv43MVwFZUZ0P3Sc4BwffPPpnHWfDvwBa+BdCS3URTalKM3d0q43nJIUZ52jp79fauE+Anja/wBZk1TRNWvrm8uVH2uGSdy5C5CuNx9ypx7mvcKACvlr44eNW1/xQdFs7lJNM087f3fIeb+Ik98dOPevXvjD45n8GeGEjsdv9o6gWhibP+qXHzOB6jIA9zntg+U/A/wMviHWX8Sah89np0/yRspImmxkEnp8uQ31xnigD0v4beGbX4ZeA7jVNfeO0uZwJ7x3P+rXokfueeg7tjmvnzx34wu/Gnia51CeRvsyuyWkPaKLPAx6nqT3NeifHrx3Le6qfCljKVtLQhrwo3EshAIU47L6ev0rxKgAooooAK2PDOmW+s+JtN0y7uDb291cLC8oxlQxxkZrHqWOV4JUljdkkRgyspwQR0INAHW/EPwFe+A9aS1mk+0WdwC1rcBcb1GMgjswyMj3B71xtfX9zolt8Uvhfp76pFGl3dWazwzAf6mYr94e2eo7ivA/D3w7tz8SpPCviq//ALO8pSQyED7QeNqozDA3AkgkdsdaALnwd+H9r411e8n1aCZ9Kto8EqxQPKcYXcPQZOPpXA65Zx2HiDUrKDd5NvdSxJuOTtViBn8BX2t4e8OaX4V0mPTNJtxBbKS2CxZmY9SSeSa+Uvi9ps+l/E7WVnHFzKLmNh0ZHGf0OR9QaAOFooooAKKKKACiiigAooooAKKK9G+HPw80nxzbTrc+J4dP1ASFIbPyw7uAAd+CwyOSMD0NAHnNev8AwH8I2uv69f6hqdhbXmn2kHlqlwodfOYjB2ng4UN19R+HP/EH4V6r4DZLhpRfabIdq3UcRXa3o65O325Oa9o+BkXhm38KGLRtS+06lKEm1FHyrxvj7oU/wjJG4dfXsADxP4seGrfwv4/vbWzQJaTAXESKu1Yw3VR7A5/DArhK+yfiJ4j8M+HNC8zxNaC8huiYUtliV3k7nGSMAeufTvXgXgH4VXXj24k1NJE0/QluGXLN5kpA52L0zgEAsceuD0oA87jtLma3luI7eV4IseZIqEqmemT0FV69s+Kviey8L6e3w88L2sNtZIim/cDLu5wdue5ICknr0HFeJ0AFFFFABRRRQAUUVPb2095cJBbQSTyvwscSFmb6AcmgDuPgzqUOmfFHSmnwFuC9upJxhnUhfzOB+NaPx7glj+J87shVZbWF4yf4hjbkfiCPwrE8F+EfE+oTtrmh2Yll0a5jleJnCyblO8YVuv3en6Gu2+MtxZeKvC+geM7O3eKVmawukdxuhcZYRsOuQQ/4HkDIoA8UooooAKKKKACiiigAooooAKKKKACiiigBwBYgAEk8ACvqj4R/DOLwnpiatqtvG+tzjgnDfZkI+6vbce5Hrj1z5R8D/B8fiXxc+o3ahrLSQkzIcHfKSfLBB7fKx/4CB3r6roAK+Z9U8J6147+LHi+702/S1vNLkDRNyGcqNqKCOnCdfp619MV4N8Kb/wD4Sz4qa94nk1AWdy4KnTAPmkjwFBJ4BC7V7Zz19wD074deILrxL4Lsr3UE2X6l4LkYwfMRipJHYnGa6uvDvFmla94X+IltD4I1qaO+1+eW7uNPlw8CHq0hznAJz2zxwew3viVffELSxor+H7+1SO5kjtZxHbqzee3GfnDfIeegyMc5oA7nxF4o0fwpY/bNYvo7WI5CBuWkIGcKo5Jry/xl4W0r4peCX8W+HdJni1Y5aMyjy5LhEJBBUEhiQPlPXgc9qxvFPga7vfG3g+y8VeIrjVdS1GV/tAWMJFHEgDFYwAMZORnjrnFe+wQRW0EcEEaxxRKERFGAqgYAH4UAfBTK0blWUqynBBGCDTK9g+PPguPRPEEWv2SKlpqTESooxsmAyT/wIc/UNXj9ABRRRQB0ngnxXc+DfFNpq9uGdEOyeIH/AFsR+8v17j0IFeyfEzSNH+IvgdfG3hqJpbu24nwm12jH3lde7Lwfp3IxWD+z5daIuuX1ld2iPq8qiS0mePdtVQdwU/wnnOeM4612V94ytfB3xt/sWGPyNL1OKL7ahwEW5bO2VRnAyNit0zjvgUAR/Anx6mraOvhi/kb7fZITbsxz5sOen1Xp9Melepaz4f0nxBbC31fTre9iHKiaMMVPqD1B+lfOvxI8JXvwx8Y2vinQH8qynuGeERggW74+aM/7LAnHtkdufffBvie28YeGLTWYE8vzl2yxn+CQcMvuM9D3GKAPMtR+JHhz4U61deGNJ8KTxwRN5kkgn2+YzAHI3biw7ZJ4xgCuU8W/H/V9Xs2tNCshpcbqVknaTzJTn+6cAL39T9Ku/HXwbr154sj1yx0+e8s5rdIibaNpGjZf7wA4zng1F8Ffh1oviO0v9T120knktbkQJbSEqg+UElh1J56e1AHCeEvh14j8bXUclraSx2cj4kvpgRGPUgn7x9hX0l4d+E/hDw/YLA2j2uoTlQJbi9hWYuR3AbIX6D9a7S3t4bW3jggjSKGNQqIi4VQOwFc5408c6T4H0kXuouZJXOIbWMjzJT3wD2Hc9v0oA83+MHhTwR4a8NPqVtYxafrUsi/YfschjLMCCSEBxtA6kAY45yRlfgLq/iTX59Tu9U124vLG1jWBLedt53kgh9x54Cke+72rgfiR8Wh4/wBEtNOTRVsVhn89pGn81iQGUKPlGBhsn8PTn1T9n2zsYfh7JdW7brm4u3Fyc/dZcBV9vlIP/AqAPWq+dfjPpFx4S8e6Z4200FRNMjOQMATR44P+8o545wevNfRVc5438OL4s8Iaho5CCWZMwu65CSDlT7c8Z96AL/h3W7bxJ4fstXtMiG7iEgU9UPdT7g5H4VneO/DCeLvB+oaQQvnSJvt2P8Mq8qfz4+hNeT/ALxQ9lfXvgu/3iRXea2ySdrDiRPYcbh2+93PPvtAHmPwZ8Ypr3hVNGuVaLVNHUQTI2csg4Vuec8YI9R74r06vDvEVonw1+Men+JLVfI0bWyYLxVXIR2I3cdgSFfjJ4bjoK9xBBGQcigAooooAKKKKACiiigANFBooAKKKxfFWsR+H/C2parLIsYtrdnVmxjfjCjnrliBjvmgDxzUreL4kfH2KKA+fpeiKnnln+VijZIAx0LkKR3weRXvteQfs+aD/AGf4Pu9YlV1l1KcYDLgGOPIUj15Z+a9fJAGScCgDx/4/+JDpng+HRoZ/LuNSlxIoPzGFOT24BbaO2eeozWt8EfDzaF8PbeeeExXWoyNcuGBDbeiZ/wCAjP8AwKvJ/Gu74l/G5NH0+dWtgy2scoOQERS0rcnBwd/Trgd6+nYoY4IkiiRUjRQqoowFA6ADsKAJa+aNf+P/AImk+02djptrpjh2j3urPLHjIwQeAw9x+FfS9fOvi3wBo3iz41f2Vo+oRW4ltzdakIxu8pweQvbc2Qcdsk+1AHFfD34hSeF/HEuvauLi/F3C0F1IX3S4LK24Z6kFRxnpX094b8aeH/F1vJJoupJctGAZIsFJE+qnBx79PeuS1n4GeDtS02K2sraXTZYuk8DlmbjHzBs59e1eP+IPhV418C3j6npL3FzbRfdvdPcrKgPqoO4e5GR70AfV1cB8W/Buo+NvCcGn6WYRdQ3iT/vm2gqFZSM4/wBoH8K8Y0/4+eLbHSHsriOzu5whWO8lQiRT2JAO1iOO3bnNdZ8A/GMl9f6po+q6hdXF7csLmDz5GcHAO8DPQ9D+HtQB3Hw0+GVn4CtpJ3m+1atcoEmnxhVXrsTvjI5PfA9K72aeO2gkmmdUijUu7scBQBkk1LXlHx48UDRPBQ0uCYpd6qxjwFzmFcb+e3VR+JoA8c8Xa7efFb4kW9vYI3kySC0sUIwRHkkuwzjPJJ9gB2r3zxFrej/CXwBDb26rvii8mzhxzNLj7zfj8xNed/s9+EWaa58WXKMEUNa2gIxknG9x6/3fTlvSuM+NHiseJfHMsFvIGstNzaxY6M4Pztnvk8Z9FH1IB57c3M15dS3NzI0k8rl5HY5LMTkk1BRRQAUUUUAFFFdL4M8I6h431+PS7ErH8peaZ/uxIO59ewAoA+n/AIP3M138KdCknfe4jkjBwB8qSuqjj0CgV454j+D/AI91DxtNcSAXsd1c7hqIuFARC3BIJDDaMcAdsDNeyQaRdeEfBVh4U8NarpqazHGTbnUDjzRuLSMEBJ6sfUDNZiX3xc0vK3GjaHrQ3ZDW1yYGx6fPgfp60AafxA8XyfD7wTFdpCby7O22iZwQu/b99uvHGcZ56Zryz4caHYfFvUdX1bxhcXF/fw7I0jTMSonJBBXA65GPx713OrfEHTGsDpnxD8IahpkMzBWMsIubY+hEi9x14GRSeIvFPhPwD8NpG8KyWcL3kTLYraMGZnYEeYSck7euW9APagDI17TvhL8M5d11pMd/qD/dtGb7S6jB5Ku21R9efQHFeG+L9Z0zXvEE2oaRo0WkWrKoFtGRtyOrYAAGeOAMVi3E8t1O888ryyyMXeR2LMzHkkk9TUFABRRRQAUUUUAFFFFABVi2uZ7O5juLaaSCeNg0ckbFWUjuCOQar0UAfYHw08bt458HPeXlqftVoxguVVQVmYKDlR7g9PWvJ9IbxBqvxuttY0Twze6TbfaY0uoxAURYOA7OcADcoJx69Mmue+FnxHn8DXV3bGwm1G2vdu23ifDCQcAqMHqDg+uB6V6xL4l+LXiVSmj+F7bQ4ZOVub5wZEHbhu//AAA9aANT4v8Aw/vPHWkWLaY8f2+xkcpHK21ZEcDcM9j8qkZ96n+FPhjWvBvgiez1Qo100sk8dsmG8vgDaWHUkjP41hQeD/i9eyF9Q8c2lsrDkW8W4jI9Aij8jUcHhrxXLr17o9h8VLiS+tI4zc28luWdAyg5GTjBzxjpkZNAHzrq8t3c61fT6grJeSXEjzq4IYSFiWBz3zmqFeh/Er4aXvgU2l3c6smoreuwMhQo+8YJJyTnr1zXnlABRRRQAUUUUAFdX8NtWGh/EPRL9h8ouRE3GflkBQ9x2Y1ylbvg7SINd8Y6RpV2XFvdXKRybDg7SecGgD6J0f8At671D4g3OhXFraXzapHFbTSxgxSGNQCnpkjAJ65bNcb8TfDcD+An8V39veaNrNzdxrd6cZcwTzjcpkC+pXcwIPTPrmpPHnw38A+E5LNJtQ12xe8fMIiQXEakYB4wDnkHqT7V0nx6n06L4a2VnPMzXT3ET2gwQWKqQzEem1j+JFAHzHRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHs/w78HfEGTwNPqfhnX4LG2v9zLa7vnkKEpkMVOwkgjIIzgZPAxP4Si8V3FxcacfiDqOmeK7Vyi6Vqe54nA6bSzMrZ4xhSevBHNd98ApHf4ZIGZmCXkyqCc7RwcD8SfzrW+I/gGLxdpgu7Ei316yIls7pflYkchCR2z0PYge+QDidPPxE0X4k+Hn8a+ICNMuXlTfDOiW7sImIR1CqMkgYyO/BzWh8VI9BE2lLoK2kXjG61CI2c1kqLKSTgtIw6rjjk9cds1XsfiH4W8QeFpdA+JMa2uo2beXdQTxSfMynh0KZYN64IPXsaz/DmoeF9OuCfhv4J1DWtSLbV1C5QrDFkf89H+7j6Ln1oA7fxZ4V10+KdJ8ZaCYrvVrG2+zT2MziNLiP5idrEfK2XPXjp0xzFcN4z8V65pFvd+Gxoem2V2l3cTyXkc0jsgJCoF7HOM/wAsVxvxAHxUs/D763qXiKy0208xEa0013RotxCj5wu48nn5j7elN1P4b+JIvFGkaTd/EvUWbUIZ2jeRpS26IKSqr5mDw2eo6HigDtdYS8Px68OO2TZ/2TcbAP4Xyd5/Ix16PXzpPoGsfDTxg3iG/wDE8WqvpcML+TcSETz2sjNGwUOTggg4AJ6jntXvmlana6zpdrqVjMJba5jEsTjuD6+h7EdjQByXxh0eHV/hlq29EMloguonbPyFCCcY9V3D8a+Pa+5/FMUc3hPWY5UV0NlNlWGQfkPavhigAqWKPzZUj3Ku5gu5jgDPc1FRQB9leC/h34a8I2tvcaXbx3F4YudQc73kDDkqeig+3b1q74x8FaR4z0ua2vrWL7X5ZW3uyn7yFuxB64zzjoa+cfhj478Tab4o0PRLbUZJNNnu44HtZFDqEdwGxnlcZJ4Pb0r1f45+JPE3hrS9Pn0bUltLK5doJvLjxNvxkEOc4GAegBBHU54ALfhPUYvi58KrrTdXlU3ozb3UiLtxIp3RyAfQKT2JB4xxXnnw41y6+GPxFvfCWtT/AOh3EohLq37tJTjZLz0UggH8M9K5L4WeN28FeLY5Znc6beYivEB477X5IGVJ79i3rXpnx98KQ3OnWnjKxIMkflwz7CMPGclJM9yCQO/BHYUAe71534y+L2j+CtfXStQ07UZXMaymWFU27T6ZYZ6VH8I/iFF4z0BbK4Ypq1hEiXAP/LVegkH1xz6E+4rif2jtPvppNEvo7cyWkaTI8kcRJjbK/fYcAHsD6NQA/wAYftB2smltbeFbe5S7kAH2u6jUCId9q5OW6dePrXj+naT4l8e6yY7cXeqXrDLyyyFtgz1Z2OAOver3wz8M2vi3xzY6XfOy2pDSyBRy4QZ2+2ema+v9L0fTtFtBa6bZW9pAP+WcEYQH3OOp96APEtF/Zygaxik1vWpkumX95FaIu1D6bmznj2H+Pq3gvwbYeBtDbStOlnljeZp3knILM5AHYAAYUD8K6WvL/it8RdI0PwxqGlWmp51i6hMUaWxDtFngljn5eM+/OR60AeoUV8i/Dnxt4ttvFekaVZavcS2090kbWtxJvjKs3zABunUnjHNfXVAHzj8SY734efF618YWdpmyu2EpCSbRK2MSofQkc9COQeeRXv8Ao+p2+taNZ6na5+z3cKzJuGDhhnmuP+LvhT/hKfAl2sKB7yxzdW+EyxKg7kGOeVzx3IFcf+z14tW60e68L3MgE1oTPbAnlo2PzAfRjn/gVAHofxE8MReLPBOoac4HnKhntmI+7KgJX6Z5BI7E1lfCDxZJ4q8EQ/a5d+oWDfZrjIwxwPlY/Ud/UGvQa8EkvW+Gvx7lj2xR6R4g2M6hSAm8kBhjoRID7YY8dCAD3uiiigAooooAKKKKAA0UGigAryH483jz6NovhuGRFn1a/VRuzgKpAySOg3OvY/pXr1eK3Sp4w/aNt4UCXNhoFvmXLAqJACeCvcSOoIPQow9qAPXdJ06DSNJtNNthiC1hWFOMcKMVgfEfVxonw81y83BXNq0MZL7fncbAR7gtnHfFdZXg/wC0V4gxBpXhmEbpZXF7IADnA3Ig9DkluOfujp3AMv8AZ38Ni51a/wDEc6KVtF+z25IB+dh8xHcYXA/4EfevoyuL+FvhuTwt4CsbK4Di6kzcTo4A2O/O0Y9BgfXPToO0oA8J/aHh1e1TS9TtdRvItPfNtLDHKyxiTllYgdyMj/gNeHeHPEF94X1y21jT3AuYGJAYZVgRgqw7ggmvszxR4Z0/xbok2k6ojtbuQwaNsOjDoynnn8O9c3b/AAa8CwaULB9FWcDk3Esrecx9dwIx9Bge1AHK+Ev2gdN1S7Fp4hs10ssPluUcvET6MMZX68/hXsNpeW1/ax3NncRXEEgyksThlYexHBrxHxT+ztaSRtP4Xv3imxn7LeNuRvZXAyPxB+oryuaDx98OpJYt2r6TDvwWjdhA7dMgj5GPvQB9DfEL4U6b46e3uI5I9Pvkk/e3CQ7mlj7gjIyemCa0fCPwy8N+DHE+m2ry3uCpu7ht8mD1A6BfwFeF/Dn4pa3D4/tX8Qa7czadesYrgTMWRSVIQhei/NtyQOma+p6ACvkjx9q0vxG+KZt9P+eHzVsbUplwyhsF+OxJJ47Y69a95+LXjD/hEfBVxJA5W/vT9mtf9kkfM/UHhc8jPJWvNf2dvDcdxeaj4juYQ7W+Le1ZhnDMCXI9DjAz/tGgD0T4h6rB8Ovhg8GkLHAwjWxs0P8ADuBBYerAbmyep65r5HJLEkkknkk16b8a/FzeI/G02nwXTSadphMMaAYXzRxI3vyMZ9Bx7+YUAFFFFABRRRQAV9G/s32MK6Jreo4JnluUgJOMBVXdx35LnP0HpXjPg7wNrXjXUTa6XCBFHjzriTiOIH1Pr7DmvqzwF4KtvAnh4aZbztcu8hlmnZApdjgcAdAAB3NAHCa7p8+q/tHadHHeNbta6WZ4mKbwrYccAnHVs/hSeCR8Vbf4gS2GuTTXGjwyP59xcRqI5F5KtE2AeTjgdBwQMVY0K8tdY/aL1u4+2RsLCxW3tlUj5+F3j1JDFq9P1vUzo2iXeoi0nuzbRGTyLdcu+OwFAHA/Eb4qaT4R1WHQ77RxqkdxDvuk3riNSeAVYENnBODjtXh3j/WvAOsQQSeE9DvNOvPMzM0gVI2TB4CBm5zjkY79e3sPw88JR+K7XWfE3jLRYZrvV7nMUd5Fl4oUG1QMgFfTIxkKK8G8eXHh668WXTeGLQWumJiNAGJEhHBcA8gH09s96AOYopQMkAdTXvOk/s3zTWKS6rr32e6dMmCC3DiNvQsWG78APrQB4LRXVeO/Bd34F8RHSbuaOcPGJoZU43xkkAkdjlSMe3euVoAKKKKACiiigAooooA7H4Y6vZ+H/iDpOraiSllDI6SylcqheNlBP0Jz+FfUKfEvwZJdJbJ4k09pXYKuJeCT056frXlvwv8ACVzrXwU160ltoz/aUsj2TSDILKoUMPTDKRn2qBfhp4V1n4TN4itoZ7PUrLTJGnWKfcpuIVJfcDnlivQEYBFAHeeO/i9p3gjWI9Mk026u52iEpZGCIAemCeprzDWfiVJo/wAR7bxdD4Su7Oa6sfKlhvS0ZuBwA6nHYKBnHOK9c8JWWleNfh/4avdY06C+lgt49r3H7xg6DaWJ9yuSD696g+JWn6pa3WieMNGslvbzQ5JDNbAZaWCRdrgYGSQM49Mk4NAGd47sIfiZ8IYdXsLZ2uliW+to0GXDAYePJAJ/iHHUqMZ4r5XIKkhgQR1Br3n4ffGPR9Hu9T0vVRPaaRJdyXFg5QubdXbPlMFycDPBHv7Vw/xb1rwv4g8VjUfDfzCWL/SpRG0YkkyfmAOO2MnHP1oA88ooooAKKKKAJI43kdUjVmdjhVUZJPtXoemeCfFvguGw8b3eliOzsZ452idx5oXcBkr1HXv0z0r1v4MfDi20HQ4PEGp2obV7xd8XmLzbRHoAD0Yjkn0OPXPqt1awX1pNa3USywTIUkjYZDKRgg0AUbPV9L1XRINahmik094/tCSuOFABJPPQjnPpg18r/FnxwnjbxWXsyDptkDDattwZOfmc555IGB6AcA5q18SNF1v4fTv4bttXmfw7fFrmCAS9sgFXHqCB7HjvkDzSgAooooAKKKKACiiigAooooAKKKuWmm32oeZ9hsri58sZfyYmfaPU4HFAFOive/hx8GPDviHwxYa7qV/dXRuFYtbwuqIhDY2kjJzxzyOtemW/wj8CW6IF8OWzbehkd3J+uWOaAPPP2fvEWk2Gganp99qdtbXLXfmpFPKEyhQDK54PIPAr3dHWVFdGDKwyrKcgj1Fcfe/CnwPfQNG/h2zjyCA8AMTDPfKkVyb+BfFHw8D6h4I1V7zTk/eTaPfMDuUcnY3QHr6H3PSgDM+IHhLTtV+OXh1dXjJ07VIGSQZMYeSNW2rvHUk7B64Ir2bT9NstJso7PT7SG2tox8kUKBVH4Dv715Vqev2PxW+GF5f6VJJZ63pQF2sayYkt5UGflbI+VhuAbj9MVT8M+L9c8MxaLea74u03W9E1OVYHKtuntXdCwJI5IDDac5x7UAdH8a9Q0dfh7qOn3moQR3kipJbW5lAkkYOMEL1I4PPTiqV/Zah4u+Evh/XdFcHXNNgiu7Rom3FnQbZI89yQCMdyMGszXj8OdE8Z6zfeMdTfWNWlO6K0ntJHW3iPKRoANh4I5J/Ik517XXtJ+HGtQWUiTWnhnWo1urN2iIjs5m+9GT2B4bH8Jz2PABFdaZoHxy8HW14ZGstVtco+0bntpP4lZc8qcZH+ORUnwj1C50mPUvAurPt1HRpmMJLH99AxyGUHkjJ7dmHANaereBJ4NSk8R+CtTGl6ncMJZ4WJe0ve/wA69ic/eX8Bk5rkfEMtn4g162svFFtceEvGEICWOrwyFrafByAr5GQSTweRnGc8UAep+L7lLPwXrdw6O6pYzZVBkn5COK+Ha93+Imv/ABQ0Hw1LpOsRW7Wcn7qTV7JT+9Q8bW/uE5xnC5x35NeEUAFFFFAHqHwF0mPUviSk0pI+wWsl0gH8TZVAP/H8/hXon7RtmkvhfSbwuBJBdtGoL43B15wO5+UfTmvLfhH41h8GeKS1xZLPBfhLZ5V/1kQLDlfUZxkd8D0r1/8AaGgik8A20rLIZIr5NhUfKMqwOfwoA+Xq+k/gx4isfF3gu58G6uv2iW1iZSkpyJLckAY9NpIHt8tfNldT4C8XT+CvFdvqsIEkZHk3EZJG+IkZHHfgEdeQKAOr8PTXXwq+MjWNy7Qae0xt5GmYYktmb5JDg49G9uc96+qiARg8ivF/jr4Yi1/wnbeKdPXzJbJAztGM+ZA+Of8AgJwc+hP4dD8FvFDeI/AUEM8qveac32aTklioHyMc+o4/CgB+uJ4D+G+sjxReWS2l7fZgVoIi3bLEIOATgZPXn3NJf/G7wLZ2H2mLVJLtyCVgggfeSOx3AAfiaw/2ibRZvAljdCEvJBqCjeMnYjI+c+xIX9K8Q8AeBrzx7rb6fa3EVvHFH5s8zjdtXIHC9zk+31oA6jxT8dvE2t+fbaYI9KspAUxH88xB9XPQ/wC6BiqngT4P614yQX9y503TSQRNNGS8wPOUXuMdycfWvdPDPwg8I+GVR0sBf3and9ovsSEHthcbR+Az7134AAwBgUAeaeFPgvoPhLX7LWbW9v7i5tlcBZ2QoWZSucBQRwT3Pb0r0uvM/it8Rk8KaEqaLqdmdZedV8nKysiYJJK547cmsD4Y/FrxL4y8SRaPd6bYNGkLSz3MZZGVRgZxkgncQMcde1AHtdfL2vxD4UfG6K/tYXi0ySQTIq8AwyDEijjGAS2B2wtfUNeRfH/QP7R8ExarHHum02YMzDGRG+Fb8M7f85oA9ZjdZUV0YMjAFWU5BHqK8v8Ajn4UXXPBh1eBR9s0kmYHj5oj98fhw3/ASO9aHwe8XweJvBFrb72+3aci21wrnJOB8rj2I/UEehPfzQR3MEkMyK8UilHRhkMCMEGgDn/AeuN4k8D6RqskqyzTQATMgI/eL8rcH3B//VXS14v8H55vC/izxF4BvWbNvJ9pswecocZJI45Voz+de0UAFFFFABRRRQAGig0UAU9SvY9N0u7vpWVY7aF5nZugCqSSfyryj4DaVO+l6v4qvAWudXujtdgS21SSxDEZOWY55Odo7iuj+M2sHRvhlqZSQJJd7bRPmwTvPzAevyhuPTNa3w40n+w/h3oViRKHFqsrrKMMryfvGUjtguR+FAHVV8x6qkfj39okWoRxbwXghkKrklIPvHg8AlSM+hB9q+hPFOqHRfCeramrIHtbSWWPe2AXCnaM+5wPxrwr9nbTRd+JNZ1meN5JoYBGkrLlQ0jZY5x97C9j0J9aAPo2ud8ReNvDvhRR/bOqwW0hXcsPLSMPZFyfx6V0VfNPx08JXp+IFnf2weVdaCQRK7DCzKFTaPQEbTz3J/AAo/Ej4yXHih4LLQ0nsLW0uRNHdCUrLIyghW4+6OScZNdF4O/aEeNY7PxVaeYoAX7dbD5vq6d/qMfStXwd+z7plpAtz4plN7cN1tYXKRJ9WGGY/QgfWtPxF8AvC+qxSSaS0+k3RHyhGMkWfdW5/IjrQB3nh7xl4e8VxO+iapDeGP76DKOo9SrAMB74q9q+lWmt6Tc6bexCS3uIzG4ODjPcZ7jqK+Wtb+Dfjbw35t1Bai9t4gW86wky2M/3OGz34BxXb/s83V+mq+INPv5pxIiRP5E7HcrZYE7Tz6Z/CgDtPBHwb0DwjJHe3P8AxNNTRiVuJkwic8bUyQCPU5OemK9Koqlq2oxaRo97qMzBYrWB5nJ9FUn+lAHzJ8efEcmreOjpSODbaYgjCjPMjAFifU9B+FetxPD8L/ggrOpiu4rTOOFdrmX6jOQW7jIC+1eMfCvQG8cfEz7XqA863gZ7+78wk72LfKuSDkl2BIPUBua7L9onxSGksPC9uxGz/Srr3J4Qf+hE/hQB4ISSST1NJRRQAUUUUAdD4Q8KX/jLxFFo+nGNZHVnaSUkLGg6k459Bx3Newy/s1x/Zl8rxM4nC87rMFCcdPv5Az9axv2ddGnm8UX2sFJBbQWxgD7flZ2IO3PqAM19K0AeQfBO3g8Nxa94UvZbddctb9pJYlI3SQ7ECsD3XOTjtu5xmun+IHjy18LaVLaWc4n8Q3K+XY2cS+ZIXPAYqOg5zz17Zrxb43+GLmw8frrGzyNP1JowLgEkLIAA2fQ8Zx7V1mj+FtS+EeqNrVlYf8JPpF1EDPdQxBbm2XPVBk7gQ2TjrjnFAFaL4Za74FjtfHNnqcl3qduPtOp2TLtMiEbpVDA8nr1Hv2rsNQ1DQvipotjcaJ4vn0a9tyZFEUwjmjJGCHTcCceoOOuCa0tN+MHgfUxsbV1s5c7WivY2iI+pI29vWuB+I+gfCufQ9S1ix1Swh1Vkd4hYXayCabGQpjBIGTjOAMZzQBteMPHB8BfD8aTD4oh1nxKcxLcNjzFUscuVUnBVeBuPJ556V8wnk5oooAUEggjqK+pvhF8Qtd8X6VqQ1SwE76fGuy5gAUzsQfkIJxu46jj1xxn5Yr7A+D/h658OfDyzhvNvn3TNdMq4O0PjaMjr8oB/HHagD5q8feLr7xn4pn1K+g8gxj7PDb4wYY1J+U9yclic9ye2AOUr0T4t+CL3wr4quLwky6dqM7zW8p65PzMrehBY/Uc153QAUUUUAFFFFABRRRQB7B4Z+O+oeG/Dlno40K0nW0iEUcglZMgdyMHn16V0vwY8c2WrXmv6Lq7QQ3Gr3st9HDjCSNKMSICT7DA9M9a+eq6bwR4V1bxd4hWw0WWKG6iQ3HnSuVWMKR82QCepA4HegD3L4ZeGtc8JfEfxBYrpd5b+HJd/2eSaXch2v8hB7kgn3A617HJIsUbSOcIoLMfQCvJIz8bdFTyhFoWthFADswVm/HMfP1qjrtp8ZvE2hzQTxaTpMLIwmgtpgryrjkFtzgZHow680AfPusXQvdbvrpfLCzXEkg8tQq4LE8AdB7Vn090aORkb7ykg4OeaZQAUUVYtrWe9u4bS2iea4mcRxxoMs7E4AA9SaALmh6BqviPUVsNIsZbu4bnZGOFHqSeAPc16P4U+FV9YfFiw0TWGgmS1iXUbg25LJsB+VSWA6sADx0P4j2r4beEIfAfgyOG58uO9lXz7+YkAA8nBPoo4/M8ZrnfgrNd+ILjxH4u1BXFxqV0sandldiDhR/u5AoA9bppYKpZiAAMkntTq8W+Ovj99I09PDWlXgS+ugftuwfNHCRwuexbPbnA7ZGQDx/4o+Lx408aT30aqtpAn2W2I6tGrMQx+pYn6EVxVFFABRRRQAUUUUAFFFFABRRRQAV9S/CLXvAmn+HbPR9K1OBNSlUPdLcjypZZT1GSAGxnAAJ49815H8ENHGq/EyyeRA8NjHJcsGUkZA2r9DuYH8K+ifFXgfwr4jtZbnWtPhR41MjXsf7qRABksXHXAHfIoAw/DF9a+DvF+veGdRv4ba0lk/tPThO6xqI5WO9FJx0cHj/69dJc+PvCNq+ybxLpIbJBAu0Ygj1weK8W8M/DUfEDxDe6xfahqc3heB2g0+a5nLTzorcAFgcRjnnj09ceqWvwi8C2tr9nXw/byA4y8ru7kjvuJyPoMCgDrLHVtN1SPfYahaXa4zm3mWQY/AmuJ+K/iS80vw8mkaKWk1zV3+zwRRAtIsZB3uAORjpnsTkdKjl+DPhqCZLvw+99oWoRA+Vc2dy7YPuHJyPbIyK8l0+P4gn4wXmkrrcY14wPbG9uVBXyBh8oNpxkAEYHUn3oA6G9+Cl54c8E3GpaX4gvLfWYrVmvEWXy4Zkxl4wRg4xnqSCR2zmjwh8HfDut/C631a8+0DVLqCSYTRT5WPBbaAvToBkHnORkduoHwcvdWBbxV421rUt6/NDDJ5UYP0O4Y/AVjfCvWrbwt4j1r4earc/6u7ZbFpD8smeNnQckYPvzj3AO68EDRfFHg3w/qV1a2l9ewWMcTTXMaSzIyrtbk5IywJ9810mu6Hp/iXSJ9K1ODz7ScAMuSCCDkEEdCCK880Oy+Hnw78fSafY3V3HrWo7IFtWWR0jDkMoGFwATjkk4x25r1C4nitraW4mcJFEhd2P8ACoGSfyoA+cpvHutfCDxje+GEuX1rRrTyxFDdna6IyK4CuM4wGx0I46CvTNJ8QeEvjJ4ck0+4hxICGlspWAlhYdHQjqOThh6nI7Vy/wAGrKPxRrvibxnqFv5zXVy0EBmUMFU/MRjpkDYOn06msTx54C1HTPihbXHgoR2dxcWb3sUcbiP94hw6xrjuCpx3yaAO2gvI9Otr34e+N5gti9sY9P1WZhGl1DjhWJwFkTge+3Pu3ysRgkCvrXxBa2/xT+Dwu4Yg1zNb/aLfapyk6ZDKAMnqGXHPX8a+SaACiiigC5pjrHqtnI7BUWdCxPQAMK+n/jyDP8MGkiBdBdwuWXkBTnn6cj86+afDlpJf+J9JtIdvmT3kMabjgZLgDNfVvxhga4+FWuxoVBEccnzEAYWVGP44BwO5oA+PaKKKAPp74G+LF8R+EZ/DuoHzp9PjEYWQg+ZA2QBjHRfu9+MV594Lvrj4YfGCfQ7r93Y3Nx9lkMx/5Zsf3UmeB3GT0wTXI/DfxSPCHjix1OV2WzJMN0F5zG3BOO+Dhvwr0/8AaG8NyvLpvie0jZ0CG3uXQE7cHKMSOg5Yfl60Ae+SxJNE8UqK8bqVZGGQwPUEdxXCXFp4A+F+otrUoj0iTUFMOIxIyPggnCKCB26ACr3wy8Tx+K/Amn3octcQILa6LdfNRRuPTuCG/wCBVzP7QNqs/wAORN5Jd7e8jYNg/ICCCf1A/GgCTXfj14Q0qIjT5J9Wn6BIIyifizAfoDXi3if4teLfF1wsMVxJYW7Eotrp7OnmA8YYg5c4OMdParPwq+GUPj6W7nvb57ays2RGWHaZJC2TgZ+6MDqQc9uhx9FeGfAHhnwiqtpOlxrcBdpupPnlb/gR6Z9sCgD5k0n4R+N9ajaaHRJbdB3vCIS30DYJ/KvSfhZa2vw0ur2Pxna/2RqV6fLtru45ieMYJQSKSoOcHGR0HtXvJYKpZiAAMkntXyr8cfFcmu+NH06C6il03T1UQmFw6s7IrM2R3ydv/AaAPqaCeK5gSeCVJYnG5JI2DKw9QR1qvqunxatpN3p0wHl3ULwtlQwAYEZweteffA3w9d6J4EW4vWuEfUJTcJby8LEmMKQOxYck8ZGOOMn0+gD5i+Ct7ceE/ihd+HdRRo5LpHtXjwDiZDuU59MBx/wKvp2vmb4y6dceD/idZeJtLSSE3IS6EnG37QhwwAx0ICkg5zub6D6L0fUotY0Wx1OL/V3duk6+wZQcfrQB5H8TpR4N+J/hrxwbYSWxDWtztPzZ2suceuxyR/u89q9qrgPjNpI1b4Y6oVx5toFuoyTjGxhu/wDHS344q18LfFH/AAlngOyu3Ym5t/8ARbjIP+sQDnnrkFT+NAHa0UUUAFFFFAAaKDRQB5D8ZIrjW9f8H+GbZsNdXrTsH/1eEA5P0Bb8zXrgUKoVQAAMADtXkk9w2u/tIWsAUSwaNpzEgS5EbMOWxnhsyKpHXgV67QB5H+0B4ibSvBsGkxNiXVJSrH/pmmC3b1Kj8al+AOjnTvh+95JHtlv7p5QSCCY1AVevuGPHrXD/ALRF2194v0XSopdzRW5IiIwFeR8Zz7hR+Ve16edI8C+ENMs7++t7O2too7fzZ5AivJjnqepIY4+tAHSVxfxT0RNc+HWrwmBZpreI3MG4HKvGC2Vxzu27gPXOO9dbb3MF3bpPbTRzQyDKSRsGVh6gjg1OQCMEZFAHxLo3jvxT4f2jTNdvIY1AAiZ98YA6DY2R+lem6D+0bqkBWPXtJt7tOnm2rGJ/qVOQfwxXssXw98HwpIq+GdLbzCSzSWyuxJ68sCR+Fct4h+BHhPWXWWyWbSZQCCLXBRvcq2f0IoA1tM+MPgbVIkZdcitXYZMV2jRMvsSRt/ImvIPGfxPtLb4uWniLw1L58Ftara3LFMLcjexYDuRgqAT3X0ArO8Y/BDWPCek3OrR6jaX1jbYMmAY5ApIGdpyO/rWt8IPhND4ihTxDr8ZbTt3+jW2ceeQeWb/Zz2749OoB9G2txFeWsNzA+6KZFkjbBGVIyDg+1eUftAeI5dK8H2+k27qsmpylZeRnyl5Ix7krz7H1r1qKKOGJIokVI0UKqKMBQOgA7Cvl347eIF17x5Hplrl49Nj8jAGS0rHLY9f4R+FAHoP7PehxWPhC916UFZrydkDlvl8mMccdvmL/AJCvBfGGvv4p8W6lrTKyfapcohIJVAAqjj0UAV9IeLZLf4e/A9rG1Ihla2SziDAhnlkHznvzje2PbFfKNABRRRQAV3Pw++G+p+O9QVo1a30qJ9tzdkcDoSq+rYI+mRn3g+HvgK/8da19lhLw2MXN1d7MiIdgPVjjgfj2r6D1Dxb4P+FejW+g2Sm5vIgFj0+1+eZ3P8TnsSeeeeeBQB22h6Hp/hzSINL0u3WC1gXCqOpPdie5Pc1Dq3inQdCcR6trFjZykbhHNOquR6hc5xXmV3D8VviFGpj8rwnpRbIUyutxIhPfb82QO3yA5/LR0z4D+FoE36vJfavdMQXlmmZAcdgFOcfUn60AWPE3jj4beKtBu9Gv/ENqYZ04cI+Y2/hZfl6g8/8A668t+HXjHxZouqaho/hy3k8TaTbMzLGcqREGwHTPK7hj5cH6V7jH8MfBEMXlp4Y04gd3i3H8zk1wfjjw3B8MbrTfGvhOxMEdrJ5OoWiO3lyxPwCeTjnjoeSp6jkA1o/Hvw+8RTT2nijS4dM1FcJNb6zaBXHHHzkcceuDSWcvwY0aU3lvJ4fWRBkNu84j6A55+grqYLHwh8Q9Ig1d9NsNShuI8LNLCplQd0LfeUg54zUNv8KvA1rM0kfhuzLMMESBpB+AYkCgDxjxZL4d+K/xBsdL0GS103bG6DUJYigvHwCqBeDxggE8nP0Feb+JfCWt+Er42ur2MkByQkuMxye6t0NfWXjnwzYal4D1CyjhitRawtcWrwRhTBJGNylcYx0xx2NcxpV9B8XPg5cW90Y21JIjHLkA7LhBlXHHG7g/8CIoA89+EXwr0bxpoF5q2ry3RCXJto4oHCAYVWLE4OfvAfga7Ob4d/EfSJRZ+GPG6jSY+II75j5ka/3eEYED8PoK1vgNcrL8NEt9jrJZ3k0EoYfxZD8fg4/HNdJ8PvGLeOfDP9sNZCzPnvD5Qk3/AHcc5wPWgDjU+CQ1q3M3jHxLqmq6jghGjk2xwjjhQwOensOenevB/H/hUeDfF13oyXH2iOMK8UhGCUYZAb3HTivpLxb4w1rRPiX4X0O0tYpdO1LKzcZcndgkegQYb359K8k/aKjVfiDZMqgF9MjLEDqfMlGT+AH5UAeP0UUUAFFFamhaJfeItZttI02Hzbu5bai5wOBkknsAASfpQBl0oGTgda+gdE/ZvQBJNe1wsc/NDYx4H/fbf/E16to/gDwpoJjfT9Cso5oyCszxCSQEDGQzZIP0oA+fvhnp9l4V8Y2//Cc6I1vBfwlbGe/t/wB0JMg55GOhAz2yM4r2rVPhxbrqqa94Tnh0HVlDK7xQBoJ1bqHj4HvkfrXU67oGl+JNLl07VrRLm2k/hYcqf7ynqD7ivnjxLD4++FOsSpp+s6gnh+WXbb3UuLiNFboGDAgOAPQZxxQB6Wtp8ZIGIOpeGLgdmZHHcDso6dacvhHx94hHleKPFcVjZbjvttFQo8q9MGQgED8DweayLK98TajZxS2Xxg0MxqAu77FAGP8AvBuQfwFcf4hm8Zav4hsfDukfEI65d3TSCZdP/wBHjgUYBMjR8FcbuOcY6cigCn4i+GNtrvie5sfh7YTTW1gvl3s89wPJ87P3EZuSQOvP5d+K1v4f+K/DkDTanod1DApIMygSIPqykgDjvX1z4T8O2nhPw3Z6TbKmYkHnSKMebLgb3PuT/QVu0AfA8cE00ixxxO7uQqqqkkk9ABXpfwh8MarH8VtPS+s7qyks4XvHS4hKNsxtBw2DglgM19W15N4W8QXHiD49eI9sYNnp+nmwDrGR8yTDgk99xl+oHtQB2/jq8ew8Ba9dRKrPHYykBhx90iuf+CkSR/CbRmRFVpDOzkDBY+c4yfU4AH4Ctn4kf8k18R/9eEv/AKDXI/DzxJp/hP4D6Tq2pOVhjE4VV5aRzPJhVHqaAOn+I/jKPwT4Sn1L5Wu5D5NohGQ0pBwT7AAk/THevjzUL+71W+lvr6eSe6mYvJLIcljW5418Y6h4316XUrw7Ix8kFuCSsSDOB9eeT3JrmKACiiigAoorY8PeGtV8U6kmn6RZtcXDcnHCoPVmPAFAGPRXrlv+z74mkkWKbVNGhnI3eSZ3Z9ucE4CVyfjP4e3/AIHEA1DUdLuZJ2ZfKtJyzpjuysoIFAHH0UUUAFFFFAHt/wCzeqf8JFrTmQBxaIAmDyN/Jz04wPzr0L48Xk9r8MbhYJCgnuYopMd0yTj81FeLfBHWIdJ+JVmtw4SK8ie23s+0KxGV+uSoX/gVfRnj/wAI/wDCbeErjRxcC2lLLLDIVyodTxkehGR7ZzzjFAGHZ+OfBPgTwfpdjJrdtL5FrGgitWE0jHaCSVUnbknPOBzWI/7RXhRbkoNP1doR0kEUfJ+hfpS+BPhV4O0aeaz1K70zXtdiOZYWdWEA4+Xysnv3YfgO/Y+IfEvg3wc1tbas9naPMAIYRbbjtzjOFU4A98dKAL/hbxhovjLT3vNGuXlRG2yo6FXjb0IP9MiuA+M9nJo02h+N9PLRXmnXaQzyRrkmJsn5vUZyMH+/R4pSD4Z+KtP8XaQII9E1eWOz1S2QkR8/MsyKDjO0N7df7xq78er6GL4Xup3N9suoY4mXpnl8n2wh/SgD0y3nS6tYriPOyVA6564IyK+OviXcz/8AC0temMrmVL0hHLZK7cBcfQAAfSvrPwsjR+E9JVpZ5SLSPLzjDt8o6j1r448a6pBrXjTWdStv9RcXcjxnPVc8H8etAHuHgb43aFPp6nxa8dpq0CCL7aLdn89B0+4pKnk5HTuOuK3n+KPgfxpNc+Eze3aRahEYBdNH5UblhjarNyG9MqBmvlKu38JeEvDniGyeTUvGtpo16HIS3ntiQR2beWVeT2GcUAfWXh/QNP8ADOh22k6bFstoBhdxyWJOSxPck815l8eb+Cz0bTby11v7FrVlclreGGTErq64Y8crgYOenbqRWTbaWkFsE1T44q1sm0BLO+UOVHUbvMJ/Q1P4SfwTeeL4fD3hbQbXXI1R7nUtV1NRJJgELlC45OWGcAA5+poA6f4FXCT/AAtsUV5WaGeZGEmMKd5bC47YYHnnJPbFeG/F/wAKz+G/HF5MLURWF+5ntnQfIc/eHsQc8e9es3aah8GtV1DUdN0k33g+/lWaaKE4ksH6Ej1U54zxwBkdTe+JHxB8HyeA723F9aajcX1qy21vHtlZHZDtdhzsK5zzg5FAHytRRRQB6B8HdG/tr4maWGQtHZsbx8A4GzlSSOnzbfboO9fTHxB0tNZ8Aa5ZOB81o7ruJADJ86nj0Kg184fBXxPpvhfx0ZtUlMMF5ataLLj5UdnRgW9B8uM9s+lfUGu67Y+HdCudZ1CUrZ2yB3ZBuJyQAAO5JIA+tAHwtRVm8lhmvJ5beDyIHkZo4txby1J4XJ64HGarUAFfUfgi6tviJ8E5tHkDie3tmsZCcsRIq5Rx0z/CcZ9RXy5Xs/7PXiSPTfEt7ok5AGporRMW6PHu4A9wx/75oAsfs+eIp9O8S3/hi7kZIblGliiY/dnTAYY9Suc/7gr1/wCJvhy88VeA9Q0uwkK3LhJI03YWUqwbY3HfHHuBXiPxAx4J+PFtrKIY4JJob9tu35kY7ZOB0ztfrzyTX03HKs0SSIco6hlPqDQB8n/Dbxk3wu8TalDrtlfpDNCI5rVIwHWVSCrEMR0Bcdf4q7DXv2jpXiMfh/RxE5H+vvX3Y+iL/Mt+Fe4av4f0jXYDBqmmW14jLt/exgkD2PUfhXmkP7PPhVNTa5ku9Qltd25LXeoA/wBktjJH5H3oA+fdd8X+IfE9y0mrapdXO858reRGP91B8o/AVuaX8J/GOo3Nj5miXNva3UqKZ5MARqTyzDqABz0r6n0Xwh4d8OQpFpOj2lts6OE3P+LnLH8TVfV/H3hTQXaPUtds4pVzuiV97jH+yuT2oA6CCIQW8UKkkRoFBPfAxUtc14R8baN430+S70edj5TlJIZQFkT0JXJ4PY9PxBA6WgDyv4+aI+qfD37ZCiGTTrlZ2Y9RGQVYD8WU/hS/AfXxq3w/Fi+BPpkpgwO6H5lPT3Yd/u5716FrmmprWg6hpcjbVvLaSAt/d3KVz+Gc188/BLVpvC/xG1Dwvfsyi58y3KZG1biInrzxkBxxkklRQB9JSxRzRPFKivG6lWRhkMD1BHcV4n8Fp59B8Y+KPBUgkWG3ke6gVwCQAyoSSO5Ux9ux6V7jXjPj0S+GfjZ4V8SRCKO1v9tjcOzADJYqzEnphXX/AL5oA9mooooAKKKKAA0EgDJ4FBrJ8TXp07wrrF8qBzbWM8wQnG7ahOM/hQB5t8JJYtX8a+OddB80y3/lRSng+VubaMY44C9+wr1+vJf2eIJIfhzcPIhVZtSleMn+Jdka5/NSPwr1qgD5i8Us3iz9ouGxeMvDDfQW3luQv7uPBk5HPOHI78171458Px+J/BmqaY0YkleBmtwTjEyglD/31ivDPg88viL4yanrhTfGFnnJlwWTe2F/HnHFfS1AHw/Zaz4k8IXhjtbzUdLnQ/NFuaP/AL6Q8H8RXoGiftB+KdOEcep21nqcSn5mZTFKw/3l+X8dpr6UvtNsdTh8rULK2u4v+edxEsi/kQa4vU/gv4F1Lc39jfZZG/jtZnTH0XO39O1AGJo37QnhO/2pqMF7prnqzx+bGPxTLf8Ajteg6P4s8P6+p/snWLO7YAZSOUbhnpleo/KvINW/Zutmcvo2vyxr2ivIg/b++uO/+zXBar8EvG+kwTXC6dHexxf8+cu9mHqqcMfpjNAH0h4l8V+HdFuLLSdcuI1OqkwLFIm5GU/Kd/YIc4yeOfTNb1ra29jaQ2lrEkNvCgSONBhVUDAAFfCV2Lo3bpdiY3Iba4lzvBHGDnnNfangq51G68GaNPq0XlXz2kZlUgA5xwSB0JGCR2JxgUAbdxPFbW0txM4SKJC7sf4VAyT+VfH3w406fxP8UtLMsiu/2v7bcM6g7wh8xuOnJGPxr6Q+LGqTaR8M9ZurcEytEsIOcbRIwQnr6Men8s15H+zlpdvceJNV1KVN0trbLHESOF3k7j9cLj6E0AXP2j9UY6joulLNlFhe5eHacgk7VYnofusMdsH1rwivQ/jTqkGp/E/Umt5GdLcJbMT0DoMMB9Dn8c155QAUUV7B8MPg1N4lSHWtfDQaO3zxQq2JLkfh91f1PbHWgCT4WR+P9X8PyaHoLw6boskrNNqjQ/OpONwQ5+Y8Y4HHqK9r8G/DvQ/BURaxjaa/kGJr6c7pX9QP7ozzgfjmuotbW3sbaO1tYI4II12pHGoVVHoAKnoAaWCqWYgADJJ7Vz3h/wAZ6J4o1LUbLSLo3LaeyiaVEJjO7ONr9D0I/A4yOa5T4y+K5tE8OQaHpjMNW1l/IiCYJVMgN16ZyFH1OOldH4B8GW3gfwzDpkOyS6b57q4UY82Q/wBB0HsPUmgDq6gurWC+tJrW6iWWCZCkkbDIZSMEGp6KAPBvhtfS/Df4gan4I1u52Wt06vYu/wBwsfukHgDcpwePvLjjv7zXmXxl8Fy+J/DS6jp8Z/tTSt0sWwfPInVlHvwCO+Rx151fhd40Xxp4RhuZnT+0bb9xdoDzuAGHx6MOfrkdqAO4rwr9nqe4tLjxLodxCI5LaZXkO7JD5ZCvHHG3rXutfP3walmHxi8XQqx+zutw7jHBYXAC/ozfnQB1fwYt0sG8X6dvRprXWpUdli2kgcA7s8j5Tgdueual+Aabfhqp3Kd17McA9OgwfyrF0OKezsfjGHDRS+ddyLzggNHKykfgQa6v4Nad/Zvwu0kNEY5LkSXD/Nnduc7T14ymzj+uaAOb+Ibyx/HHwK1xcNBYk7Ynj+8ZS5BU8Hhsxr9CenWvPf2gpi3xHjUziQR2EShAMGL5mO0+p53Z/wBoeleheO106X49eCEnT/SBHvdnyFIDOYsc4yHDfmOtefftAQ3CfEVJpbZYopLSPypVH+uAJySfUHjtwB9SAeTUUUUAFe0/s52KzeK9VvWgZvs9mEWUZwpZhx6ZIU9fQ14tX1H+z9oaaf4Fl1NoXSfUZySzfxxpkLj2yXoA9ZLBVLMQABkk9q56z8deFtR1caXZ69Yz3pJVYo5Qdx9AehPHY1R+Kc8kHww194ZCjm1K5U9mIBH4gkfjXzjp0mja9pWgeH/DmhTQ+LHnXzNR85lGQWJI+Y8YwScDGDigD6/qvdWlvfWr215bxXEEgw8UyB1YehB4NWKKAOOvfhd4H1AuZvDViu/GfIUw9PTYRj8Otbmi+HNG8OwNDpGmW1kjfe8mMAt9T1P41q0UAFFFFAFXUPtf9m3P2ERm88pvIEhwvmYO3JweM47V538H/A+q+ErDUrvXI4o9T1CcMyIVYqgz1ZeOSScDpx64Hp1BIAyTgUAZXiPTRrHhrU9N8sSG5tZIlQttBJUgc9ucV8QS3l3LbRWstzM9vCSY4WkJRCeu0dBn2r7lnW21rSbm3iuEkguI3hMsLhsZBU4PTIr4d1SyOm6te2BcObad4S4GN21iM/pQBSooooAKKKKALul6dcatqlrp9qhe4uZVijUA9Scdq+0vCnhPSvB2jJp2lw7E+9LI3LyvjlmP9Ogrwb9nbSba68V6jqUwiaaxtwIQzfMrOSCwHcbQQT23D1r6YoA8G/aJ8NGSDT/E0ZwYsWcy5/hJZlI59S3bvXoWg/CrwZotksceiWl7IyjfPeoJ2c+vzZC/8BArgPipq0Xj7xXpXgHQ5Xkniuib2ZSfLjIBDAj+IqMk+h465x1lv8SNPh8d6X4E0K0N75ebe4uGl2CHy0OQOPnICnPTpgUAeNfGTwFF4R19b+yWGLS9QYmGBDzEwA3DH93nI/LivMK9S+MGneIdS+Kt3ata3t0HRTYRJGZMwhQTsA7bt2ffOa8ykieGRo5EZHUlWVhggjqCKAIqKKKAFBwQR1FfXnws+IMXjjQAty6DWLQBbqMYXf6SKPQ9/Q/hXyFWlo+tajoGox6hpd5JaXUf3ZIz2PUEdCPY0Aer6z8OfE+p/E/xPqGhTQWT2Nx9rSYzNGxMg3jbjccnnrgfQcV6XoNtofxe8BaffeINLSS7izDK4JV0kQ4bawwQG4O3pzjnGa8U0H4w69p3jZtf1Bluo7lEhvIEXYrooADAdA49fcjoa9L0/wCM2l33j6GOPWI9N8Mx2uTFPaYaaZu24Z2bSRycA4PXINAHqeseH9P1vw7PoVzAospYfJCgf6sAYUr6EcEfSvFtW+HfxK1vTtN8K38uny6Hp0yiK5VwjMigqpI5PCkgDH512mj/ABKvvFXxBGl+G9OjuvD8GRd6kyv125G08Ac8YOScEjit34geD5vGehR2Vtq0+m3EEomiljztYgEYYAjjnr296AOb+L3iyLwf4EGk2UwGoXkYtYcspZIgMM5Huo29Ore1fKldN428N6/4Z102viFmlunXek5lMglXPUMeeuevNczQAoBJAHU19QeAfgtoum6FDN4k02G91aX55FlJKQjsmAcE+p/yfGfg/pMesfE/R45WwtvIbrHqYxuX9QPyr7DoA5eLwH4O00NcxeG9MQxAvuNqrFcc5GQeeK5X4SSw6/qfivxdDbiGLUb8QwDkNsjUckdOdwP1zW78VtX/ALG+GmtT7NxngNqOMgeb8hPUdmNSfC3S00n4a6FCm3MtqtyxBPJk+fv/ALwoA6q5tYL22ltrmJJoJVKSRuMqynqCK+avjb8O9O8KvY6tott9nsLljDLEGJVJcZBGemQDxn+GvpyuV+IPhiHxb4L1DTXjD3HlmW1PdZlBKY9M9D7E0AfFdFSOjRuyOpV1JDKRgg+lR0Aer/BXwDaeLdbudR1RBJp+n7f3O7HmSnlQcfwgAn3496+mdQ0ux1XTpNPv7WKezlUK8Mi5UgHI49iAR6Yrxv8AZrYnRdeXjAuIj05+6a9jm0mwn1a21SS2V722RkhmJOUVvvAduaAPkH4m+GoPCXjzUNMtI5Fsxsltw5z8jKDgHuAdy/hXHV6f8erYwfFC4k813E9rDIFbpHhduB7fLn6k15hQAVoaNfSaZrdhfxStE9tcJKHXquGBzWfRQB9G/tAaTaar4R0rxRZ/vWSRIxLHyrQSKWDE+mQuP96uq+Cmu3OufDu2+1zrLNZyNbZz8wRcbd3vg4+gH1rB8AGPxt8B7zQ5LjbLBHLalhjKEfPGTnqOV9OhHGK5v9nLUp4dY1rR2mXyGiWcRk5+dW2kr+B5+goA9B+Nd/rWk+BE1DQ7ye0mt72NppIX2nyyGXHuNxTivE5Pjr47ezSBdRto3Xgzrapvb65BX8gK99+LsaSfCzXt6htsKsM9iHXmvDPgd4e0HxJ4pvbfWbT7W8Fr58EL/wCrOHAYsO5+ZcDpyaAOTvfGXjDxMy2NxrOp3pnbattHI2JCeg2L1+mK2dE+DHjfW3B/sr7BEest+/lAH/d5f/x2vobxL8PdLv8AQhHodlZ6VqtofO0+6toViMUo5GSo6Hv19a87X9oC80i2ew1zw6z63au0M/lziONmBxnGCR+GR3HXgAwrb4b/ABA+F4n8UaffaXJ9lhdp0imY7ohywYOqgjjOAc5AxzivXPAXxQ0bxxbrDG4s9VVf3lnK4y3GSYz/ABjg+47ivnHxT418S/EnVooZ1klUvi1060Riqn2UZLNjPJ564wOK9o+Fvwdk8J6hFr+tXCSakiEQwQk7YNylW3N/EcEj0HPXggA9ir5W+JEJ8HfG3+041dI3uIdQXy12lgT8+OeckPz65r6prwH9pHSZGXRtYSCPy132skoHz5PzKp9uHI/GgD3wMGUMpBBGQR3ry34+abHdfDv7aNwuLC6jljdRyAx2kZ7DkH/gIrqvhzqy618PNDvQys32VYn2jGGT5CMfVau+MNLOteDdZ05Y1kkuLOVI1bp5m07Dx6Ng0AO8I6umveEdJ1NCCbm1jd8Z4fGGHPJwwIz7Vt15R8ANUkvPAM1jO483T7x4ghzuVCAwzn3Lj8K9XoAKKKKAA1598aNQ+wfCzVttw8Etx5cCFCQW3Ou5cjsUDg54IyO9egmvIf2h7zyPAVpbeXu+03yDdnG3arHp3oA6j4TWv2T4Y6Ehh8lngMpUrgncxIb8QQc9810PiPUho/hrU9S8wRm2tZJVcruAIUkcd+cUeGrL+zfC+kWJk8z7NZQw78Y3bUAzjt0rlvjLemx+FetFJhFJMscKerbpFDKPqu79aAOF/ZvsP9C17UmWIiSWKBGx867QzN24B3L37ewr3ivJf2e7WKH4eTXCA+ZPfSF+fQKB+ldr4y8X2ngvQTq93a3NzF5ixBLZQSCQTkknAHHX3HrQAeOfFMPhDwpearI8Xnqu22jlziWU/dXA5PvjsDXF+GPjt4Y1LT7VdauTpuot8symJzFu9VYZwp9+n614R458aaj498Qm9nBjhX5LW0VtwiHA49SSMk/0Arq7T9nzxhd2cdw9xpdszqG8maZ968dDhCM/jQB9BWfjzwlfTNFbeJNMd16r9pUE/TJ5/Ct6KaK4iWWGRJI2GVdGBB+hFfKV58CPHdtjybG0u8/88btBj/vvb/k1iXnwy8cWO/zvDl+RGCSYl8wY9ipOaAPorxB8OpdY+Kmi+K0kszaWkQW5glQ73dd21hwQT8w64xsHXt6HXJfDjX4vEngLS76Nh5qQiCdNwJSRPlIPJwTgNzzhge9dbQB4x+0ZfmDwjptiswU3N5uaPjLqinn8Cy/mKn+AOnJpvw7utWkwWu7l5CVJJ8uMbQCPXIf8CK4n9ozUfP8AFmmWAdyLa0MhQ/dBdjyPqFH5CvSniXwn+z9KsIG9dIPzwjyzvlXG/wCoL5z7UAfLOpXP2zVLu63s/nTPJuc5JyxOT71ToooA7L4Y+GB4t8dWFjLAZbSM+fdjOB5S9QfYkqv419jwQR28McMKLHFGoREUYCqBgAD0ry/4DeGv7G8DnUri3Ed5qUplDsuG8kABB9PvN/wKvVaACuH+IfxDsvAunR/umudTugy2lunOTjhm/wBnOOnJqTx/8QtL8B6U0szJPqUg/wBGsw3zOf7zeij1/AV4L4cOt3msWfxO1SaK7totajtrpXBLoGC/Mq8AKA4C4PBxxigDorj4Ta/q3hjUPF+v6pdr4i8tryCDcPkC/MFYk/KcdACNv4Yr3PwtrMfiHwtp2rROri6gV2K9N+MMPbDAjHbFaksUdxC0ciJJG6lWVhlWB6gjuK8y+BjNb+FdU0iQ7n03VJoGcH5W6dB2FAHqVFFFABXgHjWO7+FfxRt/Fel2ki6LqOFvURcRliTvTjgEgBx759DXv9YXi3w3beLfDV5o107IlwvyyL1Rwcq3vggcUAX9L1O01nS7fUrCZZra4QPG69x/j2rxb4LW0L/EvxtcsmZo5XjRsnhWmYsMdOSi/lVHQPFmofBUX/hjxJYXF1AS0+nz2+Cjkjp82PlJxnuDng5q5+ztew3tx4jmmV31OWRJpZz0ZWLHHXru3Hp3oA5L4warqGifELXNP028uLa11GGE3cMch2zEoM5H6cduK+gPAWtadrXgzS5tNnSVIraOGRV6xuqgFSOxrw39ovTFt/GGm6igUfa7PY4GclkY8n8GUfhW3+zjqtvjV9JWzC3JC3L3Ifl1B2hSPbJP4mgDpvjffaBaaBBJdXXk+Ird1uNKMRPmo4YfNx0Xjv3HHNfPXi3xjq3jTUor/WHiM0UIhQRJsUKCT0z1yTXf/tG/8lA0/wD7Bcf/AKNlrx6gAooooA0NH0q51vWbPTLMA3F1KsSbjgZJxk+1fb+j6Zb6Lo1nplrn7PaQrCm45OFGOa+fP2fPCj3uvzeJ50YW9irQ27ZxumZcN9cIx/76HpXafGvXPEukf2LDpN+2maddzGG5vkfBRiRgE9VUDJyPQ+nIA/4uaouuz6d8P9LmZ9S1C6ia68tdwggyclsdOcNj0HPUZzotO0bQP2gfDmk6fYxqLfRzCpjTZiUJId7f3yUGCefveort/BfgLTPBqT6g94+papdndcapdHLyA44BJOATz1JJPJPGOb+JdnLonj3wp43hf5IZ00+5ViAqxuWG7JHHDuD+HTrQB6zRTQwZQykEEZBHenUAFFFFABTSwVSzEAAZJPanVg+NbxdP8Ea5dMhdY7GYlQcZ+Uj+tAF7S9b0zW4ZJtLv7a9ijco7wShwrehxWZ49ljh+H3iJ5HVV/s24UFjgZMbAD6kkD8a4z9n6JF+HDyKih3vZdzActgLjJ71d+Oeoiw+GF5GJjG93NFbqAM78ncV9vlVj+FAFH9n6BYvhuZQm1pb2Uk8/NgKBXzHqN5JqOp3d7IFWS4meVwnQFmJOPbmvsD4f2cXhf4X6THesbdLe0M87SsPk3EyNkjsCx/CvjVuWP1oASiiigAooooA9B+EnjceDPFqm7m8vS74CK7JyQuM7HwPQn8ia+tRMJ7MXFqUlDx74iD8r5GRz6HivgmvtH4a66niH4f6TeKoVkhEEijsyfKf5UAcF8AtJtTba9rUyR/2m9+9s4ByY1ADHHsSx/wC+a6W3+C/hSx1611mwN/aXVtMJ1EdxuUsDnneGOPxrlNGFz8Ovih4rtLS3mvtHeyfU5IrddzQnllXrwfvAZycYPqa9T8I+JLfxb4Zs9btonhjuQ37pyCyFWKkHHuPyxQBH4n8MLr8UE0F5Lp+q2bF7O+hxuiYjBBB4ZD3U9a+SfHv9rnxpqcevTW82pRSeXNJAoVGIAwQAB1HPTPrX1J8UtauNB+HeqX1ndta3QVUilQEsGZgOPQ89e1eTeBvh7J42+HF+uo6LFZ30snnWGszMTLcMWJbcOu3jGTwd2QCRQB4bRV3U9Mu9H1S406+iMdzbyGORD2I/pVKgAooooAK99+EXwjsNR0b+3vFFj5yXIBsrWQso8v8A56MBjO7+H255yMeGWNnPqN/bWNsm+4uZViiUfxMxwB+Zr7ptIksNMgiby4kt4VU4wFUKuPwAxQB5z4i8Y23hHVLLwV4J0ezfWrh1/cCPZBbhudz7cEnHPsOT6H02Lf5Sebt37Ru29M98e1eP/DmCz8R/Frxf4ttgrW0LLbWkiIdkhIwzhj3wgz/10+ldp8RfGS+B/CcuqBEkunYQWsbZw0hBIzjsACT06Y70AVviD8OdK8aaXcSvagawkJS1uQ5BVhkhTzggnjn17V8fyRPBK8UiMkiMVZWGCCOoIr7W8Danq2s+DNL1DW4Eh1C4jLyoi7Rjcdpxk4yu049+3Svkbxyip4711Vt/s4+3S/ut+/HzHv79fxoA6n4EED4p2WSBmCYDP+4a+s6+I/A+oLpfjrQb2S4FvFFfwmWUnAWMuA+T6bSc+1fbQYMoZSCCMgjvQB5F+0RchPAljaiUiWfUU/dg8uoR88dwCV/HFepaVCltpFlDEixxxwRoqKMBQFAAA7CvIvju63Oq+D9Nj/4+ZL0soYhVwWReSeBye9e1UAFFFFAHxn8UNFj0D4i6vZwReXbtKJol3Z+VwG/LJNcbXs/7Rli0XjHTL4BBHcWPl5HUsjtkn8HUfh7V4xQB9Hfs4TO2ga3CcbEuo2GFAOSpzz1P3Rx/ia9wr59/Zski8/xBHsfztsLbt3y7ctxj1z3r6CoA+W/2gkUfEWF/MUlrGPKAHK4ZuvGOfbNeS16h8etQF38Tri2XdiztooiCeMld+R+Dj8q8voAKKKKAPdf2cNZEeqaxopAzNCt0rY/uHaRnP+2D07GsiFT4G/aL8tZEWGS+wdsbKnl3C52hQecbwB2yoNct8J9WbR/iXokoXKzzi1YAc4k+T+ZFd3+0FayaZ4z0PXIkKs8OFff1eJ84wDkY3Lz70Ae6eLLO41DwfrdlaoZLm40+eGJBgbnaNgBz6kivnv4EibRPihc6dqNrPb3c1jLAIpU2srBkfkHBHCH9K+kdKvRqWk2d8ECi5gSbaG3bdyg4z361yHjmw8LjxD4Z1fW9UbTL+2vFFnKBgTYIJjc4OF9yQOT60Ad5XlvxH+EFp431KHUrO9TT78DZOxi3rKvYkAjDD17j6V6iCGAIIIPIIqK4uILWIy3E0cMY6vIwUD8TQBw/gH4WaP4ERrhGN7qbja93KgG0eiLztH4kn17V31ebeNPir4W07w/qsFjr0M2pm3eO3FmfMIlZSFIYfKMHBJzxj14ryHwN8btX8L2psdTgfVrTeWR5JiJo89QGIORnnB9+aAPqeuH+LOj22sfDfV1uYmd7WI3UBXqsiA4I/AkH2J+tdjbT/abWGfypIvMRX2SrtdMjOGHYjuKi1Oz/ALR0q8sg+z7RA8O/Gdu5SM479aAPIf2c9WFz4X1TSmI32dyJQMfwyD9eUP6V7VXzZ8AtSTRfG2qeH72JY7q7QopIywkhLFkzngY3E+u0V9J0AeH/AArY+H/i14w8Ms8gjeV54I+GG0NkEn12ute4V4R4xmPhf9orQdYdHe3vokjOFKjLBoSM/wARGVb8R9a93oAKKKKAA14f+0DeB7rwppZMTxzXTzSxnlsAoq8eh3P9ce1e4GvBvjFaR6h8XPBdlMWEdw0MTlDggNPg496APdkRY0VEAVVGAB2FeWftATJH8NxGzqHkvYgqtjLYDE4/+tXq1eJ/tHzRr4Y0eAuole9Z1TuVCEE/huX8xQB1HwQt4YfhRpUkabWneeSQ5J3N5rLn8lA/Cu8vbK21Gyms7yBJ7aZCkkUgyrKexFc18MYY4Php4eSJAimyRyAMfM3zE/iST+NdbQB8633hzwx8NPjHp91qcLroVzE01q0gLrbzA98dQD9cbh6Zr2OP4ieDZbcXC+KNKCE4Aa6VW/75Jz+lZfxO8At490K3tILmO3u7abzYpJFyuCMMDgZ9OnoK80H7NV15AJ8TxednlRZnaB9d+f0oA9ng8b+FLmYwweJNJkkXqq3kf6c8/hVbxR430bw3oN1qD6haSTJEWt4BMpaZsfKAAcnJrxC//Zy8QxZNhq+nXKjtKHiJ+nDD9a5DxP8ACvxZ4Ts3vr+wSSyjxvuLaUSKmfUfeA7ZIxQB0XwV17XH+JrxwbpYNSMkt+gHyKOW346AhiB/wLFfUleMfs++FRp3hybxHMVaXUiY4QOqxIxByfUsDx/sj8PZ6APk/wCM99/bnxXubSzjMjwLDZKEOTI/UgDHB3OV/D3r1r413Z8PfCdNOtAfLuJYbAFiCVQKW5454jx265rxy+t5tR+PjwqQZX1xTlht6SA9s9hXo/7SV0y6LodoJgA9xJK0W7k7VADY9txGfegD5zpQMkD1pKKAPuvw9p/9k+G9L07zlm+yWkUHmqMB9iBdw9jjNcJ8VvEXjjRoY18LaaXtDAz3F7HH5rxEZyNvQYAznnqemK7DwR/yIPhz/sF23/opa17u2ivrOe1mBaKeNo3AOMqwwf0NAHkfwg8H6PqnhyDxbq0X9qazqDSmSW8/eiPDsmADxkhc5PPOBxXM3qeMrDwvf/DuHwddTQXF9IseppG7QiJpdwbAXA9clhgdRXQ/Ah7nS7jxT4XupedOu1aJGyrHJZWIUngfIh/4Fz1FemeJfFOkeEtOj1DWrgwW0kywqwjZ8uQSBgD0UnPtQBrWsJgtIYWIJjjVSR3wMV5H8O3ntfjN46sBmK3d/P8AK2YG7d8rD8GP1z9K9fjkWWNZEOUYBlPqDXgJn8cx/FvxR4h8MaNDfwxXAsbmNnVVZVVQAAWDbsKDkZHPTHFAH0DRXmMHxjtrF44vFPhrWtCdm2tLLbmSEc4zuABI+imt23+Knga5ZhH4ksgR18wmP/0IDNAHY0VjjxV4eMPnjX9LMWN2/wC2R7ceuc9Kzb74keDNOiMs3ibTGUAnEFwszH8EyaAOG+MdyviLWdC8BW0Uf22/mWZ7lvmNumSPujnkAk9OB+Wf4J0mL4P+ObrTNau99lq0Ua2epGPy4t67iUfJOw8+pHT8NX4bJD4z8deIPHsoklhSUWmlmZSDGgX5iB0HBA4P8TZ61f8Aiz4v0220efwpHaf2prOqR+TDZqMmMsMLIeDyDggdSR2oA4T9pG2UaroN2kWC8EsbSgdQGBAz/wACY/iad+zfp1w2qa3qW0i1WFLfdg/M5bdgcYOAvP8AvD1roR8Lra4+H1jH8QtdkS5sQxiuVuAotY2C4iLMCHwV/oDgCtv4I+H10TwM9wkzypqF1JPEXjKExg7Ebaem4KG+jCgDzP8AaK0+aHxjp1+85kiubPy40YDMZRjkDAHB3g8knJboMCvGa+ovjT4Vg1c6Hq96l62m2MzJqBs1DvHA2CXC46AryewOcGvKPiDa/DO20i3Pg29upNR3gso8xozGRzuLgYPTp7gj0APNKK07jSTDoltqZvbFxcSMgto5w06Yzy6dVHHBPXNSeG9Jk1/xJp2kxBi13cpESATtUnk8dgMk+woA+ufhloR8O/D3R7F9wlaATyqwwVeT5yv4Zx+FVfi3a2t58L9cW6dY1jhEqO2Bh1YFQM9yQF9fmx3rtIYlhhjiTO1FCjPoBivJPj/4kt7DwauhLMpu9RlUtEMEiJGDEn0+YLj159DQBL8NLGz8cfBiz0rWna7gSRoWVZCrR7HygyvIwNvXsRXCSeB5fG/jW+8OaF4g1F/DujsqzyX1wZljkORiJc4P3SAeOh9s6+nagngT9nL7VBOVvdYdxGykgh5MrkehCJnPHI9a0P2cNN8rw7rOqecD9pu0t/L2/d8tN2c55z5vTHG334APYNH0yPR9Hs9NhlkljtYVhV5WyzBRjJPrV6iigAooooAK5b4kf8k18R/9eEv/AKDXU1Bd20V9Zz2swLRTxtG4BxlWGD+hoA89+Bclu/wrsFt0Cuk0yznbjc+8nPv8pUfhWL4oZvHXxm0nw2i7tO0HF5ekqCGf5TtPHT7o/E+ma4HwD8RbjwBpereGn0m6utYe7ZbaJWBRZcBNpHU/MM8Zz+tem6JDB8KvAN74h8RSB9b1CQ3N1lhukncErCD7ck9edx5AoAT48eJ10bwOdKjP+laq3lDDYKxqQXPuDwv/AAKvlat3xZ4lvvF3iK41jUWHmzYCop+WNBwFX2H6nJ71hUAFFFFABRRXW+A/Amo+O9aaztHEFtEN89y65WMduO5PYUAclXpPwl0TxN4g1e6s9F1+90a1ii82eaIsUJJAA2ggFiCSM/3TX0H4d+F3hHw3bolvpEFzOq4a5u0EsjH15GF/4CBWV8QvHUPg+SLTNU8NTXXh++hMU13BLtC7twaPZgc7efvDOaAOds9P134RXVzqd283ijRtRIe/vEiJuYiAcMQWbcvPUn8qfY+Ibb4f6Tcax4fgTV/Bl2/2llgnRJtOdmCldp+8pYgAdVxyemdKw8DXmkWSat8O/ETizuIxKum3zefazg84B6pxxnk+prjyvwo1SW7g8TaUPDOt2rGO5t4JHCbh1KbMofpjv3oA9k0fVdE8eeGYb6GCO70+46w3USttZT0ZTkZB+tatzc2el2Lz3U8FpaQqN0kriONB0GScADoK+WPDHxL/AOFf65qNv4dilvfD08oZIb8hZeABuBXgE/TkY716Xe/GX4e+KfD01jr1reLHKo8y1eEsc/7LKeo7HigDl/jzpnh+6+w+KNL1O0mu7t/JmSCZXEwVRhxt7gYB9ivpz4hV7V/7P/ta7/soznT/ADW+z+eAH2Z43Y71RoAKKK6/wj8OPEfjN1fTbMLZ7yjXkzbYlI689T+APWgD1r4EfD+3jsI/F2oRiS4lLLZRunESg4MnI+8SDgjt9eNX43eNbnT7OHwpoxd9T1NcSCIEusROAq453Mcj6Zro7/xP4b+GHg+DTpb+2e40+1WKOzSQedM4XglRyAxBJYjHNc58K/DV3q+q33xE8R25GoajIXsYpFP7mMjAYZ5wVwq/7I75FAHafDzwong7wdZ6Ycm4I825JI5lbkjjjA6fhXnXiZj8S/jJZeGYyr6PoRM12y873BG9Se3O1Mdju+g7n4g/EfTPA1jsfFxqs6n7NZxn5vZm/urn8+2cHFP4S+EZvD3h+XU9TRv7a1ZzcXTOcsoJJVT+ZJ9zQB6EqrGoVVCqowABgAV8S+O7L+z/AB7r1r5nmbL6U7sYzlien419uV8k/Gvw5c6J8Q767aNvsepMLiCQkHJIG8e2Gz+GKAPN6+zvhh4gTxH8PdJvAqrLHF9mlReitH8v6gA/jXxjX0p+zjqXn+FtW04yFntbtZAmOFV1459yjUASfFER3vxb8A2MKebdR3KzyJkYEXmqSSCPRH79jxXs1eL2Wsab4x/aHtLrSSt3baXpbxyT4GzcGb5kz1AMqrkd8445r2igAooooA8Q/aN0dZ9B0rWFI320zQNlsfK4zwO/K184V9W/H23eb4ZSyJGXEN3E7sB9xSSufzIH418pUAe6/s2qDquvv3EEK9Tjlm7dO3+c19E18rfAC8ltviWsEZHl3NpLHID6DDD8cqP1r6poA+QPjRIsvxZ1tkJxmFeQRyIUB6+4rgK6v4k6gdT+I2u3Jl80fa2jVsY+VPkA6DoFA/CuUoAKKKKALVjdSWV/bXUbsjwyrIrL1BBByPevpH46LBq3wu0/VIXaRVuIZo3TG1ldDyfbBH518yV9N6fNH4t/ZqeO5mhiaDTzCxViqobdv3e7ryQiE+ue2aAOh+C+rNqvww03zAd9oXtScAAhT8uP+AlR9Qa4r9pSCL+z9AuNg83zZU3f7OFOPzqb9m7UXl0TW9NfJW2uI5kJfI/eKwIA7f6vPvn2qt+0bpmo3EWj30MEslhbLIs8i8rGzFdpYds4PNAHh2ntrV0wttNa+lIBIiti7Y79Frpbb4TeO7sRlPD10qyEYMzKmPqGII/EV718CPsv/CrbP7Om2UTzC4J/ik3nB/752D8K9MoA+Trr4EeObe3aVbO0nK8+XFcruP0zgVr/AAa8C28/je+TxFCsV7pGwpp9wBmR2DfNg9QuAeMj5lNd18SfjLc+ENVuNGsNGZrpFGLq6JEZyM5VR97GR3FeBtP4h8c+LZbyJLi91e6fefs6cjAAGMfdUAAZ7AUAfblFcv4B07XdJ8G2Vn4kujcakgYszPvZASSFL5O4gd/w5xk9RQB8q6NDcaJ+0UkKyfvP7XkQtt6rIWzwfVWIzX1VXyz8ZHfRfjJ/alvkTbbe6Ak+6WUBRjBzj5BnoevtX1NQB4b+0IJrBvDmswCISW1wwR2yXDDDDjO3Hy+ma9osLtNQ061vUVlS4iSVVbqAwBwfzrzv47aTa3/w0u76YN52nyxywkHuzqhB/Bv0rovhncJc/DTw9IkokH2JELZz8y/KR+BBH4UAdZRRRQAGvGdfP2z9pfw3aXKJLBBZtJGjxghW8uVgenUMoIPYgYr2Y14zqu3/AIak0PIJP9nNjB6HypqAPZq8E/aTuo/I8PWqvGZd08hXALqMIAc9QDz7HHtXvdfPP7SYtP7Q8Psm37YYZhJyc+Xldnt13/5xQB7J4Fs3sPAWg2srKzx2MQJXp90Gtu5uoLO2kubmZIYYlLySSMFVFHUknoKpeGv+RV0j/ryh/wDQBXiP7Qcfihbq3kEk3/CMmNVKwkhBLk58wZ5PTBPHpznIB2M/xy8Kr4rtNHtmlubaaQRy6gvyxRseBgHlhnqeAOozXqNfDXh3wxrHirUfsOj2b3MwG5sEBUX1ZjwBX2B4F0fVtA8I2Gma1ex3l5brtMkYOFX+FcnlsDjOB/UgHS1x/jnxV4b0GCz0rxKsjWusb4MBcoFAAYucggfMORzzXYV4P+0pEDY+HZvLkO2Wdd4HyDIQ4J9Tjj6NQB7Ro+n6fpek21lpcMUNlEmIki+6Aecg985znvnNaFeJfs/eItb1fT9Q0+/mafT7BY1tnccoTn5N3cYA4r22gD5O+G8sGrfHe1uYjIIZ7y6uI+dpxskdc4/DI/Cuo/aTdTq/h9Aw3iCYlc8gFlwf0P5VzHwKsvtXxVtJvM2/ZIJ5sYzuypTHt9/P4VqftGsT4905eMDS0PT/AKay/wCFAHjtaeh6Jf8AiPWLfStMh868n3eXGWC5wpY8ngcA1mV6D8Ev+Su6J9Lj/wBESUAe6/BbU5LjwMuk3CGG+0a4ksriFhhlIJIyMn1I7cqa9IryTTZW8D/Gy/02ZlXS/FA+1W7HPFznkZz3Jbj/AGlxjpXrdAHh8G/Rf2pJoxEiQara/LtO0f6kEsQO5eJvzzW78brVtZ8O6d4es7R7vV729ElpCjBduxW3Oc8YwxHP972rA+OjzaF4l8JeKYBJvtpXR2ABA2srKBkdSC/X0rovGem+J7zXNA8Z+C4YNQnjtGi+zTzDy9kg3B1yyg9cEg8/L2FAGt8P/F41PwO0uoRTQXujKbXUUlU7hJEvzH6kDOPXivPfBnhjx9qFvc+NdG1+HTptYle4+w3ERdZF3HbuyMc44IGdpznmp9R0nxL4W+Hc+nyzq3iTxfqmJljUYiaUZdQV4BwDkjIGTjsa9q06wt9L022sLRAlvbRLFGoA4UDA6UAeat4y+JOhQp/bfgRNSRiAZNJmLEfVBvPT6D6VSm8e+Hb6MnXPhfq5mjJBV9HjmC492xj8q9iooA+dZvEPwSuJZZ5vDF9FNIMPGInTafQKsm1Tx2q5F4y+G9lptxLpHw4u7y3CkyTSaejIPq7FiB/Kvfqoaw0q6LfNCiySiCQojNtDHacAnBx9cUAeL+D/AIy6DoWiQ21x4WvNI04ySGB7UGWJiWJI3Ngk89s/gK0fhhd+G9f8Wa54wn1GI6td3TxW1rcyLvhh42lQeSSBjjoBin/BtdO8W/CltC1WwjubayuJIGR04IY+YCDnIYFzyMY4+tc94G+Gvg/Xtd8V6Ze212JLC9MMETzFJIoucNxwTkHrnigDsfH3wXs/Gervq0GrXFleSABxIvnRtgcYBIK/gSPao7Lw58WtI0y206x8R6FNDBGI0e5jfeAMYGdhzgDGTXGfEzwnH8LtM0/U/CuvanZSzXBha3N0SGG0ncAAOnQ5z94Vx9r8b/H1sy7tYjnRRjZNaxEH6kKD+tAHtul2nxg80pfah4bELcF3id2UHuqqFBI9CcV5D8Svhnp3gvTUvG8TQ3OpzTAvZmERsytkllUEkAH14984By9S+M/jvUgVOtG2Q/w2sSR/rjd+tcRd3lzfXLXF5cS3Ez/ekmcux+pPNAGt4jtPDlnJbDw/ql3qCNHmZp7bydrccDk57/Tjk16x+zx4TF1d3fiqcgrbM1rbqD/GVBZiPZWAH1NeE19m/DHQT4d8AaVZyW5guHj8+dGxnzG5Ocfh9OlAHY183+MvDaeJf2jf7K1aSaGwvFjMbg43ItuDhCeOXUj6k19IV494wjh1H9oPwdaCbEkFu8zgDJG0SOB+O3FAGz8RPBvhWfwEtjeTx6Vb6VCz2LiTHlkL02nl84GerE9Dk1Q/Z8tJLb4bSSyY23OoSyx4P8IVE5/FDXh3xS8TReKvHt/fW0/nWUeLe2bnBRe4B6AsWPbrnFfRHwWsmtPhXpAZw3m+ZMMDoGduKAPQKKKKACiiigAooooA+ZfG+qXXw4+OF5rsOmJNHcKJYVuM7ZA6KHZSOh3Bh7elcZ40+Iuu+OpFGoypHZROXhtYlwiHnknqxwcZP6Zr2b9ojRJr7wzpmqQxPJ9gndZCCMKkgGSR16oo49TXzRQAUUUUAFFFFABX198IPC3/AAi3gO0WRt11qGL2bK4Kb1XanTPAA69y1fKGkWiX+s2NpI6ok9xHGzO21QGYAknsOa+2dY1a08M+HbnUriOZ7Wxh3MkQDOVHHGSAT+NAGtVTUdOttV064sLyJJbeeMxujqCCCMVneFvE1h4u0CDWNOLeTLkMjcMjDgqff/61blAHjPwo1V/CnibVPhzqchMsNw8mnuV/1iYLH81G786g8SfCnQvBefF2nW0+pR2L+bdabehbiOWFvlfAK5yoYtlientUfxlsLvw74u0Px/ZRRvHavHDcJ90swZiCT3ypK55xgV7NY3trqunQXtrIs1tcxiSNhyGVhkUAfNfxR8GabdaZYeMfBumONHu4WkuhAvyQnPB2D7ncHHyjHbv5BX054D0hrDU/HHw6uJX/ALOwz2u5vnEMylTj1wCuT0z6Zr501rS5tE1u/wBKuCDLZ3DwMwHBKsRkexxmgDOooooAK1tHvdaWePT9HvL2OS5lVEgtp2TzHbgDAIyTwKyas2V5Pp19b3trIY7i3kWWJx1VlOQfzFAH0H8L/g4LVby98aaNG13vAtopZxIAuMliFJGc+vvxXa/E74gp8P8AQ7doLdJr67Zo7aNjhV2gZY+wyOPcVxWl/tG6Z/ZCf2rpF5/aKrhxbbTE59QSQVzzxg49TXmHjLxXqXxW8W2S2mnJFKQLa0t1cFmySfmY4GefYUAer/BrwvBr0UvjvXVlvdYubpzBLcAlUC8blz15yAe23Axivaq8T+GnjCDwNpX/AAh3jPzdIvbaR5IGuR+6aNjuwHHH3i3OSDzz2rj/AAb8YfEOk63fQXEd54h093eRU3s8sKhvvKxBO3HY8dORQB9OV5J+0Fo4vvAUWoL/AK2wulbvyj/KR+e0/ga0tJ+N/gzULYvd3k2mXCgl4LqFsjHXBUEH+ftXJ+IvHXiH4laRfaL4T8KTTaZdSC3OoTNgEAg5xwF/EnigD52rovCdj4m1S/l03w0195t0mydbaRkUp/00IIG3nvxXsPh39nKJVjm8R6szN1a2slwB7GRuv4KPrXr+j6DoXg3SZIdNtYLCzjUySvnk4HLOx5PHcmgDyH4BaNd6J4o8U2N9EFuLURQSFfmUMGbIDflXvVeVfBFrnU9L1/xHdh1l1XU3cKw42qBgqe4yxGf9mvVaACuI+LOtXWg/DjU7yykeK4bZCksb7Wj3MBkH6V29eIfE65/4Tvx9ongXTnZ1t5/O1FgDsjHGc4PJC7vT7wGeTQAt2dWuf2X5pdUvS9zJAkglnc7jH56lVJIySV4Hrkc18319e/Fmyt7f4O6vZwmK2t4IYViXBCqqSptQY+gUfUV8hUAeh/BO8Fn8VNKBQt56ywjB6Eoef0r67r48+D0Jl+KeiYZF2SOx3MBn923Az1PtX2HQB8ReOrs6h48165KBC99KNoOcYYj+lc9Wr4k2jxRqwSPy0F7NtTGNo3njHasqgAooooAK+lvgEsWo/DvVtPkjIRrqSJzuPzB4x2zxwe1fNNe6/s2XpTVdfsdmVlgim356bGYYx77/ANKAMn9n3UzZ+P7mx8yURXlm48tD8hdGDBmGeyhwDz973NfS91awX1pNa3UKTW8yFJI3GVZSMEEV8xeAIT4b/aA/s2OBVRbu5tlTeTsQhsc98ACvTPiRr3xB8G3k+t6ZLZ32gHbmCWAFrY8DnbhiCe+T17cUAeg+HPDel+FdL/s3R7cwWvmNJ5Zdn+Y9eST7VsV8wzftFeLJIlWOw0iOTOS6xSHI9MF6py/H/wAbSRlVfToj/eS25/UkUAfQ3jLwfYeNdAk0u/JjywaKdVBeJh3GfyPqKx9I0fwd8JNFBluobQzkLJd3TZlnPoMc4HoBgfrXzxf/ABh8dag5L69LCpx8tvGkYH5DP61y2p63qmtzrNquo3d9IuQrXMzSFQewyeB9KAPuaGeK5hWaGRJYpFDI6MGVgehBHUVNXyl8O/inr3hGBbae1n1LQUyDGFOYBnJKNjHcnaePpX0j4a8U6R4s0xb/AEe7E8XAdSMPE2M7WHY/p6ZoA8N/aQsmTxBot9tUJNbPEGHUsjAnP0Diva/AmpS6t4F0W/mH72a0QtyTkgYzk/SvNv2jNIWfw5perLFmS1uTC7ggYRxnB7nlRj0yfWul+B0sk3wr08yOzlZZlG45wA5wPpQBu/EeD7R8OfEKCIyk2UhChd3IGRx7EZrA+Bl/b3fws062hcNLZyTRTLnlWMjOP0YV3WsWsl9oeoWcO3zZ7aSJNxwMspAz+deN/s23MbaRr9oEIliuIpGfPBDKwA/DYfzoA9zooooADXi2oT20v7U2lL5m+SKwZMIR8j+TK2G/4Cc/iK9pNeKTmCf9qa2FtHGXt7Ii5Y/KQxgbBHI3HayDvx9MgA9rr5s/aR/5GrRv+vI/+hmvpOvm/wDaPQjxNo0hK7TaMMbhnhz269/84oA988Nf8irpH/XlD/6AKt31jbanYzWV5Ck1tOhjkjcZDKaj0ueG50qzuLaIQ28sCPHHgDYpUEDA4GBV2gD5Z8StrnwW8Z3dn4av3isL+OOdPOiSTeo3AKSw/hJbkY4NVf8AhfPjnyvL+1Wec53/AGVc/T0x+FfRXiXwH4c8X3FtPrlh9pktgVjYSuh2nkqdpGRWWfg94B8t0/4RyHDdf38ufwO7I/CgDw+P9oDxtGAGbTpOMZa26+/DCuX8WfELxH40hjh1m7je3icyRwxQqiq2MZ4GTwe5r6U/4Up8Pf8AoXh/4GT/APxdQz/BDwBNA8aaK8DMMCSO7m3L7jcxH5g0AVPgRpD6Z8NYLiQ/NqFzJcgFNpVeEA987NwPo1emlgqlmIAAySe1Znh3QbPwxoNro2n7/stsCE8xtzHLFiSfqTS+IyB4X1YkBgLKbg9/kNAHzb+z7/yUyT/rxm/9CSj9oT7T/wALHj8/b5f2CLyMddm585/4Fvpv7Pf/ACUp/wDrwl/9CSoPjzJJJ8T7lHkZljtoVQE5CjbnA9Bkk/iaAPMK9B+CX/JXdE+lx/6Ikrz6vQfgl/yV3RPpcf8AoiSgD374reFxr3hSTULXcmr6QDeWcqZ3Ar8xX3yBx7gVf+HPjGLxt4Str8vGb6MCK8jXjZIO+OwPUf8A1q6LVoDc6PfQhnQyW8iBkOGGVIyD2NfK/wAMtQ13wffN4ojsbiTw8k32TUpIwGVRx1AOcruU56du9AHsXx90v7d8OHuwmWsbmOUndjarHYeO/LCuo+G9y918N/D0jqVIsY48MecKNoPQcYH/ANc9a47xX4yuvHthd+GvAVkNUjuIdl7qEmY4bdG/hBbGWIz9MdDziLR9P+L3hLSINOgTQ9XtraPy4kaVhIFA4UMdvTGBn+XQAgsbq78afH+dpCZdJ8MiRI1C/IsuNhzn+Ldnn/pmO1e014z8NvESeF57+w8ZWE+ja1qt89015dJsgunbJwH+6uOeM45464r2agAooooAKKKKAPF/hrMuifF/xn4dy0ME0huIYZc7iQc5GfVXz7jHpUvw5Wc/Grx6yyKLYPh0PUuX+Ug+gAf8xVfx9axeEfjJ4b8aPsjs7tzb3crAkI2wx7j6fI3HP8B445t+AZ7eD45eOrBJTM8wWcOFwo2sNynPOQZAPQ4J9KAHftGf8k8sf+wpH/6Klr5fr6g/aM/5J5Y/9hSP/wBFS18v0AFFFFACg4Oa+gNA/aGup7eG0vfDc17f7Qpezl5lb12bePwJr5+r1L4C6vb6X8R1iuMg39o9rER0DllcZ/BCPxFAHol/8ZfETz2lnpvgHUUvbvd5C3m8eYFGW2qFG7A5JzxW98OtJ8QX+tal4x8XWMVpqd3Glta26x7TBEud3BJI3HHU549CK6Lxh4Ls/GFnbRzXd1Z3NpJ5trd2z7Xibv8AXoPfjrXC65aX/gwW58RfFrULe0uCywoNODSvjBPzDceMjnHcUAfOGqWM+l6teafdALcWs7wygHIDKxB578ivtLwZoy6B4N0nS1kMnkWyguRjcT8x49Mk18i6vpb6z4g1CXw5Hq2sWoYyNdSQM8rk8s74Hc5OTX1P8NvFv/CZeD4b42b2stu5tZUbkM6KuWU+hyOvQ5HOM0AdlRXM+J/G+keEbjTINSFwZdSl8m3SFN3IKgk5IAA3L789K6agAorivif4tvfBfg59W0+KGS5MyQr5wJVd2cnAIz09a3/Dd7eal4a02+1CJIry4to5ZUQ/KGZQeOTQBrUUVS1RrmLSrySzXddLA7QqBnLhTtGO/OKAKHi/RF8R+EtT0kyNH9ogKhkXcQRyOO/IHFfELo0bsjqVdSQykYIPpX1j8F/FWoeKvCE8uq3MlzeW900TyuirlSAwHHXrXg/xe0ay0P4j6lbWKGOGXbcFOMKzjcwA7DJ4HagDgqKKKACiiigDY8Lvax+LdHe/ANmt7CZwRnKbxu6e2a+4JYYrm3eGRFkilUqynkMpGCPyr4Otpvs91DPtD+W6vtPQ4OcV90aNqEWraJYalChjiu7aOdEYYKq6hgD+dAHkHhK/f4ZfEq78FXvmLoupSibTJXbcIy2cDOO5+U+hUdiTXt1eY/Gvwm2veEP7Uso3bU9Jbz4jH95kyN4/ADd/wH3re+HfjaDxz4Yi1BQsV7EfKu4QfuOB1+h6j8R2NAG34g0S08SaDeaNfAm2uo9j46rzkEe4IBH0rzT4P6jPoOraz8PdTctcaZK0toxBG+InJ4PQcqw/3z9T7BXj3iINpv7RXh2fTUDXOoWrR3iAj5kAYbj7hVB/4APpQBtRWaRftCyzRs6NL4c82UAghyJwgByOBhVPGOR9c+N/HzTEsPiS06bR9ttI7ghVxg5ZDn1PyZr2m30bUrn45XWsXdk/9m2ukrb2lyeF3lgSB6n5pPp+VeSftHf8j9p3/YLT/wBGy0Acb4E8HW/i++vVvdYh0mysoBNPczKCACwUDkgDkjqa9O0/4UfC65wP+E589mGVWO/t0b34Kk15n8O9e0jQPEgfX7GO80m7ia3uVePftBIIbb3wyj+nIr36z+GHwx8UWialpVjFNbyH/WWt3IFzgcEbvlI44wDzQBzUvwW+G4Qqviu5jkOCC9/bkevTYO1ec+PvAfh7wtZLc6P4ws9TkaTYbNWRpVHXdlGPHTqBXtEnwQ+H2nmS+vILgWsSl3Wa7YRqo6kkYP615L8SdX+HwsF0Xwdo8RlhlDPqKE4IA5VWYlm+p444zQB5gqs7BVBZicAAZJNe06F8CNYfwr/bMl/NYa6EM9raKMFCOVDMDkMcdumRnkEV5T4bit5vFGkx3cphtnvYVlkH8Clxk/gK+zvFeuL4a8LajrLLG5tITIqSPtDt0Vc+5IH40AZnhnW9L8d+Fo/tkEFzOiiO/sp4wxhmAIYOhHHIbHFGjfDnwt4e1w6xpOmG0u/LMf7uZ9mD1+UnH9K8q8G/DDxD4ggHjQ+K5dH1LUy06i1gySrNkbirKMHGduOmM9xXWFPi14ew9zrPhjULNfl829LQn8SAvP4npQBu/FUaZZ+AdX1W90m0vpoYBHGZ4lYqXYICCRkYL549Kk+E+nXGlfDDQrW6XZL5LSlSCMCSRnAOR1wwrxyfx3qfjbxrZ+GPF2paTY6HHcH7W1mwEEhjBYZkZjwSAvXHPSvbo/H3gqCDy4vEmjxxRDYES5QBQOAAAen0oA6qvI/jb4nK6PD4R0qRpdY1aRUeGI5ZY8jg+m44HuM9q2tZ+MfhWwtWGl3R1nUGbZDZWSszSN/vYwB78+wNZPw48Jai+t6h4+8XweRq92WMEUvH2aLGCSD907RtHouc9aAO/wDCuhReGfC+naLCQVtIQhYDAZurN+LEn8a2a8q8SfGfRtP8UaXpGl3tjcQPOov75yzwwx55Csn3mx35UHGe+LXiX43eEtEtH+wXa6tejhIbbO3PqXxtx9Mn2oA0fiV49tfBmgyJFIG1q7QpZWy/eJJxvOAcAZyM9SMeuMb4PfD678KWN1q2tof7av8AhlZgzRx8HBP94nk89h6VD4a+H+ra74tj8b+NTGt9hXtdOhBC2+B8ofPcdcDPPU9q9ZoA8k/aCvPJ8BwW37r/AEi7QYcnd8oJyvGPrkjivlyvfv2k72YHQLEEeQwlmIxzuG0Dn6E14DQB2/wmdYvinoBdgoM7DJ45KMAPzOK+x6+IvAX/ACUPw1/2FLb/ANGrX27QB8MeJg0finV0Z2dlvJgXbGWO88nAAz9AKyKu6lLJPqd3NLE0cjzuzoxYlSWJIJbkke/PrVKgAooooAK9d/Z52f8ACe3W64ZG+wvthAJEnzLnJ6DHv615FXpnwIvfsvxTs4fL3fa7eaHOcbcIXz7/AHMfjQBYvxPo/wC0im0C2J1uI8YA8uRlz+BVv1r6iu7WC/s57S5iWW3njaKWNujKwwQfqDXy18VRLB8dLmYB4yZ7R425GcRxjIP1B/Kvq2gDzYfAvwH5rOdNuGUnIQ3UmB7DnOPxrZh+Fvge2j2J4asSODmRS5492JNedfEH4wax4U+J/wDZtsiSaXZJGLm2ZFBmLqHJD8kEBhjtkcg1sp+0P4PZIy1rq6sxwy+Sh2e5+fp9OfagDs/+FbeCv+hX0v8A8B1rUtvD2hacubXR9OtlUH/VWyIAOp6CvNrr9onwlDxb2Wq3Bx2iRR+ZfP6VynjH492uteG7zStK0m4he8iMTzzygeWp4OAvU49x+NAHtfirUNQ0Pwxd3miaSdQu4FHlWqcZ564HJx1wOTXyZF4z8R6b4zvNbs2/s/VLmQ+bDDAFRiSDtMZHOSB15zz1r034bfG+KzsbLQvEkEr+Xsgt7uAbiR0AkBOePUe3HevaL7wloWpa7a61eaZFNqVr/qZ2JyvXGRnBxk4yDjtQB5Z8RZ/EmtfBA3viHSI9PvobqGSaNJBymdocrnKnLqNuSfp22f2fLyS4+GzQuqhba/liQjqQVR+ffLn8MV0PxZmt4Phbr73UZkjMAQKADh2dQh59GKn8K4X9m+4mfw5rdqz5hiu0kRcDhmTBOf8AgK/lQB7fXgf7PoGma/4t0aYhrqNowSnKny3kVsH6sMV75Xz78Jrg2fxs8U2JjYmc3B3MCpXbKD0P1oA+gqKKKAA14tqqIv7U+iFUAL2LFiB1PkzDJ/AAfhXtJrxfWGVP2pNBLEAfYGGSe5imAoA9or5s/aR/5GrRv+vI/wDoZr6Tr59/aVgiWfw5cbAJnW4Rn7lV8sgfmzfnQB7d4a/5FXSP+vKH/wBAFalZPhnP/CKaPkAH7FD0Of4BWlJKkMbSSOqIoLMzHAAHUk0ASUV8++Nvj3c22vpbeFRBLZW7YmmlTcLg55C+i+/U12ng3406F4s1C00trW7s9TuSVWNlDxkgE8MPoeooA9OorO1jWLHQNJn1LUbhYLW3Xc7n+QHcnsK+dLn49a6PG0l7b7X0EPsWwdFG6PpndjIY9euO3SgD6cqnqdn/AGjpV5ZB9n2iB4d+M7dykZx361geCvHmmeO9PuLzTILuIW8gjkW4QKckZ4IJBH6+1dXQB8r/AAAdU+JZVmALWMyqCepypwPwB/Ko/j7bSwfE2SWQAJcWcUkeD1UZX+amovgrLNY/F+xtVZP3q3EEm1w4IEbNww4PKDkVrftGRuPHenSFGCNpiKGxwSJZMjP4j8xQB45XoPwS/wCSu6J9Lj/0RJXn1dj8LLiS2+J2gPEQGa6EZyAflYFT19iaAPs0gEYIyDXjPwt8nSPGnjTwXdKskH2lp4YppA4eM8fcxg5Upn8BivZq8G8Wf8Ud+0Po2t42WepqqyMMgEsDEwPPOPlb06elAHSaNq2m/DLxPe+GdRjNnpGoXJutMu9mIV3gbomPYhhweRjHSvSL4XFxpNyNNnRLmSBvs0xAZVcqdrY6EZwara/4d0rxNpj6dq1lHc278gNwVPqpHKn3FedxeGPHfw/mWPwpdR67oWQRp1/KFmiHcI/AHA45xn+E0AecqnxK+JzX/hi/v7UvpkitPBdpHC+7JAI2puOPUccjPUV6D4X1D4geBNJXTdf8OXOtWFvxDd2E6SyogB+XZ95h6E4x054rE8SePfDWpudSuP7U8K+M9Ni/deZAx8xupibaMOhPHzBf6V6V8O/HFv468NLfogivIm8u7gGcI/sT1BHI/LtQByl98dNNkUWehaHqt9rMnyx2ctvsKtj+LBJOPQD8R1qnE/x0Z5LsppQVgHW0fygB/sgjn827da9nooA8v0v4y6Raq9j4ygn0DWIMCWCSCR0f/aQqCcHrz+ZqG7+PvhhbwwadY6rqYXlpLe3AXHqAxDfmBXoepeH9H1gg6ppVjesBgNcW6SED2JHFRytovhbSnuHSz0yxgX5mVFiRR2GB+goA4K78ZeBfiZ4dvtFv75tOcgt5WoKIZImXkOOcHHoDnGc9a4j9m6GNtb16coDKlvEiueoUsSR+O1fyFaPizUT8bdTttA8MWq/YLFzNPq9zGwVcjG1RjPPp3I7AZqb4Q+HL7wh8UPE2hGdLq1trOLzZ1Xbudtrx8E5Hys/5fSgDc/aEGfhvGfsxmxfxHeM/uflf5jj/AL554+b1xXyzX1p8dgD8K78kAkTwEe3zivkugAooooAKnt55bW4juIJGimiYOjqcFWByCD61BRQB9H+DPj/ps9pFZ+KY5LS6RQpvIkLxyY7so+ZSfYEfTpXbTfFD4e3SBJ9esJVBziSNmH6rXx1RQB9TeIfipptzbx6D4CmS91y+bybfyYtscJPVyWAGQMnuOOa7jwb4eTwx4VsdKDmSaNN9xIWJ3zN8zsPYsTj2r50+Alg178So5gV22lrLOwJIJ6IMY68uOvvX1XQB4n8eP+Rj8B/9fsv/AKHBXtleHftHW066b4e1SGQr9luJUyuQwZwrKwPbHln8xXrnhu/fU/C+kahINr3VlDOw3ZwWQMee/WgDhfj1byT/AAvuHTbtguoZHyccZ28evLCur8A3Ut78P9AuJiDI9jEWIGP4QK574326T/CnVZGLgwvDIu04BPmqvPqMMf0q18INVj1X4Y6OygB7ZDayAE8MhwPzXafxxQB3dFFFAHh/we8nQviR418PN5MbtOHhVGwNqO/yqDyeJB9MVxHx/wBO+x/EZLjczLeWccvzZwpBZCASf9kHt1rq2u5dP/arlWKNdt2qQtuU/dNspJHvlf51J+0jbyNY6HcCCPyVklQzbTvDEAhc4xg4J69qAPnmiiigAooooAK+s/gdrLat8NLaJifM0+V7Q59Bhl79MMB26GvkyvoT9nHVAsOtaK4VZAUu0BADEEbSfUj7vsM+/IB71XgOkr/wrb49zae5MOk64P3XHy5c5T0xhwV9gfxr36uD+KXgWTxv4bSGyaOLVLSUTW0r8Z4OU3dQDwfqBQBr+Ndb1jQtBNzoejTarftIsccSAlVz/EwHOPp+Yr57067+JU/xVuGjt/K8S3EexzcW6skEWBggkEKuAOR19ya9X8BfEqORF8M+LX/s7xJaHyWFyNiz4HDBum4/r1Gc16fsXfv2jdjG7HOPSgDx1PGvj7wFIJPHemrqWkuQv2+wCbom9wAAfxC/XtXl3xj8YaT4z8S2V3o7NJbwWYiaR4ijFt7EjnsAR+JNfWbosqMjqGVhhlYZBHoa8q8YfAvw/rym40YLo980m9yil4nz1GzOF9tuB7UAfLNeh/BjVbzT/iVpdtBdPHb3btFPHuIWQbGIyOhOQMVtSfs8eL1lkVLvSXRRlX85xu9sbODXKaJo954d+LWkaTdiFru11a2RgkmULeYpHzY6c+n4UAes/tG63PbabpGiwXAWO6aSa5jDEFgu0Jkf3clj9VHpXzpXv37SUNvv8PzhoVusToyc72T5CD0xgHd1PVuM848o8F+CdU8c6s+n6b5cYjTfLPKSEjX3wCST2FAGf4ZtZb7xVpFrA6pLPewxozEgBi4AJIr6p+NX/JItd+kH/o+OvNdP/Z81nTtc0q6fVrOe2huI5LkR70dVDZOzg5OB7cmvX/iR/wAk18R/9eEv/oNAF3wcsC+C9EW3MRiFjDtMX3fuDpXgP7Q2r3c/jK00pt6WlrarIik8O7k5b8gF/A+tex/CG7kvfhVoM0uNwheIYGPlSRkH6KK8H+PMckfxPuXeNlWS2hZCRgMNuMj1GQR+BoA8wooooA2vDnifV/Ceovf6Jdi2uniMTSGJJPlJBIwwIHIHNaWufEnxh4itWtdT1yeS3cbXijVYlcejBAM/jXJ1e07SNR1idoNNsLq9lAyY7aFpGA9cKDQB698B/A2na6dR1rWNPhu7e3ZYLeOddyb/ALzEqeDgFevrXSzL4JtdZv8Awn418OaXpLmd3sL+G2EEc0BPyHzByrDoecZHtUX7Pt1c6aNd8NajFPbXkMiXQtZ02MoICsdp+bsnbuPWvWtd8M6L4nt1g1rTYbyNDlPMGGQ98MMEfgaAPOZfhjq8qRzeFPiRq8dg2GRJLlp1/wCAsrAEfh09a9I8P2F/pmiW9pqWpvqd3GCHumjCFvwHp09a8/uPgP4cMkjadqWs6ajnIhguAUH5gn06ntXY+DPDEvhPRjp8usXuqEymRZbtslAQBtXk4HGcZ7mgDxv9pCC+bVdFuGhX+z1gdElAOfNLZYHtjaFI/GvCq+qvjlqnh2HwbJp+rr5mozKXsFRQXSQfxZ7L2PqK+VaANvwmk0njHRI7eYQTtfwCOVuiN5i4Y/Q19x18N+FLpbLxhot0W2+TfwSbim7GHBzjIz9Mj619wSOsSM7sFRQSzMcAD1NAHwZcStNcSyMEDO5Y7FCjJPYDgD2HFQUrffP1pKACiiigArvfg27r8VdDKfeLyj7hbgxODwCO2ee3XnGK4Ku4+EH2n/hauhfZNvmea+7d/c8tt/8A47uoA6f46SND8WbOVUMjJa27BB1Yh24H1r6ahdpYI5GQozKGKHqpI6V8yfHdd/xWtV/efNawD92cN99unv6V9N267baJfn4QD5/vdO/vQB8m/GHwvq2ieONQ1K7t/wDQdRuGlt50OVbPO0+jD0P4ZFdJ4f8A2er/AFbSra+vtdgtBcQrKiRQGYgMAQCSyjoe1enfEPxr4X0bUtM8P+JdMW+gvSJHaRFZIBnAcg++enbP0r0JEWJFRFCqowqqMAD0FAHif/DNukfJ/wAT++4+9+6Tnjt6c/Wprj9m/wAPNZbLfWdTjusf62Ty3TP+4FB/8er2ms7VNb0vRVgOp38FmtxJ5UTTuFDP1xk8UAcN4C+D2i+DZhf3DnUtVRiY7iRNqxDttTJwcdzk+mK9KpoYMoZSCCMgjvTqAOB+Nf8AySLXfpB/6Pjriv2a/wDkDa//ANfEX/oLV3Hxgt2ufhTryKyKRFHJl2wMLKjEfUgYHqcV5x+zYJ/O187z9n2w/Jv/AIvm5259O+KAPoKvAPBsl0P2ldfSBkELNcfaFYnlRjGMcZ3bevbPevf68A8GY/4aW8Q5K5/0nGRz1Xp7/wD16APf6KKKAA14X8T7FIfjd4HvF27p7i3RvnBPyzjHy5yB83Xvz6GvdDXhf7Qojhv/AAjdvsURzzeY2Ru2gxHp1IHP0z70Ae6V4j+0hbQt4c0W6ZMzR3bxo+TwrJlhjpyUX8q9rjlWaJJEOUdQyn1Bryb9oezSfwBbXLMwa3vkKgdDuVhzQB23w9uZLz4eeH55X8yRrGLc3qQuP6Vtalp8Gq6Xd6ddBjb3cLwShTg7WUqcHtwa4z4N3dvc/CzRxbQNCkKyROrZILh2LMCeoJOeOBkjtXf0AfOXiX9nbUbc+d4b1BLxCeYLvEbqPZh8p/SvU/h38OtO8F6Lbia2tp9YILT3YjBYEn7qk8hQMD3xmu6ooAztZ0bTte0ubTtUtUurSUYeJyRnHIII5B9xzXi3iP8AZ2SfVLdvDmoJbWLcXCXjs7R89Y8L83GeCR9eePeqKAMvQNB0/wANaPDpemQLDbQjAA6se7Me7Hua1KKKAPk7wPBH4Z+PdrZPKblYb6a1EiNncWV0BJ4/vDP411H7SMdwNW0KVlH2XyJVUhTkPuGcnp024Hsfw5XxDu8N/H+WXEFuItWjmycBFRyrZPYfK2a7n9pLTZWtdD1RdxijeS3YbeAWAYc++08e1AHz3XWfDL/kpnh3/r9T+dcnXc/B+Gef4q6CsE3lOJXct6qsbFl/FQR+NAH2KSAMk4FeB/EnW3+Jt5H4V8JaPLqUljcbptQztijYZBCtnGD/AHieccZ61v8AxA8R6z4tvr3wT4IAkuIYmfUrtZdgjAODCD/eJwD+I7NjT+B1sLX4ZWymJY5Tcz+bgDJYOV59TgAfgKAPSqK8ktr+9sf2kL6zudQdbO+09Wt7dpTtJCLwFPAOVkPHqT3r1ugDxL4smy0z4p+DtT1axtbrTJVe3lS4ClD82CWB4wvmK3PHFdRrHwsgS8bVfB+ozeG9UONwtuLaXHZohx+XHsawv2h9OE/giyv/AJBJaXoAJXLYdSCAewyAfwFdV8KvFH/CVeBbK4kkL3lsPs91ubJLr0b8Rg/j360AYGk/EzVtA1uLw98QtPWzuZWCW+p24/cTc4BPpn1HTPIWvU5JY4YmlkdUjUbmZjgAepNZHifwzpni3RJ9L1OIvDIdysuA8bjoyk9CMn8z615OfgNqsr/2fN4zum0MMpFuVYnAzxtLbQR2PuTgdKALVx8Ydc8T31zpfgLw7NdMh2fbp/upk4DFeig4ONx/DtWD42+GviSPwtc+JvE/idtSu7MrK1lhjDs3DKqcjHU9Fr2/w/4d0zwvpEWm6TarDbxjkgfNI3dmPcn1/pUXjHSl1rwbrGnEIXns5FTeSAH2kqSRzgMAfwoA5PxZ4vtvAXw0stR0KxsE87yktbfP7obhuJwuC2AD3HrmuX+CXiK98V+NPFet6gsSXVzFb7xCpVBtyoABJPQDvXBaT4m0TxPZ+BfCuvy3aafYTTrfMzhI33f6jDZyAPunpgE4Pp6T8G9CsdI8XeMRo94l1pUU0dvBKHDMcZY8jggbsZ74oA634vwRT/CzXfNQNsiV1z2YOuDXxzX2f8UbeW5+GXiCKFNzC0aQjIHyqQzHn0AJr4woAKKKKACiiigAooooA+i/2b9MVNH1nVjEu6W4W2STPOFXcRj/AIGte51wfwe0RdE+GumLsZJbxTeS7upL4wf++Qtd5QB558brOO6+FOquyFnt2hljx2PmKpP/AHyzVZ+D11FdfCzRDExPlxvE2Rj5g7ZrpfEWmpq/hvUtPkVnW5tpI9inBbKnAzXnX7Ps0x8BXlncP+8tNSljEZIzGu1Dj/vov+tAHo3iLSF17w5qOks5jF5bvDvHYkYBrzj9ny4c+B76xkhaN7TUHRt3UkqpII7Y6VY+OF/qmj+GdO1XS9XnsZra9X93EwAmyDjI74x06cnIPGMz4WWOpeGfiX4t8OX9yLrzFjvfPZNnmsTneq5wM7znGeVAzxQB7NRRRQB4F8WLs6D8Z/CmsI75xEXVFXJQSFWAPfKkjn1rpf2g7Vrj4bpIM4t7+KQ4GeCrpz6feFct+0jClvqPhq/jyJ2WdM9RhDGy8fVjXY/Gdi/wandjlmNsSffctAHyjRRRQAUUUUAFfRvjfTbjWPDmifEjwdOy31lap5wRsM8QHIIBwSpyCO4z1wK+cq9++BvjvRNM8P3Hh7WtRS1lM7zQtdOFh8tlUFQxOByGOOOpoA9f8P8AiWDxH4Vg1jTWivZGgy0cTbB5oHzJ833eeOfY9Oaj0fxHqWo3EqX/AIZ1DSoY4DKZrmSIqSCPlG1jzgk5OOlcN4g+C4OqnWPBWsyaFcOdzQxFhExznKlTlR7YI+grOufh3rsVu9547+Ic8mjQjMtulw6LMBn5SWIAJ5HQk0AeeSRz/GL4uuqAWlvOxDMvzGOCMdc9CTgD0ywr1ubw3488C26y+GNYfxBp8eA+m6iAZQo6+W+R78cfQ0z4L+DbHTdOufEyWkkEmpSObOKbDNBa7vkGepJGCTxkYr1qgDjfBvxE0jxl50ECy2WpWxxPYXICypjgkDuAeM9u4FdlXkHx0sNPsPDkHiSEtZa7BdRx2t3b/JI5OSVZgM4CqxGSOnvg3fhP8Uk8ZWf9man5cOsWsa5YsALpehcDs2cZHvkegAK3xk8U6rZ3Oi+GNDuprW71ST99NCDvWPcFAUjnk5JwQcL70kX7P3hr9zNPqutG9X55LiOdFLydS3KEjnpzn3NWfilA2ja94c8cjTTfWukPIl6qnLBGACMATj5WLHPqR26Saf8AHrwNepm4urywPpcWzH/0XuoAxvGPhXQ/Bfh6WOx8L3/iXV9TRoVurpDdNEQMbi2DsPzZG0DJB54rn9IPiD4D6HHeanZabfRarKBLbRylJ43VSQPMCkFQM5HIBPHUmu/1j44+CtNsPPtdQfUJmGUgt4mDH6lgAv48+1fPHj3x3f8AjzWVvbpBb28KlLe2VtwjB684GSccmgD2Cw/aS0qRgNQ0C8t15yYJlmx+YSq3ij4vWPjrQ5/C/hzRNSudQ1MeQon2xhehyNrHPQ9cD14yK8H0ua0ttWs57+3NzZxzo88AbaZYwwLLntkZFfYHgW58Hanpiah4UstPtt8aiVYIEjmT/ZkwM5Bzycg9QT1oAueAfD03hXwNpei3EgkmtkYyMvTczs5A+hbH4V4L+0T/AMlCsvn3f8S2Pjj5f3knH9efWvpTUJbi3066ntIDcXMcLvFCCB5jgEhcnpk4FfN+n/CPxt431x9W8Tv9hjmk3TPcNmUrnoiDOOOBnHSgDxyvS/CvwR8VeI4kuriOPS7RwGWS6zvYeyDn88V7v4d+Hng74f232wLCJwMPf38i7uvbOFX8APfNLrXxf8E6LCXOsR3knOIbH98xx7j5R+JFAHml1+zXdrZlrTxLBLc44jltCiZx/eDMf0rufhPcaNpWnt4X+xx6Z4iswFv7eTAknYDPmA5y6kNkegPpisi78R+PviJKlv4U0+48O6SMM+o3w2SSjtt4PH+7n3Iziif4C276WblNevm8TBzMNSZyA0nUZHJAz3Bz39qANf4naJqtlqGn+OvDsLTarpK+XPB1E1t8xYY9snpzhj6Cu18N+ItP8U6Jb6rps6yQSjkDqjY5VvQiuU8FeO3vb3/hFfE8bWfie2yjo6kJdKP40PTkc479R7ZWueC/EPhbxLN4p8ALA63Ck32kysQkzZJLKMgZ9uCDnHBxQB6xRXn+jfFzwxqV0mn380uj6oQBJa6hGYvLfuu4gD88ZrvgwZQykEEZBHegDzX4x+DLHxF4Ru9VcJHqOmwNLDOSBlByyNk4wecehr5Nr7j8WaGfEfhbUdHEoia7gaNXIOFbqCcEcZAr4iuIJba5kt5kKSxOUdGHKsDgg/jQBt+Av+Sh+Gv+wpbf+jVr7ZkRZUZHUMjAhlYZBHoa+JvAX/JQ/DX/AGFLb/0atfbtAHwE33z9aSlb75+tJQAUUUUAFd/8F/M/4WzoflhS2Zs7jgY8l8/jjNcBXovwQieT4saQyIzLGk7OQMhR5LjJ9BkgfUigDT/aBYp8TI2QlWFjEQQcEHc9fTunktptqWJJMKEk9+BXzN8c447v4s21t5n3ra3ifaeVyzfrgg/jX07BEILeKFSSI0CgnvgYoA+RvjH4gtvEPxGvJrQ5gtUW1V/75TO4/wDfRI/Cq9j8WvHllZi1g8QXDRBdoMsSSsB/vMpb9a9R+IfwRm1jxVb6h4cSGC2vJP8ATkLACE55kUHqDz8o7/Xj22xsrbTbKGytIlitoECRxr0UCgD5DX4veP1DAeIbg7hg5hjP5fLxWf4o8c+KfFNvDaeIb9p44X82ONreOLBI6/Kozwe/rX2pXz1+0ZrttJc6ZoSwKbiIfapJscqpyoUcdDyevYUAeTaH408R+G4zHpGs3VrETkxK+Uz67TkZ/Cvf/hl8Y7LXrODS/EV4kOtAlRM6hI7gZ45HAb1HA9PSsT4G+CPDer+FbjV9Q0+31G7a5aArcR7lhCqpwARjJ3Zzz1A4wa9CvfhD4Dv5jNJ4ehjfGP3EkkQ/75VgP0oAm+KtpHe/DDxBFJvCra+aNvXKMHH4ZUZ9q8u/ZrtpvtHiC62fuSkMe7I+9ljjHXpXqXxNmgsfhf4gLtsj+xGJeCeWwij8SQK8v/ZruH8zxBbeZ+7xDJ5e3v8AMM5/pQB9A1886NGlx+1TdSWVu4hhmnaXJzg/ZyrN9C5/8eFfQ1fPnhGOdv2m9bMJjCK9yZt45KYA+X33FfwzQB9B0UUUABrxn9orSluPCWm6nhd9ndlMknO2ReQB06ovX0r2Y1538b7WK4+FGqSSKS1u8MsfOMN5qr/JjQB1/hu7OoeFtJveMXFnDL0x95AemTjr6muR+N1slx8KNWYx73hMMif7J81AT/3yWq78JHVvhZoO1gcQEHBzg724rQ+IcMtx8O/EEUKF5GsJcKvU/KaAOQ+AN39o+GwhM5ka3u5U2Fs+WDhgMdhyT+Jr1WvCv2bdQR9K13Tiqh4p45wd3LBlKnj22Dn/AGq91oAKK4bxD8UNB8MeL7bQNV8+AzRCVrrbmOPJIUN3wcHnHHH1Fn4geI49I+G+q6vZSrL5lsUt5YjvUmT5VYEZBAzn04oAdL8T/BUM88EniOyWSBirjJ6g4ODjB59M1lav8Z/BOl2Uk0eqi/nT7lvaozM/IHBICjrnk9AcZr5c8P8AhvVvFWpHTtGs2urrYZCisFCqOpJYgAZIHJ6kV3dl8AfG11A0k0dhZuBxHPc5Zv8AvgMP1oA+mND1qw8RaNbapp0wmtbhAykdR6qR2I6EVp18daF4s8UfDDXrnTo5giwXGLuyYh45GHB55wcDqvNfWeiai+r6FYak0D25u7dJ/JcglNyg44+v/wCqgD5j+N0Mul/Fy4vopysk0dvcxsowYyqhB+OY8/jXqfx2RNX+FEGowSYhjuoLpdy8srKyge3+sB/CuK/aP07yfEWj6gI1AubZ4i4PLMjZ6ewcfnXd36HxT+zqZZxCJF0oT8Z2qYRu9euE/M0AfK1WrCC7ub6GCxSV7qRwsSw53lj0xiqtegfBMhfi3ohJAH78c/8AXCSgD6W8DeELTwX4Zt9MgCNPgPdTgcyykcnPXHYe1cd8ELi5Sz8TaRcoytY6tJwzZ2luCuO2ChPHcmvWa8e+G4l0/wCMHj3TZLlWWW4N0sYOAS7ls49QHANAHM6l4dvviNrPivxbZ6jLZXujXP2awiUYx5IySW6jPJ+p/CvXvh54jbxV4F0vVJMm4eLy5yf4pE+Vj+JGfxrhvFHwx8Xm+1qTwp4jitdP1aTzp7KTMZ3kYbDKp6/hwcHOMnsvCGhxfDz4fQ2l/d70sYJLm7mUEqp5d9oAyQOccZOPwoAyvjfpx1D4W6i6h2e1eK4CoM5w4Bz7BWY/hXC+Emg+GWueHrqC8nl8MeJbRPNknPENxtHPAGBkgcgcE8nFeo6peWPjn4banJo9ybm3vbKVI2jQlt20/Lt67s8YrkfDHh7/AITz9n3TdKu5As7ROsExUfu2jlcJ+ihT3wT3oA9cBBGQciivNvhZ4quJraTwfrvmReIdHBjkWQH97EpAVw38XUDPcYPevSaACmOiyIyOAysMEHuKfRQB83eEfhlo2teLfGfhvW43gvbWVJLN7csvlRlnJKgjaQQ0XUdDxXWfA2w03SL/AMWaZbXKXVza3oiE/l7WeJcgHHYbg3Gaztd1GHwX+0ausapOkGmalaDfO8bEIBFsAGO++NecdG/Gtj4FzwXY8WXluQ8U+qs8b4wWU5I6896APQPG/wDyIPiP/sF3P/opq+H6++ZYo5onilRXR1KsjDIYHqCO4r4Ib75+tADaKKKACiiigAra8J6a2seLdJsBD5wnuo1ePONy7gW/TNYtesfs/af9q+IjXZhDiztJHDk/cZsKD+RYfjQB9TUUUUAFeMfBbOn+MPHWir88dtfEiQjBbEki9Pwr2evHNDjh039pbXo5JsvfabujG0/ePlNt/JCc8UAdd8V9Ot9S+GetpcIT5MBuYyMZV0+YH9MH2Jrgb/XILf4veAdbMkkjatpyQztAeJGkDIvGQNodgT9M8kCvW/FNk2oeEtXskiSaSa0lRY3bAYlTgE18/wCufP4D+GXii0/c3FlMLTcVBOUkwp9MBo2PPXdQB9MUUAgjIORRQB4D+0z9zwx9br/2lXafFm0e8+DN2I2UeVFBK27uFZc4965D9pSVBZ+G4jEpdpLhhKc5UARggexyD/wEV1nxImF98DZ7lftMCy2dvKE4VwDsO1xn8xQB8nUUUUAFFFFABX1/ofgvQtf+Gvh6z1i0i1FRp8LJO4w6hkDfKwwwAzx9BmvkCvuDwP8A8iB4b/7Bdr/6KWgDh4/gxNp4aPRfHHiHTbUniCOc4Hp90r/KrGn/AAY0v7et74h1nU/EE8bBoxeznYMeoySeffHtXp1FADERYkVEUKqjCqowAPQU+iigDxr9oD7Re6b4c0a3yxvNQwEVdzFwNq4HU/fPHevCfF/hm68F+KrnSJ5S7QENFOF2eYpGQwGePz6ivWfEV+fGf7ROi2Fi7mHRpkWQk5XfE5kkIHGOQE/4CDVP9o/Spo9f0fWMgwTWptcAH5WRi3J6ciTj/dNAHll14x8S3umtp11r2pT2bcNFJcuysPQ5PI9jWFRRQAUUUUAFeg/DT4c6p41v2dZZrHS4hie7UEb8/wACdifX079q0vhD8M08ZXz6lqqONHtHAKDI+0v/AHN3YDvjnkDjOa+jNU1DR/AvhSa8aBLXTrGMbYYUAz0AUD1JIFAGBv8ADfwZ8EFDNK0KsXRHdTNcyHAOBx7dOAK5bTrv4nfEWRr21uU8K6G7Yj3Rbp3XH3hkAt165UenSoPAHhWf4g6rL478YRSTJJLnTrKUnylQHg7T1Udh0PJOc17cAAMAYFAHltr8EtKubyO/8Tazquv3i/eNzMVjb0GOWAHpurrdL8A+E9FlSaw8PWEUyMHSUwh3Rh0IZskH6Vq6rrWmaHai51S/trOAttDzyBAT6DPU1YtLy2vrZbizuYbiBvuyQuHU/QjigCxRRRQBx/jX4faX42iha5eW11G2Oba+tziSPuAfUZ5xx7EVxmlfEHV/Amsy+H/iAZXtEJFlrQgYiZQeN+M5yPTJB65617HVa8sbTULc295aw3MJ5Mc0YdT+B4oAwb7RPCPxA0+K6ubaw1e35EdxG2SPUB1II+ma5zR/g9p3h7X7bUdG13WbSCKUSyWazgxyYP3Txyp6EHJx3qtqfwZt7e6kvvB2u6h4dupGy6QSMYmGc4wCCB14yR7V6XaRSw2cEc0xmlSNVeQrt3sBgtjtk80AWK+N/i1Zf2f8Udeh3Bg06zcDGN6K+Pw3Yr7Ir43+LN2178UtflZQpWcQ4HoiKgP5LQBT+G9q158SPDsSOilb+KXLnAwjByPqQpA98V9qV8WfDWGC4+Jfh5LmXyoxfRuGzjLqdyj8WAH419p0AfBuo201nqd3azhRNDM8cgXpuDEHGO2RVOun+IdrFZ/EPxBBCpEa30hAJz1OT+prmKACiiigAr1D4CW3n/E+CTzXTyLWaTapwH4C4PqPmz9QK8vr1/8AZ4tGl8eXdyuSsFi4PA/iZR6+1AFPx+kGqftCPb/aFWGW/s4HkBGE+WJW/I5/Kvquvk0mHVf2iFaGWLym11W3SHaG2yAkc9ztIA7kgd6+nvEWsw+HvDuoavP/AKu0gaXH94gcD8TgfjQBwni34vWnhb4g2Xh+WBGs9qm+uCTuhLjK4A9BgnPY13Nl4m0HUQv2LWtOud3QRXSMT+ANfEeo302p6nc31w26a4laRzknknPfmrr+FfEUVmt3JoGppbHpM1pIEP44xQB9xeYu8JuG4jIXPOPWuG8Z/Cfw7421BdRv3vIL1YwhltpQN4HTcGBHHtivkyWz1PTik0tvd2x4KOyMnUcYPuK+hfgX49uNZs5PDWpyTzXlohkt52G7dFkZVj6gnjPY+1AHafDnwJL4B0y+086ob2Ge486MeVs2fKB6nJOBn6Cu2rH8P+I9K8UaadR0a8F1a+YYywUqVYdQQQCDyDz2IrYoA89+NcqR/CbWVd1VpDAqAnBY+chwPU4BP4GuN/ZrA/sjX2wM+fEM/wDAWroP2gSB8NMEjJvYsD14asv9nCy8vwlq175mfOvvK2Y6bEU5z77/ANKAPaK+fvB0Hm/tM68/myJ5LXL7UbAfouG9R82ceoB7V9A18/fBhYp/ix4tnURyAecUkwG4M38J96APoGiiigANYPjO2e78D69bxx+bJJp1wqIBks3ltjHvnFbxprKsilWUMrDBBGQRQB5X+z7fG6+GzQMFH2S+liGDyQQr5P4uR+Fem31pHf2FzZylhFcRNE5U4IDAg49+a8Y+A0q2Wt+LtEki8m4iug5jOBtCsykY9jj9K9woA+ZPgBcnTfiBf6fcK8U01q6FHTBDIwJByRg/gfwr6L1m/bStGvtQS2kuWtoHlEEX3pCoJ2j618yyzL4c/aOEjwLBENYAIk+RVSU4389sPuz3r6qoA+KPE+tXvjrxvNftbCK5vpkiit9/CcBFXJx6DJ45zX1t4N8ODwx4M07QpJvtJt4isjtyGZiWYD/ZyxA9sVQ8W/Drw/4vhZruzS3v87o7+3UJMrdiSPvD2OfwrwTxp4j+JXgvU30TUPEV75QGbe4UqDNH2YNjdn1yc5oA7X4ytH4F1TRfEHhgQ6Xq03mwytbxoBLHwfmTGG5PUj09BXc/Cnxdq3jPwm+patBbxyLO0KPACBIABkkEnByfpXyjq2u6v4gmSXVdRur2SNdqNPIX2j0GelfSvwcsTe/B02Jhe1NybiPzWBPmbsjzADjjnHHHy+uaAPm27uP7d8UTTyBoxfXhcjduKB36Z74zX3HBEILeKFSSI0CgnvgYr5ptvgj4k0Lxdo808MGpaWNRgE727HIj3qWLKcEDGc4zX03QB4r+0dZLL4Z0i+WFmeC7aPzOcIrryD25KL19Km+B1zb658K7/Q5EQmGWW3kRskMkq5BP1ywx7e9dT8YrWW8+FWuRwoHdI45ccDASVGY8+ig15P8As56tHbeJdU0qRyGu7ZZYgW4LIeRj1w2fopoA8buYDbXU1uxBaJ2Qkd8HFPsb2402+t760laK5t5FkjdeqsDkGt/4g6UdH+IGu2WAFW8d4wpJ+RzuXk8k4IB989a5agD7E+H3xK0vx3ZKqFbfVokzcWbHntlk9Vz+I79s4cWnJY/tJSTLsX7bopnIVcYO4Ic+p+TOa8C8AeHtX8R+KY4NC1C3sdRt0NzFLNKU5UjhcAknnpjoDXpPhzXfE93+0BpNt4jigt9RtrZ7GURZVZYxHI4YnnOSd3GATjpQB9FVxnxTmtIfhnrxvGIja2KKAwUmQkbOv+1jj0zXZ15R+0E9yvw3jEG/y2v4hPtXI2bXIz6DcE59cUAUf2e/EFrd+E7nQlwl3YzNKVLcujn7w47Hj8vWtn4LyrD4e1jSow/l6bq08Cbm3fLnIA/z3rno/EnhqP4j+Cbnw1PaSSXsElpqC2gAJUogiDjsQ2T2PGK2/gv/AMzh/wBh6f8ApQA74r+Fr1vsnjTw8GXW9IIdljXmeIHJBxycc8dwSK6PwH450/xzoS3toypdxKq3dsesMhH/AKCSDg9wPXIHW14l8QtH1P4e+Ix498JQotu42apaqgEWOAGKjHDHqR0YZ7mgD22isvw/rdn4j0Kz1iwYNbXUe9c9QehB9wQQfpWpQB5b8arSe10bSvFdmiNc6BeLLiTlSjsqnIzz8wT3rB8J3PjTwtNf6+vhi21PRdacagy6VOpeHdz8inluDyAOvevUvGeiJ4h8G6tpTgf6Rbttz2cfMp/BgDXH/AvVxqPw4gtHkDTWE0kDDJJCkllzn/ewPYCgDp/CfjjR/GVrJJpzyR3ELFZ7S5ASaIj+8uTx79Px4r5T+I+jyaF8Q9bsZJVkP2kzBlGBiQCQD6gOBX0L8U/DE4sv+Ey8OsLLX9JUzvPGoHnQqDvD54bAGRnOQCMHIx8zeI9fu/E+v3es34iW5unDOsS4VcAAAAknGAOpoAyKKKKACiiigAr3j9my0jfUPEV4S3mxRwRKM8YcuTn3+QfrXg9fRn7N8MaaJrdwIpBJJcxo0hI2sFUkADOcjcSeP4h17AHuVFFFABXiWoXcFn+1FY7FlZp7QQyZIwGMTYI9sAfjmvba8S8eyHTv2hfBl88DmGaGO3VgMbnaSRP08xSfagD2ieCO5gkgmQPFKpR1PRlIwRXzbPJNqH7L8Kxw/Jp+pFXYH+EyMdx/GUCvpevnbR7R7n4C+NNIsGluDY37nLqI8xxujs3PP3EJIPPYUAe76BeR6h4c0u9hDCK4tIpUDjBAZARn35rSrj/hXNLcfDDw+8rl2FqEyfRSVA/AAD8K7CgDwH9pn7nhj63X/tKu2+K94bP4MXhCBvOgghOTjG5l5rkP2k4Im07w9cGdRKk06LD3dWCEt+G1R/wIVt+OrO6uf2d7ZXYNPDp9lJMzPnO0Ju55yf50AfLtFFFABRRRQAV9sfDy6ivPh14eliztGnwx8jHKIEP6qa+J6+w/g7dxXXws0QxZ/dI8TZGPmDtmgDu6KKKACqmo39vpem3N/duEt7aJpZGJ6KBk9at15H8e/FCaV4QXRIbkpe6kwDInXyQctn0BIA9+R0zQBifBKCbxF4z8TeNLq3dRNI0cLE7lVnbeygkZyqhB7A+9aH7R+3/hD9KySD9v4GOv7tq7L4WeHj4b+H2nWk1q1tdzKbi4jcYbe/8AeHY7QowemMdq88/aUvXSw8P2Cldkks0zj+IFQoX8Pnb8qAPnmiiigAooooA+0tEXRfAXgvSLO5vIre2VY4UlmIXzJX5/MnJ+g9q474+efd+HdG0e3ljEmoamkQVjjPBAP0BIyfeszxF4m0fx/pngXQ9Pn8+6uNQtri7hgfL2yIhEgbI6jcecc7fer3xGu3f4z+AbL5fLilMox13O4Bz+CCgD1XTdPt9J0220+2XEFtEsUYwBwowOgAzV2mlgqlmIAAySe1MhmiuIVmhkSSJxlXRgVYeoI60AYvizwlpfjLSP7N1aJ2iDiRZIzteNh3U4PbI/GvNW+FeueAWl1jwDrNxPMq4fTrxFYTrnkbsqM8egPoRWJ4q+IHxA1X4j3vh3wn8hspmRIoIkZnC4BZ2fIxk+wGfxrf074m+KvC1/aWHxG0X7JbTfuxqcIBXd2LbCVPvtwR6UAdf8P/iBa+NrSdHgay1Wz+S7tHOSp6bl7lc5HPIPHue2rjbLwx4W1XxQvjDR7pHvACskthdBo5sj+MLkE/4CuyoAKKztbk1WLRbp9Fggn1JYyYI5yQjN6Egj+YrhfD3xc0xpG0rxe0eh6/A+y4hlBEJbqCr8gDGOp/E0Ael0Vlf8JFoghaX+2dP8tVDs/wBpTAU9CTnpyOa5XxB8YPCGi2TvDqcWo3RyIreyPmlm7ZI4Az7/AEzQBo+PPHGn+CNAmvZ5I3vSuLW0LfNK/QcdlHUn29eK+Ob+8l1DULm9m2+bcStK+0YG5iScfnXuPhn4Z+IPHfig+KPHUcsNpIfMW1c4dx1VNvVEHoefzzXqvif4d+G/E+kfYJ9OgtioCwz2sSpJDj+6QOnbB4oA+WPhxHDL8SPDqXE3koL+Jg2M5YMCq/iwA/GvtWvkC/8ADF58M/iVpI1MebawX0VzBcqNqzxLIDnnhTxyM8e4wT9eqyyKGVgysMgg5BFAHxb8SI/L+JHiBN7Pi9k+ZzknmuVrv/jPEkXxY1xY1VFJhYhRgEmFCT9SST+NcBQAUUUUAFfQX7NumKItd1ZlO4tHbRnPblm4/FK+fa+i/hPLFo3wP17Vlkljk3XLs6HlSsYClfQ9KAPO/hVbp4j+MNndX2C/ny3xAXgyDLj6Ybn8K+qNX0u01rSrrTL6Pfa3MTRSL7EdR6EdQexFfOP7PGnm58dXl49vI6Wti22YA7UkZlABPTJXfgH0PpXqXxZ+I0vgXToLbT7fzNRvkfypZPuQgYBbHc8jA6fyIB5/4Z+HOlaD8chpM99Dd21nb/bIIpmAd3P3UYdyv3uOoAOMEivouvgu8vrrUb2a8vJ5JrmZy8krnLMx6kmtHS/FniLRVVdM1zULVF6RxXDBP++c4P5UAfcdcr448YWHgXw/Pqdyge4lOyCFcBppMcZ9h3PoK+bLH40+PLK4Eja19pXvHPBGyn8gCPwIrE8YeN9b8b3sNzrE6N5ClYool2xpnGSBk8nAyfYelAHVfDL4pv4Q1i7j1JWk0m/laaZIVGYZD/Gq9MdiB2x6Yr6e0jVrHXNLh1LTblLi1nXdHInf6jqD6g8ivnf4Z/Ba414xav4likt9KdA8EAfbJP6E45VfyJ4xxzX0RpWk2GiafFYabaRWtrEMJFGMAep9z7nmgDyb9pAj/hEtIXIyb4nH/bNq2vgLbRQ/C+2kjTa89zNJIcn5mDbc/kqj8K4n9pW7ie88O2Yz5sUc8rccbWKAf+gGvWPhlC0Hw20BHQo/2RSVK4PNAHW187fs7w258TeIJYpzhYFWON1+dkLk7jjgYwAR/tV7zrVzJZ6FqN3AQJYLaSRCRkBlUkfqK8b/AGbbJV0jXtQLgtNcRQ7dv3dils599/T/AGaAPdKKKKAA0UGigDwSDPhj9pqZruT7NDqynyccLL5igKDjrmRfzHrXvdeFfFie78PfGDwn4kWEvbCNIOh5IkfeuegO2TivdaAPmH4+6e2l/EW11aHarXdvHLnB5eM7cn8Av5V9H6Nfrquh6fqKElLu2jnUkYOGUN07da8f/aP0yS40HRtSRXZbSeSJ9q5UCQLyT25QD8a634Na62ufDawMkgaayJsn2rjAjA2j3+Qp0/nmgD0Kud8TeCtA8YJbLrliLn7MxMREjIVzjIypHBwK6KvJvEPx10jw54rvdFuNKup4rRxG9xE65L4+YBDjgdM55oA9G0jQdK0G0FrpWn29nEABiGMAnHqepPua068L1H9pKwQEab4euZj2a5mWP9FDe3euK1f4/eMr8sLJrPTkIx+5hDt+b5/lQB3Xxk8feJ/Bvi7SU0q4SOwa285omRWEz72DBu+MbemOtdh4I+LGgeMkitzKthqrcGzmblj/ALDdG6dOvtXyhqmrajrV617qd7PeXDAAyzOWOOw56D2r1D9n3QLTVPFl5qdyC0mmRK8K9t7kjcfoAfzoA+lrq3ivLWa2nTdFMjRyLkjKkYIyPavkTwU954P+Lmm2txmKaHUBZzgkoNrtsJ5HTB3c9eK+w6+UvjhpcmjfE2S9hiMKXccdzHICSGccMee+V6fT1oAv/tDaYbTx1a36oRHe2S5YsDl0YqQB2+XZ+deP19RfEvTLXx38IbbxBBcEPaWwv4mb+IbfnRgDgH88FcV8u0Ad78G7mW1+KmjCLH71pInyM/KUbP8AKvT/AIg6Ubf48+ENRgKRm9MaseWJeNyCSOmNpQceh/HyD4ZvdJ8S/Dxs13S/bUDDA/1Z4fr/ALG6vdZZP+Eh/aMtwhma30DT2Eg2kxiVw3rwpxIOe+wUAek6zr+leH7eOfVr6G0hlkEaPK2AzHtVm6tbTVbCS1uoo7m0nTa6OAyuprxX9pDUrUaPo+l7wbtrhrjYP4UClcn0yW4+hr1vwzqtprfhnTtRsnDwzW6EcglTtGVOM4IPBHqKAMXw/wDDPwn4V1h9X0zTvJuQrBXklZxEDnJXcTjg4z6fjXPfBW6g1C38U39rF5dtc6xJJEOcFSAc881s/FrxOnhnwBfOr4u7xfstuMZyzcMfwXcak+FPh2bwx8PNOs7pCl3KGuZkJ+6znIHthdoPvmgDt64T4w3r2Pwr1x43VXkjSEbsfMHkVWA99pau7rxv44zSavc+GfCFs7CbUrzfJt52qCFBK8Z+8x6j7vvQBifCGbXvBGr6bomtQMNO8RxG4scNny5FGTkdsrjI/wB2vf68j1yaKf4y+CfD2nDzRodvJJOd+WjVowoDe+FU/wDAq9coAK8G/Zv1Am317TfL+7JHP5m7rkFcY/4D1r2TxHqY0Xw1qWpkgfZbaSUErkZCkjj64rzz4D6VDpfw6OrSKqvfTSSs4OTsQlR9OVbigDW+K3iuHRvDkmhQQtdatrkb2VrbJ1O8bCx/76wPU496+ZfFng/V/Bmpx2GrxIkskQlRo33KwPHX2PFe1/D+Ob4kfEzUPG+oRsLDTT9n05DnAYZK898KxYj1cGuW/aKgkj8aadM87OktiNsZ6R4ds4570AeN0UUUAFFFFABX0t+zd/yKGr/9f/8A7TWvmmvpb9m7/kUNX/6//wD2mtAHtFFFFABXhfxnuW074k+CdQeQyQwzLIIMAYKzISc9eRge233Ne6V84fGlDqPxk0CztSss5gtofL3AYdpnIBz0yGX86APo+vG/hs5s9W+IuiSzL58V7JOApHIfeCQCMnGFz25H4+yV5D4LsRZ/HvxvCX3h7dJSSuP9ZsfH4bsfhQBe+Al5Jd/DOKOQf8et1LCp8zcSOG6fw/exj2z3r1CvI/ga89vB4q0mWONPsmrOcK2SGYbWGQcEDyxjHvXrlAHgn7SpT7P4bGzMm+5IfdwBiPIx78fl71v+LYriX9my0FvLs2aTZNJk43IFjyPxqn+0j/yKGkf9f/8A7TatfX1Lfs3RgAk/2FanAH+xHQB8pUUUUAFFFFABXvv7OfiSZp9R8MPHuhCNfxyZ+6cojLj3yp/A+teBVteF/El94T1+21awkKyRN8yZwJE7qfY0AfclFZ2h6xZeINGtdW06XzbS6QPGx6+hB9CCCCPUGtGgCKWWOGJ5ZXVI0UszscBQOpJ7Cvn/AMPt/wALY+NU2tMjNoukBTEpTKsFJEYORxubc3TOBj3HX/Gvx5B4e8NTaHaTEatqEe0BGwYoicMx+oBUfXPatn4UeCl8G+Eo0mT/AImV9tnuyVwQcfKnPPyg9+5PrQB3tfKvxeuLnxd8W5NM0qNr2e3RLKKOIBiWXLMOPRmbOemDnpX0p4j1qHw54c1DWLgFo7SEybQMlj2H4kgV8y/Cq4vbr40aTqF7DL9ovXubgsy4374pMsM9RnPPsepoAxD8KfHQnEP/AAjV5uPORt2/99Zx+tYuteF9c8NvGusaXc2fmjKGVMK30PQn2r7id1jQu7BVAySTgCvP/jHo58QfDG/NsIpXtMXqMX4Cx53kHudhagD5Eoor2P4RfCqbXby21/XbUro6fPBGxwblgeDjrsHX3+lAHoHwX+Hg8NaMuvalAV1e9T5VcYMER6DH948E9+3rnmbe+i8ZftMRSwQlrTSt8ZbcBnyVYb+DyPMIxjqMZHWvTviZ4q/4Q7wNeX8Sr9plxa2wzjEjg4P4AFse1eOfs6wJP4y1S5kBaaOy+VyTkbnGfrQB7x44/wCRA8Sf9gu6/wDRTVynwJ/5JVp//Xaf/wBGGur8cf8AIgeJP+wXdf8Aopq5T4E/8kq0/wD67T/+jDQBheO01L4d+PB490uxN1pd5EINTiQ4CngBj6Z+XB6ZBz1GbP8AwuPTdZsFjufBGv3djcrgj7Gs0cg9BzhhxXRfGSCS4+E2vJEhdgkTkD+6syMx/AAn8K2/A96dQ8C6FdFAhksYjtBzj5QP6UAeKTJ8PLxmab4Y+KrVsg5toJBn2x5gA/Kqxtvh9ub7P4W8e2jw8uLeM/KDzk5c4yAP8819KUUAfNK3ngzynjsNN+IzO5CsiSbQ49Dhj2z29aGsPhvCrTXvgzxwxL7mlmiPOfU7x3/GvpaigD5tguPhCIW/4oTxLIYzhmZZM8+uJsCum0Tx98MvDty/9leGL20miAHnDTsyYP8AtFiw/HrXtlFAHlh+P/gsAkLqZIHQWw5/8epj/tAeDVKgR6q+48lbYfL7nLfyr1amJEkYIjRUBOTtGMmgDxvW/i78M/EVslvrFheXcMb70WW0+63qDurrvCfxQ8L+K7uTT9Mlmilhh83bcRbBsXgkHJHHFdjLZ204cTW8UgkxvDoDux0znrimQ6dZW+/yLO3i3rtbZEq7h6HA5FAHyJ8WdX0zXPiJqOoaVcG4t5BGpl/hZlQKdvt8o/HPbFcPWr4jhjg8T6tBCixxx3kyIijAVQ5AArKoAKKKKACvpfxVbDwT+zrHp0CGOe4hihlI2t+8lIaXJ7j76g9QMelfPegad/bHiTTNMLBReXcUGT0G9wvb6173+0Vex2nhjRNJjkdTLcM+wHgpGuOfxYY/GgCT9nHSHtvDeraszfLe3CRIvoIwefzkP5V6tr2gaZ4l0mbTtVtY54JFIG5clDj7ynsR6iuP+B9ktp8K9MkG7ddSTTMG7HzGUY9sKD+Ncl+0P4le1sNM0C2n2Syy/a5vLfDAJwgOD0JJPI6qMdKAJvht8Ho9H1vW28TaTb3cMUiR6e0+2VJEyxLbfXGzqB34r0C8+GHgm+B87w1p6k5z5Mfldf8AcxXl/hf9oa2hsLa08RabdPNGoRrq2YP5mP4irEYPrya9N0b4oeDddiDW2v2kLnjyrtxA+fTD4z+GaAOb1P4AeDL1P9DW80992cwzlxj0w+aydF/Z50rTdaivNQ1h9Rs4ju+yNbeXvPbcwY5Ge2Oa9G8QeNvDnhi1gudW1aKKOeQIm3MjN152rk4GOTjH4kVsadqVlq9hHfaddRXNtKMpLE25T/n0oAuUUUUAfLnx5v5NW+JcelQI0j2cEUCoqZZnf58D14Za+l9Ms/7O0qzsi+/7PAkO/GN21QM47dK+V57hvFH7QCvM7R+ZrKxgnBKrGwVR+SAV9aUAcd8UtSk0n4Za7dxFlf7OIlKHBBkZUz/49XLfs+WAtvh7LdYcNd3jt83QhQFBH5H8qj/aC1mKz8Ew6Z5zLcX1ypEasBuROTuGckZ29iMgV1PwmspNP+F2gQTEFjA0vTGBI7OB+AYCgDtaKKKAA0UGigDy347aCmq/D5r5QftGmyrOpzj5D8rD9QfXj610fwz8RReJvAOl3aNI0sMK21wZOplRQGPvnr+NX/G2nHVfA+uWKwefJLYzCKP+9IEJT8dwFeZ/s7azHP4e1PQ5GC3FpceesZGCUcAE/gy/hkUAdx8VNIXWfhtrcbYDW8DXSFiQAYxv7ewP415d+zfq4W81rRmIy8aXaDn+E7W9v4l/yK+gJYknieKVQ8bqVZT0IPBFfKngOZvCXxzGnpcmKH+0JtNcqpxIpcqq49CwT6cHtQB9UXguDZzC0KC5MbeUZM7Q+OM47ZxXxt4u8JeLtK1K8vdf0y7LPKWlvBGWidmOchx8vPpx9K+0aKAPmvwB8C38QaRDq3iC8uLOC4G6G2gUCVk7MWYELnqBg8EHivV9P+DfgTTsFdCS4cfxXMryZ/Anb+lV7P42eC7jULmznvZ7J4XZPMuYSEk2nGVK54+uK72zvbbULOG8s5kntplDxyxnKup6EGgCrB4f0W3sjZQaPp8Vqxy0CWyKhP8AugYrltEHgXwv41vNC0mGGx1q7jSWWFQ4WQckBc/KCAc4GOv5d3XzT+0HbaXD4ss7+zv0OpvEEurdGy0e37jn+6SDjHsDQB9LV45+0NoYvfB9prCKglsLgKxIGTHJx16/eC8e5qh8FPiXrWv6i3hzWHN4yQNNFdOf3gCkDa397r1PP1r13xHpaa54b1LS3AK3drJCMqDhipAPPGQcEe4oA8w+B2oweIfhte+Hrlm3WzyQPhsnypASCM5xglh0xwK+ctU0640nVLrT7pClxbStFIpB6g4716J8FNeHhr4jCxu9yxX6NZON+FSQEFWI6HlSvtvJz6y/Hjw1HovjcajAkgh1SMzHdkjzQcPg/wDfJx23dhgUAed6HrV74d1i31bTnVLu2YtGzKGAJBHQ+xNfU3wg0Oe18MPr+por6vrcpvZp8DcY3wUGR0GPmx/tV8raRaNf63YWaxGVri4jiEa9X3MBj8c19eeK/HugfD4aVY30c6pcERRJBHkRRrgbj7DI4GT7UAcX4tj0Sf496PF4jsYGspdNZInuAvlvJlsb88EDkDryRVrwB9k0H4ueJfDOjyq2kParfJEkm5IZMoGVf++/0Fdr4v8AAmh+N7NINWt38yL/AFVzCQssfqASDx7EEVmeD/h/oPw2s9SvbeaWUuhea5uSuUiUZK5AAA4yf/rUAcl4us/+Fg/GPTvDhYyaXo0P2i+jYtsZiQdvHRiCo5PTP0PtFeOfA6Zta1Hxh4mkIL6hfgKpGSijc2AT2w6jH+yK9joAK8Ukntdd/aAv9TeQPY+GLBmcBg4Z1U7sA9CrOfxQV61rt+NL8P6jqLb9tpayznYAWwqFuM9+K+ePCiTad8C/GniRmEt3qUq27OWOcF1Qn2OZWP5UAdz8FLC51RNY8barEft+q3DCOUEBDEDztXsNwI5/uj3z6/XJ/DayisPhxoEESlU+yLIQQQdz5Zjg88lia6ygDzv433kdr8KdURnKvcPDFHjufMViP++Var/ga1Wz+EekxLD5P/Es3sm3HzMpYnHqSSfxrkP2hL2U6DouiW6s8+oXmVjC537ABj65da9egtora2jtokCwxII0QdAoGAPyoA8x+AFzFP8ADMRxx7GgvZY5GwPnY7Wz+TKPwriP2kbZ11zQrslfLktpIwM85VgTkenzD9a1vAOsR+APib4g8Iatc/ZrC6uDPZPK/wAu5mGztgFkIyeBlcelR/tKW0z2Xh25VMwxyXEbtxwzCMqMdeiN+VAHz1RRRQAUUUUAFfS37N3/ACKGr/8AX/8A+01r5pr6W/Zu/wCRQ1f/AK//AP2mtAHtFFFFADWZY1LMwVVGSScACvkSHVG13462eqjcYZtfh8tioHyCZQgOOM7QK91+NfiWDQ/h7d2ZkUXmpj7NBGeSVyN7fQL39SK8+Xw+3hzRfhVbTQGK5uNaS6nVhhtzvGRn3C7RzyMYoA+ia8b0h5o/2n9fQM6xy6ehK5ID4ihx9ec17JXjuv3x0P8AaM0G6mkEdvqFj9lyV3ZJLhRxkjL7Bn+lAE/w7tVs/jB8QooxgNNHL9/dy5Zz2Hdunbpz1r1uvJtOJ0X9ovU7crIkWsaYsygHKu64+Y88AbHH416zQB4v+0j/AMihpH/X/wD+02rc0JnuP2eP9LmK50OdDI4J2oI3AOOuAoH4CoPj9bQzfDV5pEDSQXURjY/wknB/Q1qfDeBr/wCDml200ayrNZSRbHO4OpLDByOmOMUAfIFFT3VvJZ3c1rMAJIZGjcA5GQcH+VQUAFFFFABXovwe8NaL4r8X3Wm65F5sP2GSSFPNMZMgZBkYIyQpY49vavOq6XwJr0/hvxppmpQypGFnWOVn+75bHa2fwJP4UAfQXwZuJ9Hh1rwVqblb3R7otFG/BaF+QyjJ4J+bj++PWvV6838f+BtW1XW7DxL4Uvksddtv3chdiqzR56EgHOOeDwR9K9IoA5nU/APhnWPEMWu6hpSz6jHs2yNI+Mr90lQdpx7iumoooA8P+MusS6/r+ieANNeQy3U8b3YjxjBOFBPJG0Ase2MHnt0nipE0n4j/AA0t7S2Z4oTeQJFGuNieSiZwBwFByfYVN4R+E9l4X8VXPiG41a71S+ff5b3AwV3dWY5JduozwOemea5f4gXUj/tA+Dbbz2aKJImEW/Ko7SPk47EgLn1AHtQB3nxSWB/hj4hF0wWP7ISCX2/OCCgzn+9t479Oc1w3h97vTv2Y7yRyhaSyuAnmuSPLdmX8DgnA9cVc+NmsNqNjZeCdKb7RqupXCGSCN8lI1+YbwOgJwfouau/Ee0Xwp8CZtKtkUpDBBaHPfLKGbjuTk/jQB8p19W+E/i/4J/4RvT7a41YWc9vbRxyRTwuMFVAOCAQenY18pV3vwi0zSNa+Illp2sWQvIJ4pQsbH5Q6oWBbnkYU/iRQB6dP4q8JfEP4oWj32rW8eg6TBvt4r1vKju7gtycPgYAxweTjpgmtz4f3NlrPxa8cavpF4k2nbLWIeUCEkbZgsPXDRuM985Bweern+Gngqe0e3fw1poRs5McIRxn0YYI/OvNv2d4kgv8AxjFGMJHPbooz0AMwFAHq/jj/AJEDxJ/2C7r/ANFNXKfAn/klWn/9dp//AEYa6P4hXUVp8OvEckrEIdPnjBAz8zoVX9WFZXwdimi+Fmi+dN5u5HZOMbVLthfwoAb8ZpHj+E2usjMpKwrkHHBmjBH4gkVd+Fk0lx8MfD8ksBgYWoQITnKqSob/AIEAG/GsX47XhtfhZexBNwup4YSc42/OHz/45j8a6H4b/wDJNfDn/XhF/wCg0AdTRRXjHxF8ZeIL7xbJ4Y8N6h/Zltp0IudV1EDiFcBjkgEgAEcDkk4oA9nor580M+Lxp8niDwf46uPFEFi+66sL9JI3IxkrtdmyCoyMEd8c17h4f1mDxB4fsdWtxiK7hWUKeqkjlT7g5H4UAadFFch8Q/GH/CF+GGvoohNezyC3s4iMhpWBxnHYYJ/Id6AOvorxD7J8YL6Ca6g8VaWupQKHk0mLyjJECMhWGwgN9Tz610vw68ea9ruq3nh/xNorWOr2cQlaRVKq6k4yVPTtggkH2oA9KooooA+GPFBDeLdZIIIN9OQR3/eNWRWp4gt4bPxHqlrbpsghu5Y415O1Q5AGTz0FZdABRRRQB6J8FdDbWviVYuQpisFa9kDjP3cBce+5lP4VqfHPUJdZ+J66ZbB5WtIY7ZECjmR/mIGOv3gOe4NdT+z1plvY6Prnim7eNEQm28xiB5aIokck9hyv5e1cN4Isv+E4+M6XTj93JfS6jMUBAADFxwTkAttHtnvQB9UaPp8ek6PZadFjZawJCCqbQdoAzjtnrXxv4nXWdX8f38GpiV9TmvTDskByCWwqgDt0xjt0r7Wrz7xN8NbbxD4/0bxVHqAtpNOeMzwrEG84xvvXnIwexJzwB6UAcC/7Nv8AxLIvL8Q4v8Zk3W+Yj7DnI7cn8q4LxF8GfGPh6TK6cdTgJwJdPBlP4pjcPyx719eVj+J9di8NeGr/AFmWJpUtIi/lp1Y9APbkigD4hurW4srh7a7glgmjOHilQqyn3B5FdP4N+IuveBnm/sp4ZIJsGS3uVLRkjuACCD9DWN4h1u58R6/e6xehBPdyGRlUYCjoFHsAAPXivYNF/Z9t9Y8J6fqH9vTW97dQrMw8gPGoYZCgZB9Oc/hQB7D4D8Vp4z8IWeskRJPJuSeKJ9wjkUkEeoyMMAecMK6R3WNGdjhVGSfavANI8M+Ovg1eXGoWlrFruiSrm6htmIYAfxbSMqQM8jcMdfb0zXPFtnd/CS+8RoTFb3FgxVXXLKzjYFI453HFAHhPwTjm1X4vQ3802ZYkuLmViOZCylT9OZM/hX1ZXz9+zZp2Zdf1JkYYENvG/wDCc7mYfUYT86+gaAPmv9oe7ku/Gek6ZEiyGKzDqEGXLyORtI+iLgdea+htItJLDRbGzlKmS3t44mK9CVUA49uK+b9YK+Kv2kVtsNPDFqCQkIuCFhHzdfQq2T6Cvp6gAooooADRQaKACvA/CiXnw/8Ajxd+HTPGNL1lnlRS/ABDvF1/iyCnvn6V75XhHxrR/Dfjrwv4whhL7H2S8HGY2DAE9ASrNj/dPWgD3evl744aZL4e+JVvrVsqot2iXMbKcfvUIDZwc54U546+1fTNrcRXlrDcwPuimRZI2wRlSMg4PtXln7QGhtqXgaHUYoy02n3IdyM8RMCrdB67Dz2BoA9C8Ka7H4m8LadrUaqou4Q7KpyFbow/Agj8KvXWqWGnjN7fW1sP+m0qp/M15B8ANaTU/Bt/4ekuXWa0kYoFkKusUg6qe2G3dOhIPesTxB+zvq0tw9zpviGK8dyWIvlZH9hvG7cfcgUAef8AxW0/QrHxvPJ4ev7e7tLxPtLC2kV0hkZm3ICpI7Zx23Y7VZ0D4w+J/DPheHQdNWxWCBmMczwlpFDMWI67SMk9u9UdR+FfjfTJpI5PDt5MF/jtk85WHqNuf8au+BPhlqfiXxSlhq9lqWnWSI0k0z27IeONoLDAJJ7+9AGbr3xM8X+JF8u/1mZYR/yxt8QoenULjd075rKs/CniTVIftNloWqXcTc+bDaSOD+IFfXOgfDjwn4bjjNho1s88YGLidBLKSO+5uh+mK6ugDwb9njRbywufEE9/ps1vIBBGj3ELI3O8sBkf7pP/AAGvea+e/Gfxa8X+Dvidf2cnlS6XC6mKyeNQrxlBhhIBuyevUgHIxxivT/h78Q7T4gWV1Pb2FxaSWrKsiyMHXkZGGHXoewoA+fPjB4euPDHxHu7pDIsOoSG+glGRhmbLAH1DZ+gIr1n4gadD8TvhJZ+INOCm6tojdxjaBnHyzJk8jG0/UoPqLHx38JjW/B39sQAfatKzJtCjLxMQGGe2PvfgawP2fPEUN7o+o+Fbzy2MZM8Mb8+ZG3Drg9QDj/vr2oA8S8IzfZvGeh3Bkji8rUIH3yAlVxIpyQOSPpXvXx8m+zt4ZmsoUm1aG8M0KCPdIVQBug5K5AzXinjnw/J4N8c3+nREIkM3m2pVtxEZO6PJPcDGfevcNe1u30nx34S8eah+80K60n7Mbvyy32eRgzh8AEgsGC8DON30oA9G8I+KLPxf4ct9YsgyJLlXjbrG4+8pPfHrXIfFbxzFo9rN4Wg0251DUNW0+ZVS35MasrIGIwSec9P7pqv8I7611HXPGV1o8U0egS3kT2YcEKXKt5rLnkZO047AiuV+P11JZ+J9Dm0mS4i1cWkod7ZiHEJOBnHOMl/1oA7D4C26RfDOCQQqjy3MrMwXBfnAJPfivT680+BDtJ8LrTezNtuJlXcc4G7oPavS6APKPj7rP9neAFsUYibUblYsKSPkX5mPHB5CjB/ve1UvG3h2LQf2dBp8cjobWG2lkETnbLI0qb855K7nJA46L6VR+JMsfiL42+EvDn3orV0mnUlsElt5XH+4g5H972r0b4lIsnw08RK6hh9ikIBGeQMg/mM0AbHhxxL4Y0mQBQGs4Theg+QdK1K4z4T3yX/wv0GVV2bLfySM55Rimfx25/GuzoA8M+JMbaz8cPCGkK8rrD5crRxqfkG8sW9OicnHAFdz4i8WalpXxL8M+H4FgNlqaSmcuhLgqCRtOeOlchaL9v8A2pr43DFvsFgDbjONmYUBHv8A61/zrn/iHJ4lvvizqeraMgZPCdtBckNLgBCgkbjPOQWyB1C/mAen/EX4c2PjzSywWO31eBP9FuiPTJCPjqhJ98ZyO4Phvj/xzPrvg3TvD2uQzx+I9LvGW8LoArhQyhsg9eRn15I619LeGtbi8SeG9P1iBdiXcKybD/Ce4/A5FfNfx/gji+JjSRoFaWzheQgfeb5lyfwUD8KAPK6KKKACiiigAr6P/ZulVvD2tR+TKGW7RjKV+RgU+6D6jBJ/3h6184V9M/s5wyx+DNTkdCEkvzsY9Gwig4oA9looooA8w8WfC278Y+P7TVtS1cSaHAF22BTlcAblHbDEAknnt2FVPirNBH40+HVinyyDV43VQOAokjFetV4p4x8q4/aR8JQPtlWO0VihwwVw0zA47HhT+RoA9rrxH4mzvB8b/AjoE5kiQ70Vxhptp4IIzg8HqDgjBANe3V4d8VP+S2+Av+u8H/pQKANHxDcTWv7SnhzG1hNphj+4TtUmbPfrkdffpXsFeV+I2Fl+0D4WunDFbrTZbZQFPysDIck9P4u3P5ivVKAOG+MFtDc/C3WzMgfyo1kTPZgwwf1qn8ELiS4+FemGVy3lvLGueyiQ4FdP4xsP7U8Ga3YiJJJJ7CZI1fGN+w7Tz6HBz2rzb9nK+83whqljtbMF95m4njDoowB/wAn8aAPC/HtjFpvj3XLOFnaOO8kALkE8nPb61zldp8V7WSz+KGvxyFdzXHmjac/K6hx+jCuLoAKKKKAClBwQfSkooA+5PCuuR+JfC+naxEVxdQh2C9A/Rh1PRgR17VtV47+zvqKT+Cr3T8qJLS8LEBsna6ggkduVYfga9ioAKKKKACvnrxZI7/tN6OjOxVJLYKCeFG3OB6ck/nX0LXzpHCt/+1X5VwXdY7gunzdCluXX8MgcUAewaT8P9C0jxRe+I4UuJtTumLGa4mMhjz1CZ6A9Oc8cDArz39ovWjb+HtM0eORla7uDPIoJG5EGAD2IywOPUCvba+Ufjzqiaj8SpYFIP2G1jticEc8uc5/3+1AHl9eg/BL/AJK7on0uP/RElefV3PwhvoNO+KugzXDFUaV4AQM/PJG0aj/vphQB9e3jKtjcM6hlEbEqehGOleJfs5KrR+J7mMYSSaBVQKcKB5h4J6/e+vHPUV7Nq8jR6ReskTSMsEhCJjLHaeBkgZ+pFeQfs324Xw7rVzvkJku0jKFvlG1M5A9Tu5+g9KAO++KTxJ8MvEJmi8xPshAUNt+YkBTn2ODjvjFR/CX/AJJX4f8A+vc/+htUfxdeJPhbrolZF3Qqq7iBlt64A96sfCy3lt/hj4ejlTY5tA4B/usSyn8QQaAOc/aB/wCSZn/r9i/k1dV8N/8Akmvhz/rwi/8AQa4n9oi6EPgSzt2Qkz3ygMHIC4VjyO9dt8N/+Sa+HP8Arwi/9BoA6mvm7Tjq/wDwvfxIlhDby6e9xINUF0gaEW2csWz9OPevpGvBU03xBof7QWqHTIoLq0vo/tV75x2xrauRu3ehBBx1zjpycAF/UI4vEfhiew+D11p0ELSkakkSNbzOGBxhnAO3r/IHqK2fgLdXk3w/ntLyQsbHUZbWME52qFRsfTLNU+r2N3pvhfd8JLHRZGuJiLiW2kjJxjIKsTtJGehJxkYFHwU0bUdF8H38GqJsvH1SdpV3K2GARG5UkHlDQB6XXgvx+uBH4j8JrcRzz2iu8kltFIVMmHTIUjoxGQD15r3qvI/ihqVp4f8AiH4K1vU7ffp8DTK8hXd5bHbhgARyOvfp0JxQBVj8F23gD7R4/tYdc1vUTH5kVlO2JI/MGGMpGWYqCQeDj07jP+HPjXUPFXxiu7u80xLHz9L8vyTuLBUYEHJxnJY9vT61qeHtA1D4fa3rHjLxX4pgOl3RZhHG8jeczsCpK4HzADAAB49AKh8MeJ7Pxl8d5NT0hriaxt9HMO90KgNuBOAenXHOMkUAe0UUUUAfDHir/kbta/6/5/8A0Y1ZFb/ja0lsvHGuQTbd630xO05HLk/1rAoAKKK6PwPocviTxlpemRD5ZZ1MpxkLGDlifwH54oA9p1VIPBn7NcFvgxz6nBHnYSpaSb5zn/gAII9Bis/9nLQopJtW15lbzIgtrETjAz8z985wE7Ac9+1b9onX9+qaZ4dgk/dW8f2mZFPyh2yqAj1Cg/g3vXr/AMOfDreGfAelabIUM4i82ZlQLl3JYg464yFz3Cjp0oAZ8QvGFn4O8K3V1LeLDfTRSR2KgBneXb8pCnqASpJ6D8QD4T8HviLY+F9Z1JfEF1cLbahtfzcF0SXJyzKPUHqB2p/x/XWR47U3jM2mGFTp4/hUbV8wfXdknPYiuNtvh14vvtKj1O10C8ms5F3o8agl17ELncfyoA+w9M1rS9atxcaZqFveREZ3QShsfXHT8atXVtBfWs1pcxLLbzxtHLGwyHVhgg+xBr4aVtY8OakGU32l38fQjfDIufyIr0Pw98evFekAx6kYdWhxhfPAR1/4Eo5/EGgDrfiP8DoREmo+DbOTzTJtmsBJkYP8SFjxjuM/TGK9y020Gn6ZaWQYuLeFIgxGN21QM/pXz14P+OOozeOmm8RXMcOj3Y2CJUJS1I+6Rjk+hJz17Yr6LjdZUV0YMjAFWU5BHqKAJK8P/aH8UPZ6XZeG7aXBvP390oAOY1PyD2ywJ/4DXuFfJ/xq1X/hIvifNa2q+a1kiWKCMZLuCSRwTk7nI7dMYzQB698B9IbTfhxFdPFskv7h5s5OWUfKpIPT7p6dRg16RqF7FpumXd/OQIbaF5nJPAVQSf0FRaPp6aVo1lpybNtrAkPyLtB2qBkDtXM/FbWBovw11mYqGNxCbRQRnmX5D3HYk0AeO/A+wn8Q/EnUfEtwGY24lm3Ek5llyOvQnBbr65r6XryH9nvSDZ+B7nUmcE390Sqj+FU+UZ4653fhivXqACiiigANFBooAK4L4v6JHrfw31RZMiSzT7XCwXJ3JyR+IyPxz2xXe00qGUqwBBGCD3oA4D4N67Jrvw209p5WkubMtayMxySFPy/+OlRz6V12vaRBr2g32k3IzDdwtET3XI4I9wcEfSvGPhHdt4N+IviDwRfeZGJpfMtfMdeq5I9MlkZTx/d6V71QB8ofCvVj4K+KZ0+/Lqkzvp8pB2gPu+ViD1G4D88+x+r6+YfjxoUmh+OLfXbOMwR36iQSRfLidMZPHQ42n65PXNfQnhXWj4i8K6Zq7LGj3dusjpG2VVscgH2OaANqiivnv9oi+1iz1fSI4ry4h0+aByqRylVaRW+YkDqQGX86APfLq7trC1e5vLiK3gjGXlmcIqj1JPAry3xL8fPDOkNJBpcc+rXCEqGj/dw5H+2eT+AIPrXgWkaL4u8bFLWxi1LUoomCgvIxiiPuzHatereGv2dWdVn8TansJwTbWPJAx0LsOv0B+tAHlXjfxtqHjrWV1HUI4YvLTy4Yol4RMk4J6k89a+jPgdp1hY/Di1ltJYZprmRpbl4+ok6bG91GBj8e9dJoXgHwx4btzFpui2qFl2vLInmSOO+WbJ59OleB/FQaj4E+Jb3Xh8y6PBcwpNF9kOyNz0b5Rx94cgj045FAH07LDHNE8UqK8bqVZGGQwPUEdxXyYqyfCn4xq0wkS2s7kt+7G7fbSDtnr8rY+oPcV9BfCrxDqXifwHaapq8qS3TySIZEQLuCtgEgcZ47Vw37QPhGa+0y38T2iqTYr5V2O5jZhtYeuGJB9j7GgCH47aDZ654X0zxppo83asavIq4328gLIxBweCRxjPz9sVynwt+KiaPFF4Z8SmOfQnysckke/wAgk5wR3TP5fSux+DGvQeLfA+oeDdU2SyW8LIiOeXt34+vyscZHTK9+a8C1vSrjQ9bvtLucedZzvC5GQCVOMjPY9R7GgD7ltLa2tLZIbOGGGBR8iQoFUD2A4rx651K38JftBX154iuvJsNV00RWtxIoWNeU+Vj6AxsMn1GeDmvGPDfxL8WeFYltdN1RvsgPFvOokQfTdyv4EV6XY/HDQPEdvFYeOPDcMkQYN50aCaNWxjdsble/Qk80AdR8A7kz+H9cVJS9umpv5Kg/KqkA/KOwOc165XlPwa1PQ7+fxSnh+BrexW/SWKEpt2o0YUHqepRzivVqAPE9L36r+09qUqxKo0+zIfc2cgIigjjrlxXsd9aR39hc2chYR3ETROVPIDAg49+a8g+D8UDfELx7dR3kU5a+dE+cM7r5rnfx1B45HFe0UAeP/s+3UieGtX0e4wk+n3xDRfxJuHf8VYfhXsFeR+CdMuND+OPjCzj+SzuYEuwgBVWDMCCB0JBZxn6165QB4j4Ft/tP7QXjC7llkMlusiqDzkFlGPwAGK6Pxh8IrXxDqd3qml6tdaNfX0flXZgBMdwpxkMoI64GecHGSCa534Vyb/it42udTlittSaby1tcgbwXYkjJJ42r/wB9V3nir4leGvCVrI97qMU12uVWytnDylvQgH5R7tj+lAGho2n2HgfwfbWM18Fs9Ogw9xOQuepJPpyTgfzr5M+IXikeMfGd7rEYdbZysduj9VjUYH0zyfqTVjxz8RtZ8c37PdytBp6n9zZRt8iD1P8Aeb3P4YrjaACiiigAooooAK+uPgfaRW3wp0uSPO65kmlkyf4vMZOPwUV8kAZOK+5fC+lLofhfTNMWEQm3tkRowwOGx83I6855oA2KKKKACvC/D5XxD+0trN5lZYtLidFJTgFAsWOehDFufb8a90rxL4GLPe+JfGmsTupee7CuAMZYu7E/TmgD22vEfipM5+MfgGA7fLW5hcfKM5M6g89T90cf4mvbq8O+Kn/JbfAX/XeD/wBKBQBv+OP+S0/D/wD7ef8A0GvUq8t8cf8AJafh/wD9vP8A6DXqVAFbUv8AkGXf/XF//QTXhH7Nd5Jv8QWWF8sCGXPfPzD8q99kiWaJ43GUdSrD1Bri/Bnw80T4ePqd5Z3dwUuRuka6kXZFGuSOcDpk5JoA+efjd/yV3W/pB/6Ijrz6u6+JV6nir4lazf6LHNeWzvHGjwoXDFY1TIxnglTj1FYMPg3xPcEiHw3q8hHXZZSHH/jtAGHRW5N4N8T25Am8N6vGT032Ugz/AOO0R+D/ABNN/q/DurPyB8tlIeT0HSgDDorvdD8Faxo+ow3/AIj8Eaxf6UqsZoYo3RgMH5sryMdecfWva/DHgn4XeNPD8N/pmhRmDO1kM0iSxMP4Xw+c/ic8GgDwr4ceOJfAviVb/wAvzbSZfKuolA3MnXKk9wcH36V7ve/HvwZb6fJPaTXV1cBcpbiBkLH0LEYH1/nXMeIvh3N8NNaPi3w1p8OqaSist1pt0u8xRnqVJySPfqO+4ZrqPBmnfDTx1CNY03w7p6XcTDzrV4gPKbtlB8pHvjB+tAHb+FNbm8SeGrHV5tOlsDdx+YsErhiFPQgjGQRyOBwa3KaFCqFUAADAA7U6gArwPwK6a/8AtFeItVihjeC2EypIHDAEFYg6n/aAPTs1e5313HZWFxdysqxwRNI5ZtoAUEnJ7DjrXiH7PFr9qvfE+sPavH5rxRxSnO3kuzoD0JH7snuMjpmgD3iviDxjq0ut+MdX1GYANPdSELkfKoOFXIAzgADPfFfTPxfvtei0PTdJ0CcQ3er3gsy+dp2lSeG/h6cn0zXzJ4q8L33g/X5tH1J4HuIlVi8DFkYMMggkA/pQBhV3vwdi874raGiu0ZDyvlQpJ2xO2PmBGDjHrzwQcEcFXV/D7xTa+DvFsGtXVg94IY3WNEl2FWZdu70PBIwfX2oA+uvFt3LY+DNcu4CBNBp9xKhIyAyxsR+org/2f7ZYfhv5vk7Gnu5WL4xvAwAffoR+FXdU8XN4g+CGreIJrBrFbqxnjSEuJTtbMYOfl65/D36G98H7ae0+FWhRXETRuY5JArDBKvK7KfoVIP40AUPjt/ySrUP+u0H/AKMFdV4KRo/Anh2ORWR10y2VlYYIIiXIIrhv2g5Z1+HltBAW/wBJ1KKJ0UZLjZIwH/fSr+Ven2CldOtVZSpWJAQRgg4FAHi/xF8LJ4u+MGnaXqurtZaa+nGaH5xyysdwUMcAng5weFrct/hJrGl2wttH+Imt2luoCxROPMSMDsBuAHfpiuI+KmmTeLfHvidZLo28XhzSkmiULu80lVcjtjO/HfpW54O+Dmkav4O0vUbjXteWS6t1lKQXKxouRnAUqen1oA3ofht40t1AT4pakwBDDfZ7+n1kOR7Vi6p8BbzV52vL3xxfXF9IuyWea237l/u48zge2cVqt8CNGJbb4i8RAFcDN2hwfU/JyOnH61D/AMKE0/8A6GrX/wDv8v8AhQBl2HwA1HS1mXT/AB7d2qzDbILe0aMOPQ4l5rQ0P4O+IvDsUsOk/ES8tYpSWeNbHKljjLYMhAbgc9eKuXPwYlby/svjrxJFhcP5tyZNx9Rgrj6c1Efgvdbnx498Q7SPkHnHIPv83Pf0oAsf8IP8S/8AopP/AJILWZ4g+E/jPxTLavrPjiG5Nq2+EDT1QI3rhSATx3q63wXufOLL488RCLHCmcls49c+vtT2+EWtPF5bfErxIY8Y2mZ8Y+m+gDO134R+MfEloLfWPHzXUIcMIWtcJkZwSAwBPPpUFn8LPiDpmspqdh4xskuIrZbSORrf/liowqlNpXj8T71sf8Kj1ver/wDCyvEm5RgHznyB6ffqu/wl8Wlx5fxU10L3DGUkcf8AXb1oAuy6L8YkmLQ+KNBkUjlZLYoF+mIyT+Jpv9k/Gn/oYfDP/fpv/jVVU+E/jGKUOvxV1o4/vJIw/IzYqc/DTxqSQ3xS1LbwQfspznP/AF0+lAHAeKvgp4zvnvNevtYsNRvmHmXHzMpIC9sqBwAABxxivFa9O+ImqeLfCmpzeFJ/Gd5qdv5SvKxcq3z5Oxzkt0wcE9CO1eY0AFfQnwA8NRWOjaj4uvY1JYGK2YjlETJkIzxycD/gJrwG3t5bq4it4EZ5ZWCIijJZicACvpX4lajb/Dj4SWfhewx515A1mhHdcZmf8d3/AI/QB5V4ftZ/ih8X/PnEnkXF011MCM+XApyE9Om1c+/evqfWLe8m0O8t9LnW0vWgZbaXaCI3x8pweOteP/s7+HJLXSdQ1+aIp9sYQW7HHKLksemQN2B15212nxZ8Zf8ACHeDJpLeXZqV5+4tMHkE/ef/AICO/qRQByfhnS7H40eC9IufEtxcPfaRcSQytA4Xzgdp+YY4yAvTngnvx7LDEkEMcMShY41Cqo7ADAFfH3w08Y634X8U2sOnGWe2vJ0jnskG4TAnGQOzehH8q+stX17SdBtzcarqNtZxqu7MsgBI9h1P4UAT32m2Opw+VqFlbXcX/PO4iWRfyINec+JfgR4U1lJJdOSTSboj5TbnMWfdD2+hFYviH9oPS7bUbe20C1a7h85ftF5OjKnl5GfLTIYnBPXGCOhr2iN1lRXRgyMAVZTkEeooA+WvCPwR8Qa5q80erxyaXYW0pSSWWMh5sH/lmD1B/vdPr0r6c0zTrfSdLtdOtQwt7aJYowzFjtAwMk9au0UAQXNzFaWk1zK22KFGkck4wAMnrXyt8LtKPjP4t/b53DxQSyanN5oy0mHGBjBBO51J9s85xXt3xo146F8Nr7y8+bfsLFCO28Etn/gKtXIfs46L5Oi6trRZs3E62yr2wgDE9PV8fgaAPca8H/aI1OSf+wvDkLx5nlNy6lhkH7iEjGQPmfnvz6V7xXzjKp+In7Q4UFJrDS5AWypK+VC2SCCOhc4Pb5j60Ae9eHdHh8P+HdP0iAfu7SBYs+pA5P4nJ/GtSiigAooooADRQaKACiiigD5++NWnTeGvHuheNrZUZTLGJAFxmSIhhuwQTuXj6Lj0r3TS9Rg1bSrTUbVi1vdQpNGTwdrAEZ9+aw/iF4bj8U+CdR05lBm8sy25OfllUZXp6nj8a4z4A69/aHgqbSppgbnTrhlEZJ3CJsFc5P8Ae3jj0FAGr8afDUniH4f3EkCM9zpzi7jRRncBw4/75JPfpXG/s7+KvMgvfDFwwzEPtVr7gnDrn6lSB/vele6TQx3MEkEyK8UilHRhkMCMEGvj3U7K8+GHxQUAzY0+6SeJgxBmgyCBkYyCuVPbqKAPsevnX9pK7d9b0GyKr5cVvLKp75dgDn2+QfrX0DZ3UN9ZQXdu4khnjWWNxghlYZByOOhrhPiN8K7b4gXFndf2nJYXFuhj3CESqyk56ZHOe+aAOV/Zvu5H8OazZFl8uK7WVRjnLJgn/wAcWvW9W17StBtxcarqVrZRHO0zyhN2OwB5J9hXiumfC7x/8Pbqa+8J6nY3xlXZLBIoTzADlRhuM++4Y55ra8dfDfX/AIieH9H1K5Fnp/iK2iMdzbMf3TAnOAylsY6jr9480AUfFf7Q9nZzyWvhmwF6VOPtdySsRP8AsoMMw+pWvEvFfjDVvGWprfavMryImyOONdqRr7CvT/C37PWqS6gJPE1zFbWSMcxWsm+SX0wcYUe/J9h1r3DTvBnhvSrP7LZ6Fp6QgYIMCsW+pbJPQdT2oA4D9nzV0u/Ac+mmSPzrG7cbFBz5bgMGPr8xcceg/H0/V9Ltta0i70u8DG2u4mikCnB2kY4PrXndz8V/BnhDxPe+HX0yXT44ZcSz21qqxlyMklVw34gHNegaJrumeItNS/0m9ju7ZsgPGehHUEHkH2NAHyppr6h8I/ipCt6wYW0gScpyJYH6kfgc/UV6F8dfB8OpaZb+ONJZJI/KRbkxjIkjb7koI+oH0IrU+P8A4PbU9Dh8R2iFrmwHlzgLy0BJOf8AgLH8mP41fgb4kttf8KX3g3VHErxK/lRseXt2GGUcdiTz/tD0oA+c6K6Txr4WufBvim70ic7kT54JOP3kR+63H+ciuboA+mP2drS6i8H6jcSqBbT3mYeOSQoDHOemcDGB0PXPHrl/eR6fpt1eysqx28LyuzHAAUEkk+nFcP8ABSwax+F2mFnD/aGknGB0DMeP0rstaSCTQdRS6CG3a2lEok+6V2nOfbFAHw7JfT/2hNewSPBJJIz5jcgrk5xkV0Fj8SfGenYFv4k1EgYws0xlAx0AD5wK5OigD2r4N+KtZ1r4qzT6neSXc13aOkrsAcKpBUDHCgH09a+lK+NPhdqDaf8AEvQZA5US3SwNhiAwf5cHAOeSOOnA6dR9l0AfHnxjt47T4r65HECqs8cp5z8zxIzfqTXCV33xkhWD4ra4iFsFon+ZiTlokY9e2T07VwNABRRRQAUUUUAFFFFACg4IPpX2X4f+JfhPxBplvdrrNlaTOimS2ubhY3iY8FfmxnnjI68etfGdW9PsZtS1K1sbcAzXMqxJnpljgZ/OgD7lh1jS7lC8GpWkqg43JOrDP4GrwIIyDkV5Jbfs9+EY7ZI559TllAG+UTKu498DbwPb9TXBfE3wWvwys9Pu9B8S6tH9olMQt3uMMABksCm3gHHGO45oA+kblZWtpUgfZMUIRsA7WxwcHrzXkXwAsLu20rxBd3IJWfUNiyEY3sgO4gemW/n6V4xbfFTxxahhH4lvW3JsPmkSce24HB9+te2fBbxfoUHgS30691q0g1FJ5WkiuJhGxLOWBG7G7IOeM0Aev14b8VD/AMXu8BDB4nt+fX/SBXrF94q8PafCZrvXNOhQLuy1ynI6jAzk/hXkuq/HbwufFsEo8Orf2tp8sOp4UTpkfMY1ZcgdvvDNAHReOP8AktPw/wD+3n/0Gu+8Ra7Z+GtAu9ZvywtrVNzBRkkkgAD3JIH415PcfGD4catrelare2Oqre2Tt5E8kWPIDDBLBXOR+BNHxd8VaB4q8I6do+i6va3l5qF9CIkikztGSMuOq8kdRmgCrYzfFb4lWb6tY6hb+HtMkVhbRqzIZQeMggFu33uPVRVDXvEvj3wp4cn8JeKNKXV/7StpLazvYJmZ2JGOSAS5Gc4IBPcmveNN0+30nTbbT7ZcQW0SxRjAHCjA6ADNeS61qN/eftKaLYwBvIsbUhlBBG1kZmbB6dVHH90UAVPgP4pgs7ebwXf2z2eqRyPPEsibDKMAlSDg7gMnnt9K9yrw74xfafDfj7wv4vt08qGJ/JuJ4k+bhuQ3rlGYDnnBFe1288VzbRXELh4pUDow6MpGQfyoAmooooAK+etZuX+FPxvF+rCPRdaHmTBIyVVWb5xycblcbuOgbpzivoWvKvj3osOofD1r7y2a50+dJEZVyQrHawPtgg/8BFAHqZUMpVgCCMEHvXiPiD4b+IfBniaTxT8O9hEgIm07AOFPLBQcBkyB8ucg4x7dx8J/Ev8Awkvw+064faLi2X7LOo9U4B/Fdp/Ou4oA4/wDqvi7VdLnl8W6RDp9wjqIfL48xdvJK7mIOfp16cV2FFFAHCfF3U10z4ZazIykmeMW6jcRy5A7Eds//XFQ/BnQf7C+G1hneJdQJvpA2OC4AXHttVT+Ncb8fr5r+88OeFYGdprm4EzRINxOT5aHHXOS+PXmvaNNsIdL0u00+3G2C1hSCMZJwqqFHX2FAHnfxKuJV+IPw6tw5EL6jK7L2LL5YB/AM351y3xc+FfiLxH4luPEGkLbXUTQIptg+2XKjBwCMH1657Y9eo8RW8k/7QPhFkjLpDYXEkhxkKNsgBP4lR+Ird8SfE/wr4T1Q6Zq17LHdrGJCkcDPgHpyBjNAHyTo2ganr2sx6VptnJNeuxHlgY246ls9AO+a9r1b4C6TpHgG/v59Sun1aztZLl3jx5LFELbApGccYznP8q5nwF47W3+Mt3e2OnD7Hrt20RhXO9Fd8hhyec8kdOuMcY9d+MHiuz0TwVeaYX83UtUjNtb2yMd5DcMx2nOACfYnAwQTQBjeOdRtrD9newVS4S6sLOCBXkwxyikA4HJ2qSR7GvUNEtobPQdOtbdNkMNtFHGuSdqhQAMn2FeTeONIlvvAnw68I3UU0V3dXNnFMoXPlCODbJnnqN2fwPNeyxRLDEkSDCIoVfoKAPKvjncxHSvDmnBna7udYikhhCkl1QMrYwPWROOpzx3r1mvG/iPaSX/AMavAkC3AAVxNsOTjZJvJx05C4/DntXsMkqwxPI5wiKWY+gFAHzz/aUMlp8YdRuHid28qBJUJlwHaRAqtgHGdo9BgelewfDf/kmvhz/rwi/9BrxbQI9Mk+EvxH1eXEkN5eFUYEnOGBhO3qPnkB5H8q9z8FI0fgjRFe2W2YWMOYUIIX5R3FAG/RUUsscMTyyuqRopZnY4CgdST2FfMniXxF4v+KPi3ULXwpLdvp1pxFbwTiENHkLvb5huyeeegP1oA+oKK+dbD4UeI9EtoZtI8WpF4pjAupdLE+35c+zHdkjqRtPTtz6z8OvF83i7w601/EtvqtnM1rewDgpIvfB6A/zyO1AHY0UUUAFFFFABRRRQB8X/ABOYn4meIiSci9cc+lcjXWfE3/kpniL/AK/X/nXMwQyXM8cEKl5ZGCIo6sScAUAer/APwxJqnjJtalgD2emISGfp5zAhcDuQNx9jg+lQfFzWZPGnxQh0Wxk82G2kSwg2nIaVmAcj/gR2/wDAeten36f8Kn+B5Fogt9VaKNWbOSbmTG85GR8o3Y7fKPWuL/Z/8J/2jq154nvod8dqfLtnfndMeWYe4GOf9r60Ae76Tpdv4a8M2um2iFobG3CKB1faOT9Scn6mvkXx7431Pxxrn2vUI1gjgzHBbITiJc98/wAR4yeOnQV9oV8m/GOz/wCEf+LVzd2YijM3lXyBUGFfuSDwSXUsfXNAHp3wN+H76Hp0niDVrIx6jdgLbJKPmhh65x2LHHXnAHTJz518YPBV1Y/EfGnhryTWma4ht48tIrk/MMemckfj6VrwftH64tmUn0WwkucY81HdV+pXn+dcRovxG1ex8fweLNSla+uNxWZW4zGRgqvZcA8YoA1NP+Bnjm+jDvp9vZgjI+03Kg/kuSPxr3H4Wavqo0+bwr4iiMOs6MqKQTu8yAj5H3cg+mQe1c9qv7RPh23tA+l6ffXtw38EwEKr9W+b9BXjM3xI8Q3XjqHxU9wFvkKoI4BtQxg/6vHdTz1z1oA+y6Kit5fOtopSu0ugbb6ZGcUy6u4bKzmu7iQRwQoZJHIztUDJPFAHzl+0B4mOp+JrTw3anfHYqHlCg5aZxwvvhdv4sR2r3LwToCeGPBemaUqYkihUzD1lblz0HG4nt0r5r+HtnL46+L0V5exCZDcPqFypBZdqncAeDxuKjnr0719b0AYHjLxAPC/hHU9ZIUtawkxhs4LkhUBwO7EV5D+zjoHy6t4kY8k/YYx/3y79/wDcrT/aH177L4c0/Q4pP3t9MZZVB/5Zp0zznliMcYO0+lei+BfDSeE/B+n6SF2yxxh58d5W5bue/HBxxQB0tFFFABRRRQAGig0UAFFFFABXz1MJfhf8ePtUg26RrsjDdkBVWRwTnjA2Pg/7uPXn6FrzD41+EB4j8EyX8CIt9pQa63kctEFPmJnPphu/3cDrQB6cCCAQQQehFeKftB+E5dQ0iz8RWkKFrANHdkD5zGxG0/RTn/vquq+DXiRvEfw9tftEpkurFjazMxJJ28qTn/ZI/Ku6vLSHULG4srlA8FxE0UinurAgj8jQB5V8AvFLat4Sl0W5dTcaWwEeW+Zom5HHscj8q9dr5S0SeT4PfF57fUHZrOMmGWSPJ3QPgq2Pb5SR6jvxX1NbXMV5axXNvIJIZUDxuvRlIyDQBPXF2PxT8G32oXNiNcgtp7diri8BgBIODhnAB+nWu0r5e+Onh/QdM8RJqGl3sbX1/I73tmjBvLfjL8crk5yD3yaAPpi01Czv4y9ndQXKKcFoZA4H5Vy/ij4neFvCcLG81JLi5BwLS0ZZJT9RnC/iRXx3DeXVvDJFBczRJKMSIjlQ49wOvU1teGPBWv8Ai67WDSdPllU/euGBWJP95+n4daAJvH/iW18X+L7vWbOyNnFMFARiCzFRjccdzj3+te6fs62skPge/uG27J75imDz8qKDmqfhz9nfSYLDPiK9nur1jkraPsjjHoCRlj78fSuw0HTfCHwotZNNbW1tkvpjOi6hcIG6BeOBx9aAO1vLWG/sbizuUEkFxG0UiHoysMEfka+Otf07Ufhl8QpIbS5InsZRLbzKcb0PIyAe4OCPrX2Pb3MF3As9vPHNE33XjcMp+hFcP8TPh1ZeN9GlkjhVdagiItZwcbsciNj3Ukn6E59aAOM8faXZfFL4a23i/R4JJNVtEAaKFcuwyBJGVz/DksO+PrXgGnWa3mp21nNILdZpliaRwcICwBJABPGewr1P4N/EVfCV+/h3WFaOwuZ/llckG2l6EEH+E4GfQ1658WdDuNZ8KRXmm2MV3eafcx3agRhpGjU5ZUPqeDjnOOmcUAdrpenW2kaXaadaoEt7aJYo1HYKMUuo2MGqaZd6fcqWt7qF4ZQDjKspU8j2NcLpfxs8EajsSbUZLCZsAx3cDLg9wWAKjHua7Cw8SaHqu3+z9ZsLov8AdENwjE/gDmgD5O8ffDTV/A1+xlje60x2/c3qJhTnOFb+63HTv2rh6+9rq1t761ltbqGOa3lUpJHIoZWB6gg14z4g/Z10u6mkn0PVZbHJyLeePzUB9A2QQPrmgDwjwvJPD4s0eW2eOOdL2Fo3lICqwcYJJ4Az619y187v4Turz4r+GtD1Xw3o+n/ZFN3NLpS7YruNcEZDDsy4I64Y+1fRFAHzr8f/AAXdrrEfimztWltZYhHePGM+W68KzexGBn/ZxxxnwuvvmWKOaJ4pUV43UqyMMhgeoI7ivnXxN4Osfhn40k1268Ow6v4SuiIhC7b2tmbBJwRjIIbbngg4znmgDxCivrHw3pXwo8W2StpOmaPK7qS1u0YSdM9QVPzDGcZHHoa1j8IvAbEk+HLfJXbxJIOP++uvvQB8cUV9jS/CHwFKm1vDluB/sySKfzDUw/BvwC0YQ+Ho9oGOLiYHrnrvzQB8eUV9cSfA7wC4XGkSx467buXn82rjvEXgn4S6RbtbxNJcapMNlraWd6000khOFUKCQMnjmgDwOwsLvVb6KysbeSe6mYJHFGMsxr6P+GPwXXw3c2+ueIHEuqxndDbxvmOA4PLH+Jue3A9+tbXwt+GEHgqzGoXuJ9auYwJGIGLcEZKL756nv/P0aR1iRndgqKCWZjgAepoAkryP9oDw82qeCYtWjchtKl3snPzJIVU8eoO0/TNaut/G/wAF6Le/ZVvJ9QcHDtYoJEX/AIESAf8AgOa5PxF8WF8c+H73w/4T8N6te3V/GYHeWJVWFW/i+Utnv1IA657UAfOlFfSll+zn4fFpam91TU/tGz/SBE8YUtj+HKHAB9c59q0/+GfPBvnB/N1TaBgp9oXB9/uZz+NAHyxRX1HL+zt4OdspeazGP7q3EeP1jNVB+zh4byudY1XA+8Mx8/8AjvFAHzPXd/CjwvceJ/HdggWUWlnILm5lQD5AvzKOf7zAD8c9q9C8X/CfwH4R0S4L3+qT6rcRMmn2zSq7yzkEIAiICRuxmvSvht4EtvA/hxYl/eahdBJbyQjq4HCjjO1ckDPPJPfFAHYXVxDZWs11cSLHBCjSSOxwFUDJJPoAK+Z/CXjDW7n4lax4qsfDF34hNwXii2Fs2qFsoA+0hflG3kA49MnPZfFHxXqPii//AOEF8HK93NIdmoywBiIxkDYWHAX+8enb1r03wh4XsvB/hy10iyRQI13TSAcyykDc5+uPyAHagDxrx78VLfWPCF/oOu+D9S06+mGIRMcrHIpBDBiFPHsOhx0Nen/CW6W6+FugyCWaT9yyFpmBbKyMpH0BGB7Yrrr2ytdRtJbS9t47i2lXbJFKoZWHuDXhen+F/iZ8M766HhyKLWNEMjOtq0gb5ex2naQ+ODt646dKAPfKK8UX4ueOkYW83w2v2uSM4WOYZHOSBsP8+1JP8VviPIgS0+G17FKTgNNbTuv5BV/nQB7ZVa+srfUbCeyu4xJbzxmORD3UjBrxmPXvjjq7BoNCs7BD/ejRAPwkcnt+tWjB8dYJjJ9r0m4Vh/q8RBU/8dB/U0AZvgyO++D/AIyuNC1ss2gao6m01HGIlk7bj0UkcEeoB6c17vXgni2P4w65ot1oWo+HdNuba4I/0i22FhtIPy5k4+pXPXFUNB174r+ArADVNBu9S0uIfcnPmPEo9HUkgD3BAHTFAH0VRXl2jfHjwfqW2O/kutKnxhluYiyhvQMufzIFWvEnxe8KWOgXs2m63b3OoLEy20UQJLSY+X+EjGSDzxxQBw8Lnxz+0k3nKXttCLBBjG3yG4J5yf3rZ/LtxXq3jzxnaeB/Dj6pcR+dMzCK3gDbTK57Z7ADJP0rxfwXovxT8INd+IrXQhfNqK77qG8kHnPyTuILBt2SeOSc9KkvvF/iPUfFOlav488I6pbaBpTNIsUFnKiLKR8sjl+Hwcdxj35DAG3aXHj/AE3xVF498TaBLPZG0a3NlYEGW0jYgg+WTknIyRnvzjGB0tzaeBfjNYpukkF9bj5kXEV5bjPKsCD8uT7jJ61O/wAcfASKpGrTMSMkLaS/L7HK1x3iTxr8Ltcvl1mDVNT0/WoV/d32nwPHK2AcBgRtb057cZAoA63wr8FfDvhXXLfV4bi9u7i3JMQuWQohII3YCjJAPHoeaw/h9F4Zn0q98f6xNBNrsk08sxvZwfshVztRQenyhMHGewx0rK8IftBRmUWfiqDan3Uv7eM8+8keTjPqufpXWt8MPh14kuD4jjjWWCZmuJWhu2EL55JbnjuTgjvQBhW3hLxT8TLHS/FOs+Km0pObiztbK2Km3U5wQ+4HJABzzx3rmn8E6h4w8YJaaH411bVdJtk/0vUbmR2ED/3EJIDk47cDua2vFus+KfG+mXel/D6yI8M2UZtZp4isf2jaMFI8kZQLgYHXPocV6d8P10pfAmkf2JE0VkYAQh+8H6OG/wBoOGB9x6UAedazZXB/aK8MW8dzJcraWAJEshLqqrICzE4BJ4Jx1r07xrqg0XwTrOoZAaCzkMeVyN5Uhcj03EV534atpdd/aG8S6v8AvvsukwrbAs4wshVUC467Ttlbjv1686fx6uYrf4YzxyEh7i6hijwOrZL/AMlagDivD1lZ237MOszXiFUuXeQMFILOJFWPkdRvUfrXr/w9mluPh34flmcvI1hFlm6n5RXC65oJ0b9mqXS3Rpniso5nCyAYZpllJyR0BJOMZIGM55r0XwjbRWXg3RLeEERpYwhQTn+AGgDE+LOrHSPhlrUy53TQ/ZhgA/6w7DnPsTXk3w/W50T4dHWPA8FtqXiieTZqNvI++SCEOwXbGCODhSTz1Ppx6j8Z7L7Z8K9YHmbPJEc3TOdrrxXm/hDHw9+Ftv4p0GxOtavqsqxTFVZkt1BPyELz1AB9SR2xQB6LBoFodXHi1rG3HjltPDSaf9twhk2BenOOAFz0/HmuX+EGr6tqHxA8ZDXI0tdQkaJ5rRThUZSUOBk5AG0Zyeo9a318I2V7rVt8RZtPv4fEQsvtDaSJgN8qx7QpyuQcYXsM4/HkPhZ4ku/GHxl1vW7mxFqTpZhMa5IjxJEACT3+U+nQ+lAHvNFFFABRRRQAUUUUAfFvxN/5KZ4i/wCv1/513HwF8HvqniKTxHcxqbHTiViLrkNORxj/AHQc+2RXL+MtJvNe+Mmr6XYRGS6udRdEX+ZPsBkn2FezeM7u2+FHwhh0bTJwt9On2aJ8/MztzLIPTv8AQkUAeb/ErxNc/Evx9Z+H9Gy1pBObaDJwskhOGkPtx+Q96+ivDPh2w8KaDb6Tp0YSGEct3kc/eY+5P5cDoBXjH7P/AIJJkk8XXqfd3Q2KnHcYd/bj5R9TXvzusSM7sFVRlmY4AHqaAH1xviz4aeGfGV19r1S1lF75YjFzDMyMFGcDHK9z1Faum+MPD2s6tLpel6tbXl5FGZXSBt4CggZ3D5erDv3rdoA+TPGXwd17w/4ghs9Js7rVbO6IFvPHF0Y/wvjhcepwCOeMHHqngH4I6Votg1x4mtrbUtRlH+qYFooF9AD95vU/l6n1+igD5m+Knwui03xjpa6DEltZa04gRHJEUEwwCN3OAQcgezY4GK9J8FfBTQPDMttqF6z6lqcPzBpBiJH7FU9R2JJ9fTHSfEHwi3jTwydNhuxaXKTRzwzlc7WU+3PQnp3xXURB1iRZHDuFAZgMZPc47UASV5N8fPFEmjeDItJgys2ru0bMO0SYL/nlR9Ca9Zr5f+JN1dfEL4xweHbSZTbwSrZxOqkhTgGViO+Du/BRQB3PwB8Iy6Vol1r97aLHNqAVLVjgsYBzn2DNj67QemK9nqtY2cOn2FvZ267YbeNYkB9FGBWB4+8S/wDCI+CtS1dcGeNAkCkgEyMQq4z1xndjnhTQB4qsU3xM/aAk82BzpunSlXVgCI44cgA/70g9/vdwK+kq8W/Z68O/Y/Dl5r8yfvNRk8uJj/zzQkHHHds55/hHpXtNABRRRQAUUUUABooNFABRRRQAUySNZY2jcZRgVYeoNPooA+fdEQ/Cr42vpAcw6DrAHltIcKAQSnJOPlfK59DnvivoKvM/jf4XHiDwJLewxhr3SybiI99nHmAfgAf+A1a+D/iu48U+A4ZLyQyX1m5tpXOcvjBVjx12kZ69M98UAcn8ffBf2/SofE9haqbm0+S8ZR8zRdmPrtPGfQ+gq/8AAbxc+t+F5tDumXz9KCrEeAXhbOOO+0jB46FfWvWpYo5onilRXjdSrIwyGB6gjuK+TZmvPg98WJBC0rW8EoOBx59s/OOeDxxn+8vbFAHfeJtM+N2tCeFTDFaSMV8ixuYo/kOf4yQxGOOv4da4K2+Bnj6ebZLpUNsp/wCWkt3EV/8AHWJ/Svq2yvbfUrGC9tJVmtp0EkUi9GUjINWaAPk+3+C3j2xu47ldEtbnyZUcRPcxFZMEHBBYZXsQcV9TWalLGFTbpbkRrmFCCsZxyoIwCB0pb29tdPs5Lu9uIre2iXdJLK4VVHuTXlXi3496BpNsYvD+NXvGBG7DRxR+5JGW+g/OgD1e6urextpLq6njggjXc8kjBVUepJr5p+NPj/w54vWytNGjeeazkJa9aParKR9xc/MRnB5AHFefeJPGWv8Ai2687WNRluADlIQdsaf7qDgfXrXpHgD4FXWt28epeJnnsLV+Y7RABNIMcEk52D2IyfbrQBzPwb1G8tfiXpFtb3c0UFzIyTRI5CyDYxAYdDyM19eVw+ifCbwf4f1i21TTdOlju7Ykxs1zIwBIIzgnB4JrtlZZFDKwZWGQQcgigD5l+O3gh9H18eILG02adfYE7IOEn5zn03Dn0yDXc/BX4ljXrCPw1qsmNStYwLeVjzcRjt/vKMfUc9jXqmqaVY63p81hqFtFc2sww8cihgfQ/UdQa+T/ABv4U1X4X+M1nsZ5YYDIZtPu4ychcn5ScfeA4I7g+hoA+pNU8J+HdaZ31LQ9PupHGDJLbqX9fvYyPzrlL34HeA7tCE0qa1c5O+C6kz+TEj9Kk8AfFHRvFmiwfbL+1tNWRQlxbyyCPe2DlkBPzA4zx0712n9taV/0E7P/AL/r/jQB5PP8PviL4Xj2eD/F7XNmjbktb7BZfYFgykdf7tW28U/FvSINt94Ns9RYDPm2c3b0Khjz9BXpn9saYwJGo2hCjJInXgdPX3FWRPD5qxebH5jLuVNwyV9QPSgD5/1HxF8QNI8U2fjvXvCvlafbxm1MSEZjiY5JPzFgfdhjNep6R8UvBmsWcc6eILK3ZhzFdyiF0PcHdj8xxXYOiyoyOoZWGGVhkEehrkJ/hZ4Hubl7iTw3Z+Y5JOzci8/7IIA/KgDcsvE2g6nIYrDXNNupB1WC7jkI/AGtCeCK5heGeJJYnG10kUMrD0IPWuEvfgr4DvYXUaL9mkZcCW3uJFZPcAsVz9Qawj8MvFnhQCXwP4uuTEhGNP1I74yvoDjH5KPrQBv6x8GfBGro2NJ+wyk582ykMZH0Xlf0rjL1/HPwct4pftia94TikCssi4lgQnGM/wAPJAByRnHAziumTx5400m3Ka98P7+ecfKsukuJ0kOP7oyVHvzWTrB8bfE+3GjN4fbw94fmKNeTXzZndVYNhVxkHIHbsMkdKAPU9I1S21rSLTVLMsba7iWaMsuDtIzyPWr9UdK0y20fSbTTbRStvaxLFGGOTtUYGfer1AHjXx3/AOEuksLSDRYrt9HdCbw2iksWzwH287cfhnrXO+CfHXwt8K6faypo95HqqoDLcS24lkD4wxVi3yg89MV9D1WuLK1us/aLWGbK7T5kYbI9Oe1AHmjfHLSr5WTw/oOuaxddoobbAH1IyR+RrFbwn8RfiHqMb+K7oaLoTYZ7C2lwzL2UqCcn1LHjPTjFe028ENtCsNvFHFEowqRqFUfQCpaAOd0PwP4Z8O26xaZotpEQMGRow8jfV2yT+ddAqrGoVVCqowABgAU6igAooooAK84+K3xHfwJpNvHZW3manelvIaVCYkCkbmJ43HngA9wTxwfR6rXljZ6hD5N5awXMWc7Jow4z9DQB8zeC/Hujw6teeJvE8N/rfil322UUcIKouBgrzhTnI4HAHHWu/vpfih4/WS1tbKPwrpMmFd55SZ2GOcEDOD6YX0z1r1HTvD+jaQ7NpmkWFkzfea2tkjJ+u0CtKgDm/CPgrR/BemfY9Lt8SMB51y/MsxHdj/IDgV0lFFABRRRQAUUUUAFFFFABRRRQBhal4N8M6vLJLqGgabcTSnLyvbJ5jH3bGf1rK034XeDNI1eLVLDRIoruIlkcyO6qfUKzEAjtxxXZUUAFFFFAGfPoWkXUpluNKsZZD1eS3RifxIpIdC0e3YvBpVjExGCUt0U4/AVo0UAZ11oWkahbtb3ml2VxC3WOWBWB/Aivnv4g/BrW4fE8954X0iKfSZyrrbwygGI4G5SGIOCckY6A9q+laKAPGLGb4vTWcdhpXh/RvD9lAgjjDlSQAB/tN+e3vVTw5b/FH4c2hgl0aLxDphZ5PJtrj95ExyTtOM4JJOAp5z0Jr3KigDwj4QeN9FjuvEd94h1Kz0/WNTvhJIsrGJSoHAG7gYLN3z61Y+MvjDwnrOj6Npyavb3kY1aKa5WzcSlYVDq544z83AzzXf6n8LfBWr3ElxeeH7dpZHLu8TPEWY5yTsI9azIfgj4Aj3btEeTJz893Nx9MMKAJPiQNN1L4Naq9tdRiwazjlt5UYbWCsrIAT6kKPXn1rf8ABFoLHwLoVssvmiOxiG/GM/KDXgnj3WJPBGneIPhuttLLpdw8Nxp00kvNvGWWRlxglhuVgORzk96+hPC6LH4T0dUUKosocBRgD5BQBynxqlij+Fmq+bGX3GJVwxG1i4wff6V5v4I1az+Engyy17UJbu/fxB80NpakeVCqHksScb8EfqOxNekfGoTH4Wap5MQkwYt+UDbV3jJ9setcD4M8S6b8MvA2mp4ju7rUF1kC7trKGBXS1jzgsSxGd2c49R06kgHSTaDb2niOT4sXmpak2nJZ/aItPeIiaPKgbD82NvJOOACfbJi8AeN9M8Z/FO8uNH02SxjfSSbovtBnkWVNrEL3G9xnOSDz0FWZ11Xwz4m1Hx3rPiea58KG3D21qm4tIHA2J5fCggng9+M4ycY3w38R6R4p+NGq6loumGxt30ghg6hWdhLHliqnAzkevSgD3GiiigAooooAKKKKAPDPCH9h2fxj8b61q99aW0tjMVt/tMiqRv3b2XJ7BccA/f8Az4DVZr/4wfFRo7BJTaM4ji3NxDbKcFz2GeuB3OOe+B8Sbq0vfiLr09mD5TXbLyScsOGPQdWB47e/Wvf/AILeBJPCvh1tR1GBU1W/wxHVo4cAqh9CTyfwHagD0PStMtdG0u102xhEVtbRiKJB2A9fU9ye5rw39o6bUYLnRUS8lTTrmKVWt0kYKzoVJLL0PDLj6GvoGvOfi34E1Txzo9hb6XdRRy2twZGjmbCMCMZ4BOR2+p9sAHg/we8UW/hbx9BPeyLHaXcTWksjdE3FSCT2G5VyfSvrwMGUMpBBGQR3rzDw58CfCekQRtqUL6tdjkvOxWPPsinGPrmvRb28tNJ0ya8upEgtLaMvI5HCIB6D2oAuUV43rf7Q/h20R10eyvNQm2/KzqIYs/U/N+ld/wCBfFI8ZeErXWvsv2ZpiyvFu3AMpKnB9OKAOlooooA474m+Kh4Q8EXmoKzC5lH2a2KkAiVwdrcg/dwW/wCA15Z+z/4Ua81C78X3uXaNmgti+SWdh+8fJ9jj/gR/HD+Mmuv40+IVloGjyC5W2YWcaBgFe5Z8NycDrtXPTg819B+D9BXwt4S03RAyM1pCFdkBCs5JLEZ9WJNAG7Xzt8cNen8S+LNN8F6QrzyQSAyRqcB53GFHPHCnqf7xr3XxHrMXh7w5qOrzAMlnA8u0nG4gcL+JwPxrw/4KeHpPFHiTUvHerBZnS6cQg4x57fMzY/2Qwxx3GOlAHuejaTaaDo1ppVjHstbWMRxgnJwO59STyfc1o0UUAFFFFABRRRQAGig0UAFFFFABRRRQBHIiyoyOoZGBDKwyCPQ183SSTfBT4uF08w+H9QwSvOPJY88Y5aM5x3I9Nxr6Vri/ib4QHjTwdcaem1byI/aLViCf3ig/Lx6gkd+uccUAdhDKk8Mc0TBo5FDKw7gjINeU/HLwWuueFW1u0t0OoaaN7uOGeD+JffH3ufQ464Nf4FeMk1LQj4WvGdNR0wMUDjG+Hd0+qk4I9Mfh7AVDKVYAgjBB70AfP/wE8eSC4bwhqMw8sq0ti7scg8ZiHtjLD6H1r6Cr5N+Jnhu++H/xBXUtPjW3sppxd2DwrtVCCCUwOmD27jH0H0V4F8ZWfjbw1DqdsFjmX93cwZ5ikA5H07g+lAHl/wC0drSpZaRoaCTfI7XbsGwu0Aqox35JPtj348V8K+Gr7xb4gt9H0/yxPNk7pThVUDJJxz+VfZOq+FdB124hudV0eyvZohhHnhDED056j2NOsPDOg6Vc/aNO0PTbO4wV823tI42weoyoBxQBzPgT4W6L4Jty6qt9qTgb7uaMZX2Qfwj9T61ueJ/GWheELP7RrF9HD8pMcI+aWX/dXqfr09SK8g1f9oq6ttQvrax8PwlIpHSGSec5OCQCygfjgH8e9ebWlr4l+LXjUq0zTXc2WeSTPlW0Y5x32qOgHc+5oAt+P/iFqfxH1e3igtXhs42CWtkhLs7k43HA5Y5AwOnbuTX1nwN438KaDHqV9BcWticZEdwD5ZbpuVT8uf519E/D74Y6X4EsmYmO91J2LPetEFZBgfIvJwvX6557Y434p/GDQ20bU/Dej51C4uY2t5Z1OIos8HB/jP049z0oA3fgp42PifwsNNv7t5tW075ZDJy0kRPytnvj7p78DPXJ6zxp4O07xp4fl06+iUzBWa1mI+aGTGAwx26ZHQ18l+DPE8/g/wAVWOsxFmSFsTRI2PNjPDLzx/8AXAPvX2ZpOp2+taTaanaljb3USyxllKnBGehoA+I9a0PUvDupy6dqtq9vcRMVKsOG91PQj3Fe0+HPg34F8R6NHqlj4mv5bdk+fLRI0THjDjB2nPY9ex71s/FH4YeLfHGvLeW17pX2G2iK20Ll0k55IPykEk98gfSvnTUNPvNJvpbG+t5Le5iba8UilWB+lAH0XB+zp4Yk2yf21qckZ/55tHz+O00n/DOGheZn+3NS246YTOfrivmzcw7n86nhvru3BWG6mjB7JIR/KgD6Mf8AZ8ty+Y/FepqoI2BkBIx05yKQfs+xiVpB4v1IOwAZhHycep3V88/2zqny/wDEyvPl6fv24/Wpk8Sa6iFF1nUVQ9VF04B/WgD6H/4UfqUUQitPiDrEKjOBtYgc+gkHv+dWYfg/rlvAyw/ErX43PdHcLnsceZ/Wvm5fEWtIMJrGoKN27AunHPr161PH4u8SQyB4/EOqo46Mt7ICP1oA+iU+FHjBFdR8Vdaw4wcxyE/gTNx+FH/CsvHcCeXD8T9QdAODLExPvkmQn9a+eZfGfiidiZfEeruSNpLXsh4znH3vWiHxl4pt93keJNXj3ddl9IM/+PUAfQf/AArj4ioh8v4lXLMBlQ8bYJ9zuNV3+HvxTd2b/hYQyTk4ZwPyA4rw1PiD4xTaB4p1j5W3DN5IeffJ5HseKuW/xV8c2q7Y/Et6w/6aFZD+bA0Ae2ReCPi1HHsHj+32joWjLE/UlM0kngn4uBjLH49tml27QrIQp59NhH44zXjH/C3vHv8A0Mlx/wB+4/8A4mpG+MHj0oq/8JDMAueRFHk/U7eaAPYP+EP+Mcao0XjiwZ85IcHHr/zyOec/h+VSp4c+NyLgeMdEPJPMQP8AOCvHovjP4/hUqniBiCc5e2hY/mUp3/C6/iB5m/8At7nGMfZIcflsoA9cl8P/ABxVQ6+LNGkZeipGoz+cAFRf2R8d/wDoYtK/79w//Ga8mf4z+P5M58QMMjb8ttCv8k68daki+NfxAih8sa6G9Ge1hLD8dv8AOgD11rH44mMKNV0MHj5gq5/9AxSvp/xwGCusaEcjJARePbmP/Oa8fj+LvxCvb6JItekM0jCNEWCJQxJwBjbjvXpa+G/jgyI48S2qllBKtImVPof3fWgDWFn8cAP+QjoJ99o/+IpqRfHBbjBuNDZNpO5gu3P4DOf0rOt9C+Okc8hHiCzG3gNI0TK30Hln9QKSDRfjqtzK39vWYx03tEytn0HlnH4gUAaXl/HCYvIZtCgAbiIhSD9ODx9TR9p+OHz/AOhaH83T5l+Xjt83485qh9j+PJgH/EysA4J422+49P8AYx/k57U+SD47yRKFudOiZOpUQEvwBzlSO2e3U+wABebUPjfFCcaNoUzEj7rqCB36yAUttq/xuE0iSeHtCKZ+V5JRj8NsufzFZog+PIgaP7RYFy2RKRb7l9hxjH4VF/xf23mTi1uV6k/6IB6YP3T78f8A1qANdte+Ny9PCOhNyekw/rPSf8JB8cP+hO0P/v8Ar/8AJFY8A+Pwm3SNbMqc7ZPsm2T2+Xn+VWhqHx5Oc6NpowO7wc/+RKANL/hIvjR5OP8AhCdH83+99qTb+Xnf1pkfiH42BgZPBuisvcLcKD+fnmoYNZ+OMC7JPDGj3JJzveWMEcdOJh/KpD4j+NokVf8AhDtEyQT/AK0Y49/PoAsN4p+Lq7ifAmn/ACnBxeIfy/ec9e1MXxp8VFkxJ8PYWUDBC3QGT9dxqA+JvjUgYv4N0dgp24WQZyRx/wAt+RyKYPFvxoin2zeCdMZQfmEbdfofOIoAuf8ACa/FLbj/AIV3Hu3Zz9rGNvpjPX3/AEpR44+JkcTNL8OQ2OfkvB0x6cknrVZPGvxaYt/xQFtgHHMmP5vzTT4y+L3nYHgO08srwPM5z658zGPbFAF1PiB8RFjE8vwznaHuqXgD/ltJ/Sof+Fk+PCGH/Csb7fj5SZ2wOT1+Tnj/ADzUEXxC+J8D+Xd/DppWAAJgZlGfr8wxUn/CyfiL/wBEzuf+/rf/ABNACn4l/ECNGMnwyvSMcbJGJz9NhzT3+Kfi+OMtJ8LNY5+UbJXbJHsIsgdearS/E/4hW4HmfDK9bJ48vzG/PCGnL8WPGivmT4Waw6EfKF80Ec9/3RoAki+LHi4MDN8LNc2Mx5TzCQPp5XX8qtf8LY17/omPib/vw/8A8RWTdfFzxxaM5l+GmoRoGxkiUj8xHg0y5+OuqaTHbyaz4A1GxglwBNLMyBuP4Q0YB+maANKX4yapA+yX4deIUfrtaNgf/QKhT416gznPw/1zy+gZVYnPfjZ2+tUIv2kdGLsJtAv0XsUlRifwOKjb9pPTAx2+Hbsr2JuFB/lQBqD472pMi/8ACJa7uGdoEQ5AHf07+tNP7QOkJMscnh7WkZucGNM4HUgbuaow/tJaMxPn6BfoO2yVGz+eKsP+0f4bB+TR9VYepEY/9moAm/4aB0cTiFvDutLIc4Ty03E4z03Uz/hovw2ImLaPrAmBxs2R4x9d/wDSm/8ADR3hryQ39k6t5ueV2x4x653/ANKnH7Rng/HOn63n/rhF/wDHKAOE+JnxG8H+O9ATydI1JNbhx9nnkSNVQFhuViGJYYzgY6/jXXaP8f8AwtY6NY2k+m6wJIIEibbFGw+UAcHeM9PQVd/4aM8H/wDQP1v/AL8Rf/HKZ/wv/wAFXJzPp+qAjCgyW0bcZ/3z7H/GgDI8YfGTwb4s8GatpLW2qrNPCRAJYI/9aOUOQxwNwGe+M4rh/BPxA0HTvDzaF4w0T+1rO1fzdPAhVmhZiS6ksRhScHj3znPHqyfG34dyygPBcID1d7EED64yanl+NXw5kBlklklkI5BsWLH8SP60AcJovx2Rta1IeI7CSXQp0VbSyt4Y2EAU8Ag43ZHUk8EcD0g8OfE/wppvxO1fxEdNuLGxubMW1vHbwoMYKkl0HAJ2joT+OePRl+L/AMNDHv8AtaDkjYbB89M5+7j2qM/GL4ZtjMgODkZ09uv/AHzQBND8efAsqkvd3kJB6PasSfyzUn/C9vAX/QSuP/AST/Cslfil8Jmzm1t1wcc6V19+Fp6/EP4PTuskkGnK2cbpNIJIwOOkZ9T+tAG23xs+H6oWGvFiBnaLSfJ9vuYp/wDwuv4e/wDQwj/wDn/+IrA/4TL4H/8APvof/gjb/wCNUv8Awl3wSCLIbfQsHIGNFOePbysigDoU+MXgGVGdfEUQCDJ3QSqfwBTJ/CsHxd8a/C0Xhe+/sHWWn1OWEpbLHBIpVjxuJZQBjr61SufHXwVgB8vS9LuMLkCLRByfT5kHP6V5VJo9r8TfiVJb+EtM/szTpgGYGIKkKqPmcquQuT0A7kCgDpfgn8OG1u/h8U6pGv8AZ1tIfs8Trn7RIM/N/uqfzI+tdj4c8W3Hhb4ta94Z8SazcPaXcok057qQuqFjlUBOSoIbHUDK+9ep6Fo1n4f0Sz0qwj8u2tYxGgHfuSfcnJPuTXzD8b9K1KH4hX9/NprQ2Uwj8q4SM7JMKASW6bs9fwoA+sKK+Zvht8bLrQjFpXiaWW703hY7r70tuPQ93X9R2z0r6K0rWNO1uxjvdMvYru3cZWSJsj6H0PseaAL9UtU0631bSrrTrtd0F1E0UgGM4YYOM1dooA+DdU0650jU7nT7yIxXNvI0ciHsQa93+B9x43sZYtLm0aYeG5N0wnuozF5WRnMZP3gSRxz3II5r0a5+GXh2+8cS+LL2Ka6vpNh8iZlMCsqqqsF25zhR1JGa7UAAYAwKACuO+Jfi9fBXg651FADeSn7Paqf+ejA4J9gAT+GO9djXyx8Steu/iN8SoNC0iVprOKYWtqqjKlzw8nHbOefRc8UAbnwC8Hy32rT+LtQiZootyWjv/HKfvuPXAyPqT6V9F1keGtDt/DfhzT9HtzmO0hWMvjG9sfM34nJ/Gl8R69Z+GdAu9Yv3229sm4juxPCqPckgUAeQ/HDxX/aUtn4F0eQy39xcx/aVXsT9yPPuWB49BXrHhLw5beFPDNlo9sBiCMeY+OXkPLMfqa8W+C2g3fifxlqPjnVVbCyOYTt+V5n+9gnnCqcfiOeOfoWgAooooAKKKKACiiigANFBooAKKKKACiiigAooooA+c/irod18O/G1n418PyNCt3MzSJglVl6sD/suM8fX8Pd/D2u2XiXQrTV9Pk321ym5c9VPQqfcEEVJrWj2Ov6TcaZqUAmtZ12upOPxB7EeteEeCNav/hV4/n8H6yrrpN5P/o8rEHZuOEkB6YPAb0I9sUAezeNPCtp4x8MXOkXXys43wS4BMUoB2t+uD6gkd6+Z/AXi6++F3jO6tdRt28h3+zXsDZBTDffHuOfqD9K+uq8Z+OPw8bWtNHiTSrcNf2an7UkajM0X973Zf5Z9AKAPYIZ4rmFZoZElikUMjowZWB6EEdRUOpaja6TptzqF44jtraNpZX9FAyfqfavEfgL49ia1PhDUZtsysXsWduGU8tHz3B5A75Ppz7Zqul2etaXcabqEImtbhNkkZJG4fUcigD4h1q+i1TXr+/hgFvFdXMkyQqABGrMSFGPTOK+ydG0Tw/4A8ONHAtvYWUChri5kIUuRxudj1J/rgVhJ8LvAfhyym1AaAk32RGuC0sjyt8oLcBmx26V4T8Rfivf+PI4rCO0Sx02KQyeWJCzyHtvPTj0x19eKANX4n/GO78TmbR9Cd7fSM4eVcrJcjHIPont37+lc34H+GGveOGE1qi2umq+2S8mzt9wg6sfpx6kV0Pw5+DWo+Jzb6vq4NlpG5XVCv7y5Xg8D+FSP4vyFfTtrbQWVrFa2sSQwRKEjjRcKqjgADsKAOKtvhj4J8O6U0i+H7a7NtEXMl2oleTaCcndxk+wx7Vwdp+0fp8aiOTwvLBEuFQQ3SsAo9tgx9K9E8e/ELRvBGmsb1luL+ZCILFT80nbLf3V9z74zXyBqF0L7ULi6EMcAnlaQRRDCJkk7VHYDOKAPsHwF8Q9L8f2t1Jp9vc281psE8U4Hyl842kHkfKfTp0rG+K/wzj8b2Iv7JhFrNrGRFn7s69dh9D1wffnjpwP7Nl4U1XX7HZkSwRTF89NjMMY99/6V9E0AfBFxbzWlzLb3EbRTROUkRxgqwOCCKt6ZoOr60XGl6Xe32z732aBpNv12g19MfFb4Vw+LrN9V0iCOLXouT0UXSgfdPbd0wT9D6jxTwR451v4b6+9nOkyWPn4v7F4xuyOCRnBDAe46DNAHOSeD/E0P+s8O6snJHNlIOR1HSqVxo2qWn/Hzpt3D/wBdIGXvjuPXivq/xHr/AIn1LQrfXPh/NpeoWflF5IZEZpXPXC4OMgfwnBz69K8xH7RHiOzmNvqGgWPnRMUmQGSJgw4IwScHNAHiLKyMVZSpHBBGKbXvUn7RlvcMnneDYpWAxlr4H8sxcVLF8dYp8Onw73/KdrJOGzz/ANcemR+lAHgFFfQT/F9xbtLJ8KnEMxG52b5ZD7nyMHpWbJ8YfCbzFL74aWQYLtbekTMDnJXBjHH+cUAeH0V73D8VfhWzETeAY0XHBXTbVjn6ZFB+IXwcMRY+C5Mhvu/2fDk57/fxjj1oA8Eor3hfiD8GnYIfBcqAnlm0+HA/KTNDeMvgoAtsPCkzR9TKLUcfU791AHg9Fe+r40+CdvARH4XaTbyFNirMfxZv5moB4q+B8ih28M3CM3JU25GPyfH5UAeE0V72mv8AwLnUpJoskIOQS0EoP5qxI6/pUwX9n6UhFIVm4BzfDBP14oA8f8DpdyeONEWx2/aTeR7NwBH3hnrx0zX27Xzf8QPCXh/wH4z8Kf8ACOvc2t5Lcq8kZZnATeoDBj0P3hjn8O/tfjDxhp/grTbXUNTjma3nultd0QBKFlZtxBI4G0+9AHS0EgDJOBUME8VzBHPDIrxSqHR1OQykZBH4VR8Q2z3vhvVLWKZoHntJo1lXqhZCAw5HTOaALFlqFlqMbyWN3b3MaOY2eCQOFYdVJB4I9KuV4r+zhMW8J6tD9oDBL0MINmCmUHzbu+7GMdtvvXtVABRXFeMvib4f8D31pZ6n9qluLhd4jtow5Rc43Nkjg89MnjpXYxSrNEkqHKOoZT7GgCSisLxL4s0bwfYw3utXRt4JZREjCNnJbBPQAnoDWvBPFdW8c8EiyQyKHR1OQwPIIoAmri9X+IdjpHj/AEnwm9tJJPfrlplbAhJyEGMfNkg554967SvCPircjT/jR4NvIY4zMDEG45bMpAzjnoaAPd6KKimnjtoJJpnVIo1Lu7HAUAZJNAEtFcT4G+IVt48udVWw065hs7J1VLmQjE2c9ux4zjnrzjv0uuaxbaBol3q12JGgtYzI6xjcxA7AetAGjRWJ4X8S2Pi7QbfWdOWUW024BZl2upBIIIBI7dia26AOe/4TLSf+E1/4RPfN/afk+djZ8mMZxu9cc10NeFQakj/tSyCZfJ2wm3TJzvPk5BHHf+le60AFeCftJapcJBoekqQLeVpLl/dlAUfozfnXquq+OdE0jxRY+HLqaX+0b3HlpHGWC5OBuI6Zwa8t/aO04XC+HJ4txneWW3VcgA52n880AfPNFeww/s7eKpIQ8uo6RE5AOzzJCR6gkJjI9s0rfs5eLP4dT0UjA6yyjn/v3QB47RXr0/7O3i6NQYr7SJSeqrNICPzSqx/Z98bAZDaYfYXJ/wDiaAPKqK9XX9nvxmSAZNLUE9TcNx/47Uq/s7+MDFvN3o6n/nmZ5M/+gY/WgDyOivWW/Z78Zq5CzaU4B4YXDYP5pUY+AHjYvt/4lwGCdxuTjr/u596APKqK9Tm+APjeJQyJp8pzjalzg/XkCm/8KC8ceU7mGx3KeE+1DLfTjH5kUAeXUV6VF8CvHjoGfTbeMn+FruPI/IkVA/wS+ICuwGhKwBwGF5Bg+/L0AeeUV6Afgn8QVGToH5XkB/8AZ6F+C3xAbdjQD8pwc3UI/L5+aAPP6K7kfCDx75byf8I5PhBkjzY8n6Ddk/hXKQ6XfXGrLpUVrI9+03kiAD5t+cbcfWgCbQ9Ev/EesW2ladCZbq4fao7D1JPYDqTX2N4L8JWPgzw7b6VZqpkADXE2OZpcfMx9vQdhiud+Ffw1i8C6Y13d7ZNau0AncYKxLnPlqfyye5A9K4r43fEnVdM1X/hGdGmms9kQkurmNtrvuGQqkcqAOpzk5xxjkA9D8RfFHw54c1u00iSaS8vp5VieK02v5GSAN5JAHXp1/SuyubaC8ge3uYY5oZBh45FDKw9wa+Dre5ltbqK5hbbLE4kRsZwwOQefevqr4dfF7TPGOzTr0fYtYC48tmGyf3Q+v+z+WaAOS8c/ABJS194PYRvyXsJ5PlPp5bHp9GP415BoXiLxB4D11pLOW4sriNwLi1lBVZMfwyIevU+4zxX2zXMeKvAXh7xmkf8AbFlvmjUrHcROUkUH3HUexyKAMDwP8YdB8Y3UWnskmn6m6cQzEbJG7hGzyfYgGvRq+Q/Hfwr1vwTPPdpC91oyyARXsZGVB6B1HKntnGM455xXZfCj4u6u2q6Z4W1hPttvO/kQ3RY+chOdu4k/MM4HYgeuMUAfRVFFVNS1G10nTp7+9lWG2gQvJIxwABQBwfxj8aSeEfCQhspNmpaiWhgbuigDew9wCAPdhXJfs/8AgpIbNvGF180twHgtFI+6oOGf6kgj864lnvvjV8VRGXnj0sOSBni2t1HJHUBmx/303p0+o7W1gsbSG1tYlighQJHGowFUDAAoAnr5++K+rX3jnx5YfD7RmAWCXM7lhseQpuJOM8Iu7I9c8cCvU/iF4zt/BHhifUmaN7x/3dpA5/1knuByVHU/lkZri/gb4Vlt9MuvFupxltR1Vy8TyIAyx5JLD03k57cAduoB6foGjWnh7Q7PSLBNltaxiNPU9yT7kkk+5rToooAKKKKACiiigAooooADRQaKACiiigAooooAKKKKACvMfjH8P5fGOhR3mnRqdUsAzIuPmmjIyUGOpyMgeufWvTqKAPK/g/8AEg+LdObSdSKJqtjGozuOZ4xxvwe44z9c16kVDKVYAgjBB714H8XvD0ngvxHp/j3w4ht5WnxchUzGJMcMR2DDIPv7mvXvB/iix8Y+HLbVrJwQ42zRg5MUoA3Ifpn8QQe9AHzh8S/AV98P/Eq61p+3+y5LrzbSRVBMDg7gjKfQ9OxA/Cve/h14+tfHeg/aQI4L+E7Lm2Uk7D2YZ/hPb8q3fEmgWfijw/eaNfhvs9ym0suNykHIYZ7ggGvl2X/hIPgp4+YQusp2cMyER3UJPp+HY8EUAfUviOzu9R8NanZWEkcd1cW0kUTSfdDMpHP518z2/wAA/HEuS8FhAR0El0Dn/vkGvpXw54gsfE+g2ur6fIHguEDYzyjd0b3B4rXoArWX2v7Db/bvJ+2eUvn+Rny/MwN23PO3OcZ5xXJ/ED4g6f4F0eRpJI5dVljzaWZzmQ5xk46KPXjOMDmuR+M/j7xR4MvNPg0fyILS6hYm5aLe/mAkFeflAAKkcZ614BZ2mteNvFEdvG8l9qt9Ifmlfljgkkk9AACfYCgCPV9Y1fxdrrXt9JLeX9wwUBU5PYKqj+Qr3T4WfBdbIQa74pgDXf3oLBwCsfo0g7t7du/PTrfhx8K9P8DQC7nZLzWnHz3O35YgRyseecep6n26V6LQByGv6h4Y+G+kXGuHSILYSOI3NhaokkrHJAJGM8g9TXnl7+0lpixN9i8P3cr448+ZUGfwDcV7XdWtvfW0lrdQRzwSLteORQysPQg18tfFv4ZQeB7iDUNNlZ9MvJHRYn+9A2Mhc5ywIzg9sc+4B9C+CPGNn438OQ6paBYpCdk9vv3GFx2JwPqDjmuc+Kfwvi8cWkd7YeTb6zbghZGGBOv91yBnjHB7ZNfOPgrxjqHgjXo9SsSHQjZPAzELKncH0Poexr6+8LeIrTxV4dtNasldIbhSdkgwUYHDA+uCDzQB8t+DPGut/C7xDcWtzauIDIEvbGUbW47r6Njv0NeteLPCOh/GTQk8S+G7xV1WOPysOcBsZPlyD+FueG9D3GMdd4++HOkeObBjOnkanHGRb3a8EHnCt/eXPb8q+ZoLnxP8K/FjLtazv4hh4nO6OZD64OGU4zQB6v8ABu80TwzcXfhbX7BNM8RmfeJLxAPOXjaqse/cDoc5Gau+Mfin468FXxj1Pw1p/wBldyILqOR2jkH1zwfYgH2q1ay+Fvjn4ZCXIhs/EUEfzMgzLbnPBXON6H0zxnseaybHxFqGh3CeBvijpy3elSnyrbU50Lq5z8pLnggA/eHzLxnvgAwm/aQ8QZXboumAZ+bJkOR7fNxWjD+0m5yt14WR0bA/d3uMDvwUOf0rD8ffBS+0NW1Xw4JdT0x23CCNS8sSkZzx95fcc/zryNlZHKupVgcEEYINAH0S/jj4S+O3W01nTDYTt8qz3EAiIJ/6aRk4xgfewKz/ABH+z9DcQfbvCGqLLA0e5Le4cN5h/wBiQcYPHUfjXgddL4W8c6/4OuxPpF8yIeHt5PnicZzgqf5jB96AMrVdF1LQr5rPVLGa0uF6pMhUkeo9R7iq1tbT3lzHbW0LzTyMFSONSzMT2AFfUVve6B8bvBFzbmCGLVoUK7ZceZby44dSOdhP9QRVHwT4PtPhL4R1HxP4gRG1VYmLbWDBF/hjQ4+8xxk+49DQByvh/wCCOnaTpyax491aOzhxuNmkgXHGcM/c+y/nVib4ifCfQ4PsWk+Do9RSMbfNmtI8PyP45MuemeRXkfibxTqnizWZdT1S5aSRsiNP4YkzwijsB/8AX61jxxPPIscaM8jkKqqMkk9ABQB7Lc/GPwpczgL8MdMucnCmXytxJ9vKPtUvxb8OaBaeCtF8QWnh1tF1O/kTzLeM7RHuQuVZOmQemAp9QOg0fht8JotDgj8X+MG8g2iG5is5Bjygozvlz3HXb2wM+leW+PPG2oeNvEUt5cSt9iikZbO36LFHnjj+8QBk98egAAB6f8cf+Sn+EfpH/wCjq9g8Y+Gbfxd4YvdIuVwZUJhkKgmKQfdYZ9/0J6V4/wDHy3Gma54Q1FZmaSMPHum+YfumjYM2OSTuOfpXvdtIZrWGQkEuisSBgcigDyL4MePbe6sE8H6lIsWpafmK3LPkTopPC57rjp6dOlemeItTs9I8O6hfX1wsFvFA5Z3bHY4A9STwB1J4r5g+MWjS+HPiZd3VvmCO7Iu4XiGzax+9gjvuBOfU13fxmsLm6+F3hvVJdSuJGhSJZY5X/wBezxg7yAACwwefc0AUv2ctahh1LV9EkKrJOiXMRJxu2naR9fmBx9fSvoV3WJGd2CqoyzMcAD1NfC2hQ3dx4g06Cxkkju5bmOOF4mwwZmAGD68175+0BJrGmaNpUtrrN5Fay7ra4gicosp253Ng5OQCMHIoAz/ClnF8TPjRqviWcGbSdMdfIDD5W2/LGMHPHylyPXnjOK+gK8u+A2lrZfDWG8wu6/uJZiVJJIVvLGc9D8h6e1eo0Ac1418I2fjXw5PpN2djH54JgMmKQdG9/Qj0NeP/AA7+IVx4C1W48FeMpDDBav5cE5G4QnOcE/3CDkHHGfTp9C18+/tH6RbRy6Lq6Li5l327kAfMq4Iz9MmgD2688RaVZaBLrkl7G+mRR+abiE+YpX225zXyD8RPE0Pi3x1f6zZiVbWXYsKy/eCqgXp2yQTj3r1/4MaJB4k+Deu6NcOyR3d9NGWXqp8qLB/A4OK+epoZLaeSGZGjkjYq6MMFSDggjsaAPsPwJ8RNG8aWcUNpdltUit1e5t5I9jAjAZh2I3Hse4rI+NPii20fwFe2Ud1D9uviLdId2X2n7xwDkYHc8cj1rjf2d/DE8LX/AIolLJHLG1lAhXG8blZm9wCoHHv6V5t4WsYNc+LdpaagDPFPqTmUOc78Mzc565I5z1oA+mfhpop8P/DzRrF12y+R50ucZ3uS5zj03Y+gFdVNEk8MkMqho5FKsp7gjBFSUUAfP/gjxfF8M/GureCdXjNtpL38j211K3+qDfcLf7LKF57Hr3r3C+1nTtN0ttSvb23gslUMZ3kATB6YPfPb1r54/aK0uO28XadqUeFN5abHAHJZG+8T9GUf8Bro9N0+31r9lwRzs0r2sE8ybGyUkSZ2Uflxj0P0oA5O28d6U/x/PiKW5V9JeQwJcSqQETy9oYDGQM+vY19NQTx3EMc0MiyRSKHR1OQykZBB7ivg+0g+1XsFvu2+bIqbsZxk4zX0Z8b3uPDXw50PTdLvJ7eCOVLQ+VIVLxpEQAcHkfKKADw5bweOvjrq/iJZVksNBVLeBSo+dyrKDyOQGEjA9c7ah/aNme307w5NGQHjupHXPqApFdN8D9Gj0z4aWl15ciT6hI9xLvyM/MVUgehVVPvmuT/aUjQaXoEoUb/OlXd7bV4oA1PjRqHiFPD/AIcGj6hNbNf3AglSCQxtK7qNg3AjAzuzz3HpXPf8Ks8YW0MUmufEVdOLgABr2VuR2yzKDgelXPj9dtD4P8LwLHIGaXzRKo+VCsYGCfU7sj/dNQfEXSU8ffC/SfGunytNd2NqBdKAWZ1yA+QOAVbcx6cZPYUAS2/wz1hJQ+mfFuR2kJUsk7AtjHHEpz2/Sk1XwB8XLGEz2PjK41B1A/cpeyRsQuMYDfKTxzzz3zmvnuup8M+PPEfhW8in07U5vKQjNrK7PC46YKZx09MEdqANG8+JvxBsrmSzu9evoLiBikkbqqsrZ5B4qv8A8LX8df8AQy3n/jv+Fesa9o/h74x+D7zxLoFoY/EsCDzYQ3zll/gYdGyo+VvoO2Byvwa+G9r4iurrWtcjVtOsJfKFu/AklADHf/sqCMjvn0zkAwbH4gfE3W7gx6dqmq3cpIBW2hDYz0+6vFdZb+FfjdfzmWXVL+034yZdTVVHT+FGOOg7D9TWp4w+Odto050nwVY2hhhyhumTEWen7tFIBA9Tx7d682vPi948vWbf4hnjB7QxpHj/AL5UGgD0w+E/jdGPl8SxPk84uhxnvynSnf8ACJ/G/JH/AAk8GMdftI/+IrxiXxv4snBEvibWHBGCDfSYx/31TYvGniqFQsXiXWEAOQFvpB/7NQB7LN4X+OUQBTxAk2eyXSjH/fSiqV4/x08PWUk8lzJNbopkkkUW05UAc9QW6DPpWX8MNP8AHXi/V/t8viXWrXR4HD3F095IRKVx8gycMcdc8AdewLPiz8R7rxfrDeG9BMz6bFL5ZEBLG8kBxkY6r6DnPX0wAYsPxs+IRmQDWllJIGz7FD83twma9j8AW3xDnn/4SPxfrv2TTxGzNYyQxruTGdzYAEYHX+9wc4zWT8PPhdp/ga0HinxjNbx3cSB445WBjtfcnoz+mOnbJ5rgvH3xM1j4g6gND0KC5TTHfZHbQgmW6PqwHJHfb+JoA0PH3xq1bXb2bR/DBktLHzPLW4gJ8+47cY+6D2A56c9q9A+EvwqXwlGmt6vl9ZmjO2P+G2Vuo92I6nt09zP8MfhNYeE7W01fUYjNrxTeWY/Lbbl5RQDgkZILfXFdT4r8e+H/AAdayS6pfRm5Vdy2kTBpn9MLn36nAoA6mvm/4t+B/EfiH4p507SbmaG7hiEdyEPlLgYO5+i4weDz09RXLeLfi34g8YX6Ri7fSdMEgxBayNkDP3nYYLkdew9q+q9JvbXUNKtrqzvEu4HQbJ0bIk46/WgDzvTPgX4Tg8NDT722a4vnX97frIyvv5PyjOABnGMc45rwfx14C1f4f6wizOZLZzvtb2HIBweAT/Cw9Pyr7KrkfH/i3QPCugO+uQxXYuAUisXUMZz3GCCMepPFAHnnw1+N1vexQ6R4qkitrhFVIb48JIAMfvCTwxx16H2r22N1lRXRgyMAVZTkEeor4S1S4gvNVvLq2tVtbead5I7dDkRKWJCj2A4/CvQPhd8SdZ8Oa5pukS3Yl0W5uEhkhnPEIZgN6t1XGc46H9aAPpvX9d0fQNN+063eQ2tnI/lbpRkMxB+XGDngH8q8d0yz8AyfGXw7feELyKWWeS5e5tIkbykPkuwdcjC8/wAI6cYAxXXfGzw5q3ijwXa2OjWbXdzHfpM0asoIQJIpPJHdhXmfgT4PeNdN8UaRq9zDbWEdvcLK/mTB3Cjr8qnuOMZ780AfS1eC/H/xorxQ+D7FvMldknuyoDcZOyPrkNkBiMdNvPJFeqePfFkHgzwld6tLgzAeVbIf45iDtH04JPsDXjXwR8JXHiPxDc+NdZLzLDKxgaXJMs55L5PULn8z7UAd98G/Ap8I+Gftt/b+XrGofNMGALRRg/Knt6n3Iz0r0tmWNSzMFVRkknAAp1ePfGn4gTaTbp4W0Vt+qX67Jmjb54UbGFGDkM2fyoAwL9ZvjN8UxZx4bwvozkPNGTtmGRn5gcEsRgY/hGa97iijhiSKJFSNFCqijAUDoAOwrlfhz4Nh8FeE7fT+Gu5cT3cn96UgZA9h0H0z1Jrr6ACiiigAooooAKKKKACiiigANFBooAKKKKACiiigAooooAKKKKAKWpabaatp89hf26T2syFJI3GQQf6+/avAba5uvgT4/uoLiK6uPDGpDMRBBPB4PYb15BHGQc+lfRdYHizwppfjHRZNN1SLch+aKQfeifGAyn8enegDWsL+11SwhvrKZJ7WdA8UqHIZTXPePfBlp438NTadPtjuF/eW0+3JjkHT8D0IryrwX4l1X4WeKl8DeJiraXLLm1vMkLGGyQVz/AWPI7Emvf6APk/wN4x1f4VeLLjR9XhkFiZvLvbZs/uz081Ox7HPIZfwI+qba6gvbaK5tpUmglUPHIhyrKehBrz34pfDGDxxZfbbIiHWraMrExwFnXrsb+h7Z/LyL4bfEzUfAeqnQNfE/wDZCyGOSKRSXs3yclR1xk8r+I56gHffG7wr4s8W6hpNroumfadPhjZ2kEsa4lY4OdxBACgc9OfasL4dfB7xZoHjPT9av5LW0htHZmCSCR3BUgqAOMEEjOeK9+trqC9to7m1ningkG5JYnDKw9QRwRU9AFG51jS7GXyrvUrO3kxnZLOqH8iamtb21vofOtLmG4jzjfC4dc+mRXxP4xvJr7xprVzPMZXN7KN5OcgMQPwwAK93+Amm2OjeBr/xHcXoVbiRvO3PhIEjz19+Sc+hFAHrGtaxZaBpF1qupTCG0tk3yOfyAHqSSAB6mvkr4hfEXUvHmp5kBt9Ngcm2tAenbcx7t/LOBWr8VfifL42vvsGnlotEt3JQE4Nww/jYdh6D+tbfwW+Gkmr6jD4l1i2/4lkBzaxSrxcSdN2D1Vf1IHUZoA0/hT8GluY4df8AFVsDEwD21g/8QP8AFIMdOmF/P0r32GKO3hSGGNY4kUKiIMKoHAAA6CpqKACuY8Z+CdK8caMun6krI8b74bhMGSJu+D6EdR06egpNa+IXhPw/PJb6nrtpDPGcPCpMjqfQqoJH5VyV18fPCcerQWNnFfX6SuqefFEEQEnHRyCfyFAHjHibwh4q+Feurf2s88dvuK2+o2xIVh/dbHQ/7J4ODjIr0bw58W/DvjjTf+Ec8d2kELTYXz24hlbPByOYm565x15Fe3Xtla6jaS2l7bx3FtKu2SKVQysPcGvA/HnwDeBJdQ8IlpkB3Np0jfMB32MTz9Dz7npQBu3Nj42+FaNNoTt4j8LqCy2cvM1svJ4IBJUDHI4/2R1qIWnw9+NFp5kXl6T4lkXLhcCYMOuRwJhgdeuPSvP/AAL8YNd8GTR6ZqySXulQZjNu4CzQY4wpPPH90/pXoepeDfC/xQifxN4K1QafrcbhnePdGPM7eYo5RuD8y9eTzQB5h4j+CvjDQGZ4rH+07YDPm2WXP4p978ga4G4tLi0maG5t5YZVOGSRCrD6g17FqXjz4sfDy7WHXvKuoDlYnuYVeN/cSJtJPsTn2q9a/tK3SR4u/DMMr46w3hjGfoUb+dAHm/g3SPGi63bX3hjTtRW5QgrNHGVQjIyGY4Xae4JxX0D8WPA3iHx1ZaXbaZe2cMMDl7iCeRgpcgAMCFOcAt1A6++K881j9o7V7i3VdI0W1spOd0lxKZz7bQAoHfrmul+36p8Rv2fryVbiW41SMt54TaWdo2DFcKFAyuCByeR1oAydI/ZvcqG1rXVDZH7uyiyCO/zNj+X+Fbd9qvgz4NXD22n+FtSlu8APfNESrZXIAmfjvghRjg55FeBaH4q13wzcNNo+qXNozEb1Rsq+Om5TwfxFereHvj096BpvjTS7S8sJfklmihzx6vGcqw+mOnQ0Acp46+L+t+NLVtPWNNP0xvvW0TbmkweN74GR7AAcV50OoxXr/wARvhxpTaIvjLwTIk+iuoM8ERLeV1y4zyB0BU8qfbp4/QB7x8fHebSvBL30wd3imaeaEK4JKw7mXBAPcjBANe+WG0ada7SSvlJgkYJGB2r53+On/Ip+Af8Arzk/9FwV9D6YQ2lWbKQQYEII7/KKAPnv9o+L/ipNEk3phrRl25+YYfqR6c/oa7zWdX+HXiLwRb+HdQ8U2LRLBGsc6TBXRkXh8HoeOh9cVm/GHwBfeK9b0vURqFhp+mW9u0VzdXk2wRfNkHnrnPHPbnFcdDofwW0O3/4mGv3esXIX5hEHCkjP3QigDPuxoA5r4e3Xhnw78UFudS1Xfplk8n2S78htsrfdRmHVRgk9Dgj8a9R+NOpeHvFPw7+2afr9jPJY3KSxwxTozSEnYV25zkBi30Fci3iD4GoxjXwnq7rx84d8frPnvUkfh/4OeKy0GlavdaDdk/ILpyEOen3yQe3G4GgD1/4TWy2fwu0CKNmZWtzLll2nLuzkY9AWwD3HNdrWT4a0hdB8NadpKT+elpbpCJtu3eAOuMnFa1ABXkn7QsNo3w+t57gMLhL+NbchQTkq+4E9gVBP1Va9brgPi34fHiPwSbN9Q02w23Mcv2nUJDHGuARw3YnOOQeM/UAHJfB/xH4W8JfDuNNS8RWMVxdXElzJC0oLxn5UA24z0QH8a4n4tT/DzVXl1bw9qTSa1LMvnwwo4hkBHzP8y43dOh/DOau2fhT4RaBbhdf8Wf2teZJb7GX8v6Dyw35lufarTa38CtOAEGhXd5uwGISVse/7xx+lAHpPhb4h/D2LSbTTNK1u0s7e2jVEiuswFfqXABPXJBPNefaToGhW/wC0bb/2TdW11ZyRPfItrLuWGXa2VJBPcbsejCqhvfgRqDlW069sWLA+YPPA/IMwA/Cuy+GfgbwdY+I7jxF4Z17+04FhMMcDEFrct1JPB5AwAVHU9ewB65RRRQB43+0UufBunn7I0uLz/XgnEPynrjjnpz6Vf8A6z4N8J/DnTdMvfEOkM80LTXC+erb2flgV68A7cEc7a3Pij4c07xL4U8jVNcXRreGZZPtMh/d56YZSyhuvHNeSwaP8ENIhaK+1291W4BAZlEoA/wB3YoGPxNAHJ6LpXgy8+Jk0H9vtZ+HYJPOtrmZSGmwVITJA29+SOi+pr1744yaTrfw3S9ttUspTb3McsOy4U+aG+UhQPvHDZ+gJ7VyMdx8BsPG1rfDbwJG+0Zb3GG/mKnf4b/DLxWUj8K+KxaXspUR28sofd3ICPtcnHv2+tAHunh7TIdH8O6bp1u4khtrZIlcHIYBRyPY9a8g/aU/5A2gf9fEv/oK17TYWiafp1rZIzMlvEkSs3UhQBk/lXi37Sn/IG0D/AK+Jf/QVoAn+PUUb/DfRZWmVHS4j2IRy+YyDj6da8u+GnxLu/AuoGKdTc6PcsDcW4+8h6b0z3A7dD046j1X43GG4+Emk3H2eRiZYGjcjHl5jPUZ7jjvXz9oOg6h4l1q30rTIWmuZ2AAA4Ud2b0A7mgD2rUfhn4T+I7XWueCdbggldd0liY9qLIemVGGjB57EE5xXlWs/D3xboVy0V7oF98oz5kURljI9nTI/DORXvWjaT4O+B+mS3eoanJNqV0oR26vJjnakY6DPc/nWBqf7SdurKNL8PzSL/E11OE/IKD/OgDgvhtrmu+AvFME8ukak1lfbYp7cQuN6k8Oq4+ZlyceuSMjJr1P4q3Gl+BPhvcaXolp9lbXbliygv/EAZGOTkHAVce/Sucsfj/4g1jWtP06x0LT0e6uo4QryOxYMwAAOVAPPU8e1egeP9C8O/EQnw0+swwa5YkzQxq43KSvRlPVTkE45GB75APkeivUtV+AnjXT0L20VlqKjtbT4bH0cL+lVtM+BnjnUGHm6fBYoTjddXCjHvhdx/SgDzavW/h78LluIR4l8ZqLDw/CnmIs8nlmf0J7hfyLZGM5rpbLR/ht8LLUXOs3kOueIYcB7eMrL5Uo6hU6Lg93544xnFUntfF3xy1WG4nSTS/CcUp2ZbggdSBx5j8EZxhefxALHif4iaj4+nTwf8PLWeK3k3CedVEe+Pocf3I+eTwT0xzg9Fonhzwd8GtGj1XxDcwT6zJnbLs3vnH3YU7D/AGuOvJAIFN1jxV4H+D1nLp3h6yhudXkUB445NzZHQzSckeu39BnNeX6L4T8X/GDW7rWbmcLAWw95PkRp/wBM4174B6DgdzzyAT6z4j8V/GrxDFpVharFZo5ZIEJCRrnHmSt3IB/wFe2fD74VaV4F33Yla81OVNjXDjARTjKoO3I69a2vBvgrSvBGkCx02LMj4NxcsP3k7DOCx9Bk4HQfia6agBpYKpZiAAMkntXy54s8Iap4++LmvJ4ddNQgSSJpLxpV8qIGNeCw9CCoAycL7VwfibWdT1XXL576/nnJuZG2ySEqDuPQdB6YFd/8FviRZeErqbR9VAjsL2YSC6z/AKl8Y+b/AGTgfSgC/qH7OetW2mmay1i0u7pVybdo2jDHuFbJz+IH4Vy3gP4jaz8P9XFjO7yaWJitzZP/AAHOGK+jD8jivreKWOaJJYnV43UMrqchgehB7ivEPi/8Ivt5uPEvhuAm7JMl5ZxrkzEnJkX/AGuckd+vXqAex6PrOn6/pkWoaXdx3dpKDtkj6cdQQeQfY1wHxs8ExeJfCkurRyFL3SYZJ1/uvEBudSPXC5B9sd6+fvCHjzXvAt8x024IgZsz2c4Jjc9OR1B9xg8fhXvnw7+LEHxDvrvRL/S47ScwM6r529Zk4DLggHPOe/GfSgDxD4Y+ApPHfiLyZWaPTLUB7yVDhsHO1V9yQfoAT2xXqfjP4DaaumS3/hWWe2vbaNpPs0jmRZtozhSeVb06jp0616f4S8GaP4LsZrTSIZESeXzZGkbexPYZ9AOBXRUAcL8LvGy+M/DCtOCmp2O2C8Q55YDh+g+9gnHY5FdfqWo2uk6dcX97KsVrboZJJG6ACs3T/DmgeG7nUtUsrOGykvCZryfecHGSScnCjknjAr5++IvxD1H4jawvhjw1BLJpplCxoi/vLp153H0UckD0GTjoACnL/wAJD8cfHjGFWh0yBgMnPl2kJPf1dsE47n2HH0xoukWeg6Pa6VYR+XbWyBEXOT9SfUnmsb4f+DrfwT4Wt9Nj2tcv+9u5R/HKRzj2HQewro7u8t9Psp7y7lWG3gQySyOcBVAySaAMHxz4stfBnhe71Odl84KVtoj1kkPAAHoOp9q85+EPgq+1G/bx/wCJ5Gub+8Ja0WZfmXnHmkEccDCgcAHPpjEgkf44/Ew+fG//AAi+kBiAMqWVumT2Zyvt8q+ozX0FDDHbQRwQoqRRqERFGAoAwAKAJaKKKACiiigAooooAKKKKACiiigANFBooAKKKKACiiigAooooAKKKKACiiigDiviB8PNO8eaYqT5hv7ZG+y3KkjaTjhh3U4H05xXC/CDx5PZzt4H8UNNBqULlbR7k43DgeVk9+pXsRx6Z9vrzj4qfD1fFukDUdOUxa5YKZLZ0ODKBzs478fKex9qAPR68a+MnwtbxDFJ4i0SBm1WJQJ7eNcm5UcZH+2B+YGOoGXfCX4oT6vcf8It4lJTWIAY4ZZBgzbeqt/tjH44Pfr7HQB8z/CH4nv4YuY/DOvOsWlvIfLnlyptXPZv9kn16Zz0r6J1COe/0a4j0+7EE88LCC5UbghI4YevrXlfxb+EsnieU67oMaLqgUCe34UXAH8QP9/oOeo9Mc8H8Mfire+EL5fD/iEytpauYhuXMlo+cd+dueo7dvSgDZt/2a7xnP2rxNBGuODFaFyT9Cwqtf8A7Pvii3tpLXTfEFncWhYuYZWkhDsPunaAy5x6nj1r6KiljmiSWJ1eN1DK6nIYHoQe4qWgD5d8N/AvxNP4nt4teso7fS42DzyidG8xR/Au05yenbH5V9OQwRW0KwwxpFFGoVERQqqB0AA6CpqKACiiigD5b+Pfh+20jxrDqFrG0a6nCZpeDtMgOGIPqRgke/vXlMcjxSLJGxV1IZWHYivsjx58OtM+ICWC6jdXVubJnKNbleQ+3IOQf7oqlpfwZ8D6ZbtEdHF4zHJku5C7fTsB+AoA6LwfrcXiLwjpeqxMzLcQAsWOTuHytn33A1u1Xs7O20+zhs7SFILaFQkcSDCoo6ACuc8f+MH8DeGjrI02S/AmSJo1k8sKGz8xbBwOAOnUigDN8bfCjw74033MsRsdTIwt5bgAk9t69H/Q+4r551Hwv40+FutQ6p5EkBgfMV9b/vIW7YJ9D0wwGfSvTD+0nabI8eGZ9xI3j7YMKO+Ds5/T8K9d0bVtM8X+G4b62CXFjeRkNHKgI9GRlPocgigDy7w38ZvDHi7TV0jxpZ29vPJ8rmWPfayehyclDyevAxnd6YXi/wCAzTKuo+CrqO6t5jvW1klXCqRwUkzhh9fbk10HjT4CaZqnnX3hqUaddkbhaMMwOcdF7pn8R7CvKNN8UeN/hVrMlg7SwbOGsbsF4XGTyvPTOfmUjPrQBxuo6XfaReNaahZz2lwvWOeMo31we1dx8I/HY8F+Jdl6+NKvsR3JOT5ZH3XGPTPPsa9T0fx54H+KyRaT4o0qC31IkpAkzEg5/wCecoAKk4HHGeOtc94u/Z6uYmkuvCl2J05P2K6YK49lfof+BY+poAwfix8OE0eQ+J9AdbnQb1hITG/meWz7myMDHl4Awc98V5NXsHg7x/rPwzvZPDXi7TLqTTCMfZ5QC0AJOWQHh0PPGceh9eivvhX4M8f2s2q+Btajt7hmLNbkfulJxwUwGj6+49BQByPwU8WnSvE48PXrLJpWsfuWik5USkYXgnHzfdPrkVyfj7wzP4T8YX+myQNFb+a0loW/jgLHYQcDPHB9wa0tS+G3jbwjfxXj6RPJ9mdZUuLTMqghuDleRz64Nek/tDabcXeieHtaECARb4rhwMEFwpUfTKv9M+9AGP8AFFDe/B3wJqc7s9ykax7uxDRAnj/tmte8+Eo4IvBuhx2sxmt00+3WKUrt3qI1w2O2RzXg/wAR/wDkg3gb/tl/6KavTdP+KPgLRfDWmxJrkCxRWscccEavI6BUACkAEg8Y5oA1/H/ga28faCunXF09pJFKJYZkXcFbGDlcjcME9xXhd/8As9eL7Zm+y3Gm3iD7u2VkY/gy4H517GPjX8PSP+RgA/7c5/8A4iuj07xZoereHpddsr9ZdLhWR5J9jLsCAlsqQGGAM9KAPmGT4IfEBJSo0NJAP4lvIcH83BqW3+Bfj2b/AFmmW8HOP3l3Gfx+Umve0+MPgF1THiOEb8gZglH55Tj8auaf8TvB2qapb6bZa5DPd3DbYo1jf5j6Z24z+NAF3wVodz4b8HaXo93cfaZ7WHY8nbqTgewztHsK6GsfX/E+j+F7WO51q+SzhkfYjurHc2M44BrIt/ij4IuoxJH4msFU9pHMZ/JgDQB19cZ8RfAUXj7RobJ9QlspIJfNjdU3qTjHzLkZ+ueK3NE8TaL4jNx/Y+p2979nwJfJbOzOcZ+uD+VZ938QfCVhqk+nXev2UF1Adsscr7dp9MnjPPSgD551H4C+N7J8WtvZ3654MFyq8epEm2saX4ReO4kLt4duCFJB2SRsePQBsmvp3/hZPgr/AKGjS/8AwIWukhnjuYI5oXV4pFDo6nIYEZBFAHx5YfCXxzqEgWPw7cxAnBacrEB7/MRXt/wg+GF/4JkudU1W7xe3MRgNpCwMaLuBDE/xNxx6Anrnjs0+IPg6SYxL4o0neM9btAOPcnFXdL8VaDrl3La6VrFle3Ealnjt51chQcZ4PTJHPuKANmiqd/qdjpVt9p1G9trODcF824lWNcnoMsQM1Ui8TaDPZTXsOuabJaQnEs6XUZRD/tNnA6jrQBhfEXwHF490BLJrlre5t3MtvJjK78Yww9D7dK+btX+EfjjSHJk0Ge6jB4ezxPn8Fy35ivryyvbTUbVLqyuobqB/uywSB0b6EcGq9zrek2V9FY3WqWUF3Njy7eW4RZHzwMKTk/hQB8YSeCfFUSlpfDWsIBjJaxlGM9P4a6Dwx8K/GOtatbx/2XeaXEHDNeXUTRCIDncAcEn0x39OSPrme7trXb9ouIod5wvmOF3H2zUN/qmn6YsbX9/a2iyPsjNxMsYdvQZIyfagCeGNoYI4zI8rIoUu+NzYHU4wMmvDv2lJ4v7P0C33jzvNlfZ324UZ/OvdVZZFDKwZWGQQcgivHf2h9MgufB1nqDTRx3FpchUV2AMiOMMFGMkghT9N1AHP/FWWRPgd4JjWRgjw2u9QeGxb5GfWrPw9j034Z/C+fxjqaodS1NT9lj3fM68+Wg9Mn5jjPGPTFO+JlnFN+z/4TnfO+CGy2YPHzQYNZvx/c6baeF9AjuQ0Ftbsxj2FckBUVyc4PRuMcc9c8AHjusave67q1zqWoTNLdXMhkdie57D0A6AdhWdRXfeAvhdrPjeaO5VDaaOHxLdycbgDyIx/EevsO5oA6D4GeDjqfiFvEl/Eq6ZpY3xySjCtN2IzxhRliex2/hxfjzXItZ+IesatYSbYnuiYJY2PIXCq4PBGdoPtmu8+KPjvTrTSl8C+DxHBpVt8l1LAeJT/AHAe4zncepPtnPlejaHqevailjpVjNd3L8iOJc4HqT0A9zxQBuWfxP8AGtjGscHiO92Ku0CRhJgf8CBq7a+JviN42vBYWWq6veykfNFbSGNcerbcDHua9A8J/ANLaI6j41vY4oI0LNawy4Cj1kk6AD0H51d1j4x+FPCGl3GjeCdMVpUyqTJGFtwx/jznc5HuBn1oAm8N/Bvw74X02PXvG96ksyJvmhmkAt42POD3dh9cE9jXNfEL413F7J/ZPg+V7PTY12G5jTY8vGMKCMoo/P6VzOn6N44+L2sLNcz3E8Izm6uAVt4R6KAMZ9lFe9eCPhN4f8HRQzvCmoaquS17Mn3T/sKSQuPXr79qAPK/h98Db3Vnt9V8TBrXT2AkS1DfvZuc4b+6pH4/TrX0Za2trp1nHbW0MdvbwrtSONQqoo9B2FWa4v4r3sVj8MtceWUxmSDykIzyzEADj1oAn174leEvDUJN9rNu8o6QWzCWQ/gvT8cV5zB8eLvW/Gml6ToWjIbK5uo4ZGnJaV1LAEqAQF+XJ5z714NpGjajr+ox2Gl2sl1dyZKxxjnAGSfQCtTW/C3ifwLfWlxqVjPp8+8SW86OrAOpyCrqSMjg9c0AfVk3w28GXGoS3s3h2we4lJLlo8gknJO3pnnrivEvjV8NrPw00GuaFaPDp8zFLmFfuQPxtK9wG546Aj3wPTfhV8Tk8b2P2G+2Ra1aoDIBgLOvTeo9fUdvx49C1DT7XVNPnsb2FZradDHLG3RlPagD54+D3xXt9Bt08N66zi1aXFpcgbvKLHlW/wBnPIPOMnt0+kQQRkHIr5D+J3w2ufAeoo9uZrrRrg/ubl1HyNz+7YjjdgZzgZHTocZVj8SvGVhFFDb+I78RRldqu+/AHQfNnj26UAdj8QvhX4uvfHmsXumaRJd2VxP5scqOgB3AEjBbPByPwqH4aeHPFfhT4kaXPeeGdSEUjGGWQ27bI0f5S5YcADOTz0r6mooAKKK+fvix8YpBNe+GfDjbQu6G7vckEn+JY/THIJPvj1IBU+NPxLXVXbwlocvmW6y7b2VB/rHB4jU9wD1Pcj069h8GPhtJ4YspNb1iDZq12u2OJwCbeL+jN3HYDHrWF8EvhnbrZQeK9ZthJcOwfT4n6RgdJSPXPT069cY95oAK+fvir4pvfG/ii28C+GJvtEBkC3bRDIaUMcgn+4g5J6Z+ldF8Y/iU+gwy+F9Ki8zU7632ySg8wo+RgAc7yOnpnNa/wn+HUXgvRFu72FG1y7UNNIRkwqcHygfbvjqfUAUAb/gbwVYeBtCXTrMmSRzvuJ2HMr+vsB0ArqaKKACiiigAooooAKKKKACiiigAooooADRQaKACiiigAooooAKKKKACiiigAooooAKKKKAPJfib8KDr9w3iLw5J9j12HDlEOwTkc5BHKye/fA6dasfC74nN4lP/AAj2uRvbeIbVWEgddon2nk46hwOo9ifYepV5R8UPhjJrrjxF4bLW/iG3Ic+U/lm4xjB3dnAHB4zQB6vXjfxZ+EsOuW9xr2gWjDWQQ01vEQBdAnk4PRx198dzVv4b/FX+1J08NeKY5LDxBEREDOpT7Q3oQQNr+x69vSvWaAPlr4bfFPUPAt8dE18TyaQjFDE6nzLRsnOAecZ6r+I75+mtO1C01TT4L6ymSa2nQPHIh4IIz/kV558S/hPaeNYTqGneTaa4mP3kmQk6/wB18dD6MBnsfbxTwh4y174UeJbjT76CU2qy7Luxc454+dM98Dg9CKAPrmisbw94m0jxXpq32j3sdxCcbwDh4z/dZeqmtmgDzPx38X7LwLryaVNpVzdu0CzGRXEa4JIGMj5unUcduxrz2+/aP1d75Tp2h2MVoG5W4d5JGH1UqAfwP41uftH6eH0XRtTS3jylw0Dz4G7BUsq56kfKx9PzrxHRPB3iPxG6jSdHurlWziRU2x8dfnOF/WgD7U029h1LTLW+tyTFcRLKhOM4YZGccZ5q5XHfDTQdX8N+CLLTNbuBJdx7iEDbvJQ/dj3d8fl2HArsaACopoYriFoZo0kicYZHUFWHoQetc74w8c6L4HsIrrV5ZMzEiGGFd0kpGM4BIHGRnJHWuZi+PPgWVNz3l3Ef7r2rE/pkUAcd8TPgfxca14SiJb5pZ9OHOe5MQ/8AZPy7CvNfAPj3U/h/rv8Ay0aweQLfWTD7wHBIB6OPw6YNe/3fxy8CW9i00OpTXUwXK28drIGJx0yyhR6da+cNJ0m98feOzZ2SpFPqVzJMS5ysSkl2J9cDP1/GgD7G0XWrDxDpMGp6XcrcWk4ykigj2IIPIIPY0zW/DukeI7M22safBeQ84Eq8r7q3VT7giuJ0/wAO6t8K/h7Na+GrVvEF61158iSDyuGUKSqjJONq/LnPJOeMV4f4g+L/AI41S+YSalJpgik/497RfKCMvYn7x56gkj2oA67xd+z5fWam68L3X26Mkk2c5CSKP9l84b8cdutcdpXj3x78PrgWEs11FEh5stRiLLj0Xdyo/wB0gV7X8Mvi5Z+MUi0rU9trrirgD+C5wOSvoeMlfy9u+1/w/pniXSpdO1a1Se3kHRhyh/vKexHrQB5Na/FPwB49sYbHxjpiWswPHnqXjBPdZF+Zc++O3Jqhe/BedLqPWvhx4ljSFsshN0eD6JLGDkex/M03xL+zqzTvP4a1VERuVtb4H5fYSKD+GR+NeahfHfwyvnaNdQ0o7tpcKTDLjPrlG6GgD0iT4n/EfwI62/i3QUvbdcD7Tt2b/TEqZT9M1yPxG+L83jzSodLi0r7BapMJXzP5jSEAgfwjHX3rp9E/aHeWMWnijQ4LmB/klltT1X3jbIb8wK6DVtJ+FvxJ0wrpWo6bpepuQyTJGIZAeAQ0Z27x2+vQ0Acr8R/+SDeBv+2X/opqTRfCHhH4ieAI4/D8KWPiywt089Gdv3zKMEkE4Ic85AyCQDx16L4z+Gxo/wAIdDsY7gyJpc8UW9lwZPkZc+3rXDfBfwnrF/4ng8QwTvYaXpz757o8LKB96IdjkdT0A98UAN8AfCPUNd1SebxFb3OlaRZfNcNOhiaQjOVUt0Awct2/Guh1z4zWmga5ZaX4PtbZvDNirRXFsYgEucn5tpPIHJwe5JJBFdp4+dPid4RvLXwZ4gS4msm8y5s4CR9pHZCePQkdQSPxr5hS0uZL1bNIJGumk8oQhTvL5xtx1znjFAHs3ifwLo/xA0WLxV8O4EWbcI7zTF2xlWJ6gE4VhkcDgjkc5zftdO0b4I+Go9S1iC3vvF92GNrGBvWHAxweMDn5mHJJwOBmtDw3baZ8DvCY1bX3nm1jVNitaQYOwAZ2jPGVycnOM8D3w/il4at/GmmRfEDwq73kckQ/tCEOC0QVQAdvUEDhgPY9MmgDF8GfESz1SW70T4hNPq2m6hKjRzXD7vsj8gkHgqvI+6eMcDk1cu/gVqUvjb7Fps3/ABT8ircLqDkELET90Y+8w/DPB4rg/BXgnU/G+tLYafHtiUg3NywykCHufU8HA7/rXuqeLfBmkGL4XXF5cT2f2Y2c2oNMAqu2RsLDp1x6Doe9AHJeMPHGm/D2yi8K/D6WOKaFw99fqqyM7DkLuIIY+vYdB3FILTQPjJoU0tpFBYeO4Y/NlVflW82jHHO3njnqD145riviN8OrzwJqSncbjSbkn7Ldbfx2t6N/McjuB1Xw78BLoNva+P8AxReR2Gm2g+020BYeZOcZTvxk9F6nFAE/hH4YWvhS3k8U/ERYLaztCfK0+Uq5mcDIzg4bODhOc98DrQuvjprQ8aR6lp6mDQowsS6W20qYwME5A4buMdOByOvX61aaP8ddDm1HRbi4s9b0wFFtLh/ldOSuRnaN394dOhyMV4J/Y+of21/Y/wBll/tDzvI+z4+bfnGPzoA9R1r4Z2XjG0XxF8OpRdW88u2fTZGWN7Vj25IAA9M9MYyK6FYdB+Bnh5Z5BFf+MbyIhepWMHGQPRAe/Vvp0n8M2Vn8C/D8uqeI7hp9U1RkjFjalWKKuTxnGSM8np0Az1rl/ib4Li1bT2+IXhq9m1HTL1jNdI53PbknnHooPBX+H6dACbwr4xtPiPaS+EvHt6DJNJ5mn6hwjxy/3eBt5ycZ+npjFh+DXiN/HbeHWilWyRgz6j5RERhz94di3ouc5/E1yPhXwrqni/W4tM0uHdI3Mkp4SJO7Mew/n0FfSdxr2iT27fDVfFFyNbNn5A1EnBMv93dn75/u9wcZzQBwPjvx/D4Fgs/B/gO7Nv8A2axF3OFD/vAeUJYEE5yW7Z49ga3oVh8YPDP/AAlmhbIvE9tEBqNirZaYqMDA7EhflPfp1FeUeKfDWqeFNcm03VoSsyMdr8lJlzw6nuD+frg16F8GvCd7Bep44vrg2OiaesjFycNPhSCB/s5PPrjH0AGfD34aAxXHibxmlxp2jaePNRJj5TTOpB5B529uMEk4BrsD4l8J/HGI6DeQXGl6xE0jaczNv3DGSQQMdFyynsOCex8S44/il4Jg1/wtqL3Vtphd7jT9rBicDkr/AHlGfqCcGvnu2uLizuo7i1mkhnjYNHJExVlbsQRyDQBt65oGueGdfufDkxnNwHCiOEsVnB+6VA65H+Fdlr/wel8N/D4+INW1iO31EBW+wsowckfIGzy/OeBjg/WvafC0Wpav4RsPEOv+GoZfFFpCwt2nVEll4+U5I/d5z0PTk8Zr5y+IniLxLr3iOZPEiPbz2zskdljCwAnoPXt83OfWgD1b4oR3sPwI8LRbCiRR2a3KSDDKRDgDB5BzWl8WfhzrXj/VNK1PQ5bN7ZLXZullK5ySwYcHIIIrP+Iktze/AnwlZ2ltLey3UVoCYQXYFYeeADk54+tcvonw3+KWu2ENpeajeabpsarsjvL1wAvoI1JIIHYgUAb2l/Cnwf4IgXUfHet2086AN9kD7Y89cbR88n5Aexqj4l+JeueMx/wj3w90i9t9OVAjtbxYkZT2+XiJevfkdcdK37b4W+BfBkkWo+M9ejvboLv8u8lEaOQeojyWfGMYyQe4qHWfj5oOhKdO8JaIlxbxjEcuPs8I/wB2MLkj/vmgDH8Nfs+zBDe+LtSis7VIy7w2sgLrjk73I2qAOuM/WtqX4mfD74e2Elh4P05b26zsZ4gVVyOMvK3LjPTGR6YrzKW4+IXxRvZPLXUL6AyfcjyltFnt2UfjzXpXgn4AQWrJfeLJkuZQVZLKBj5Y6HDtj5vTA49zQB5xfeJPHnxV1M6fCbm4hcgG0tQUgQZyC/bj1b0r0bwh+z3bRCO78V3ZmlDBvsdq+E+jtjJ99uPrXten6bY6Xai2sLO3tYR0jgjCL+Qq3QBXsrK206yhs7OBILaFAkcUYwqqOwFWKx/FN5cab4R1q+tJPLubawnmifAO11jYg4PB5A618WjxBrWyRBq1+FkJLqLl8MT6jPNAH2wdf0gaoml/2pZnUHztthOpkOBn7uc141+0N4ugWxtvCls5Nw7rdXRU8BADtQ/Und/wEetc1+z5pNnf+M7y+uHRp7G23wRNgkljtLj/AHRx0/jHTv6L8aPh63inRRq2mQB9XsV5Cj5poeSV+oPI/EUAbfwobw7ceCLG78P2dvbFo1jugigSeaow288k88jJ6EVr+OvCdt4z8K3Wk3AAkI8y2k/55zAHa305wfYmvlPwH45v/Aeti8tV822lAS6tycCRc/ow5wa+xNL1O01nS7bUbGQSW1wgeNgex/rQB8UW1xrXgzxGXgkm0/VLKQoeMFT0IIPBB9+CK+pvh78UNJ8cWccBkjtdZVczWbHG4jq0ZP3h3x1Hf1ND4q/C+PxvajULBhHrdvHtj3cLOoJOxj2PJwf6dPDvhv4Rvb34p2GlahFc2ctk5ubhSNkkYQbhwfVto+jZoA+lfiF4bk8WeCr/AEi3SJrmUK0BlYqquGBByPbNeGn9nTxUEjI1LSC5PzKZJAF9OdnP5V9N0UAFFISFBJIAHJJrwD4r/GNJI7rw54akbqY7m/R+CO6x46g9C31x60AaPxX+MNvY2tx4f8N3IkvmzHc3kZO2AdwhHVu2eg+vTnfg38LF1iQeI9fsy2njBs4JOk7Z5cj+6O2ev4Va+E/wba5a38QeKLYfZsb7awlX/WejSA9u4HfjPHB+g40WJFRFCooAVVGAB6CgBURYkVEUKqjCqowAPQVwHxS+IsHgfRTHavFLrNyNtvCxBMY/56MPQds9T9DU/wATvH9r4I0B/LkDatcqyWcPUg4/1hH90fqePWvPfhv8MdX1jXI/GPjbdceYolht7pvMeYlcK0gOcKBjC9eBwAMEA2PhV8Org3CeNfFTzza1ckywRTnmMHo7d9xHQcYHbPT2WiigAooooAKKKKACiiigAooooAKKKKACiiigANFBooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAPN/iX8MLPxjZy6jp8Qt/EEKZimT5fOx0R+2fRuo45xWF8O/ildjUx4P8ZJ9j1S3HlR3Mx2iQqPuuTxuOOG6N9SM+y1xfj34d6T460wpcILfUYx/o96q5ZPYjjcvt+VAHaVxnj74eaV450oxTosGoRjNveKg3KfRvVfb8q808O/EXXPhnqkfhPxxbPJZw4WC9QFmWPsQf+WidPdeRzjA91sr221KxhvbOdJ7adA8cqHIZT0IoA+QLiPxZ8JvFTJHNJaXCN8siZMNygPvwy+x5Ge1fRHw++KOl+OYRbtts9WQZe1dx8/ByY/7w457iur13w/pfiTTX0/VrKK6t3/hccqfVT1U+4r5v+Ifwm1HwPL/behS3FxpkbCTeDiW0OeMkdRnHzDH9aAPp+4toLuBoLiCOaJvvJIgZT9QaeiLEioihVUYVVGAB6CvA/hz8dfu6Z4ynJJIWHUQgwB6SAf8AoQH19a94trqC9tY7m1mjnglUNHLGwZWB6EEdRQBPRRRQB89ftJ3SNe+HrXjzI4p5Tyc4YoB2/wBg9/8A69L4A+E9N1ubVtR1XS7W9t4dkUIuEEgVzkt8p46becVH+0XqzXHirTdKMKKlnbGYSA/M5kPIPsNgx9TSfDf4n6D4I+H97atDM+tNM8kcaxfLKSAEy3oO/f0zQBS+OGo6CuvQ+H9G0azs304fv54IVi3MwzswAMgAg59SeO5639nrwo8FreeKbmPH2gfZ7PI6qD87dPUAcejV45oukX3jTxrbWMkjrc6lc7pp3UsVDHcz8nnjJ68+vNfZOjaTaaDo1ppVjHstbWMRxgnJwO59STyfc0AaNeU/Fz4d6Jrmg3uvIYbDU7SMytc7cLMoydr46k9m69O1erV4T+0H4xktbW18LWchR7gC4uyp52chUPsTkkew7HkA+f7T7V9sh+x+b9p3jyvJzv3dsY5zX138L/8AhMk8OyReMkYTpIBbPKytK0eB9/Hv3PPXPavJPgB4SXVfEFx4iuYg0Gm4SAMMgzMDzj/ZHPsSMe30tQBTvtSsNLg87UL22tIenmXEqxr+ZIrhfEvxk8G6LC0aXq6tMQQILLEin6t93H4mvCfjRrz638SdRjEm6CwItIwDwNv3v/Hi1dr8Cfh7BeR/8JZq1t5ipJt09GHyllyGkI74PA9we4FAGpoegaL8XI9Sm1DwY/h4xkGG/tm2tK5zuBGwKxHBPHftXKeI/gB4h0pLi50q6g1O2jBZYwGSdh6BcEE/Q8+lfT1FAHwtqo1y1WKw1YX8Swj91b3e9Qg6fKrdOnaut1D4rapc+A7TwpZ2lvYWsVuLeeSDhp1Axz6Z6t6kn1r6o8QaTb61od5YXFtFcLNC6qkg43EcfTnHNfOnhmz0Dx14WPgqaytdN8U2Af7HegYW5YEkqxAznsc54GR0xQB5/wCE/EupeFPENtqultmdDtMJztmU8FGA6g/zweor6iGhabZwS+PR4SkfxG9oJns0IaQSbeQASAH9SBuPOAScHg/CXgvTfhNp0/ivxnLbtqCfLaQRneUPI+Tn5mOR2+UZ59OGX4z+Ix46bXhcTCyeQZ0wzFohEONoHAzjJ3Y680Acn4t8Sar4p8QXOoatLJ5pdlSBycW65OI1B6Af/XPNdR8G9V1+z8ZR2ekWj31ld4S/tznyvL6F27AjJwT1zjvXceJ/h7p3xRlt/FHgm8tVa6fbqEczFQj4BLFQCQ/PI78EetN8SeJ/D/wr8KyeF/B1xHNrVwNt3exuHaJhwxYj+LqAo+7yevUA6n4iXWpfD7wa0fgrQ7W3sX8z7ZdwgZtySACFzknkjcchcAelfLbMzsWYlmJySTkk13/w9+J174QL6dfRHUNBucrPaSHOwNwzJn2zleh9utd9P8LfBpvk8b/2rHH4NaMXJtjG+Sc42DuFz269vegC/wDBe3vtc8GXsPi22S80KKWI6edQVWXOW34Lc4B2YzxyQO9cv8db7xU95b2WoWSWXh+OU/YFidWWUqMbmwcggHABAxk1zvxO+Ip8YXkNhpaNb6DZfLbxLlfN4HzMvTjHA7c+prpfAvjKy8baIvgDxixczfJp1/IdzpLyEBJ/iGcKe/3e9AHlvh3XNV8O6xDfaLcSxXikKPL58wZ+6V/iB44r6j07Rop9Ji8eX3hOL/hMPsZlMCO2WcKQuFJwGKgdsjOMnFcXpfhXQPgjv8QeIr7+0b92MVhDBFhgO5AJ646k8DtkmvLLv4l+IZfHUnimG8eK5LYSHdmNYu0RHQrjr6nnrzQBieJdb1HxB4hvNR1Qv9rllO6Ns/uueEAPQDpj2rrPhT4t1vRddXSrCwk1XT787LnTgu4EHALjg4wOueCOvbHbeI9D0r4xeH4fEPhOCGPxHGyR39puCEg5yWzgMR1Ddxx1AAm1LUNG+C3g46RpU8dz4tvUBuJlwxhJHJPoo7L1PU0Ab3jcr8IvCMsngvQxF9vlIur3mQQf3ScnP8RC/wAI+p5+aDdXBvDeGeT7SZPNM2479+c7s9c55zXpXw5+KNzpGrz2XiS4m1DR9Sytz9ocyeUTn5gD2OTuH49q3NQ+Bv8Aafii1ufDt7BL4VuyJWuUnVjAufmVeTu46H8+lAG94U/s/wCN3heK28TW10mo6TIAb63UKJVIHG4gjJ7r9CPQcd8YvGM02pN4M02D7DoullYjAFC+ayjg/wC6O3r1Pto+N/iNYeFrO18J/D6Y21tYy757yJs73B5AP8YJ5J6Hp0rSvtP0j42+Fhq9i8dv4wsoMXFuvHnY6Agn7p7MOmcGgDzX4eePr3wJrq3Ue6awmwt1ahsB1/vD/aHb8uhr2dPBnhKPXx8UhdomgiD7cLQW/HmkY3dfXnaB979eA+F/wyF5cTeIfFsJstG05smO8QxrMw67t2PkHf1PHrWtD8dF/wCExNo1nAPBzN9nFr5CgrF03kAdO+304oA4zxP8U9Z1vxxa+IbZvso09/8AQoM5CL33epYdfyr0LxbL4b+Knw2k8UC4tdN1vTIm85GYAsyrnyucFg38B9Tj1rlvil8NV0m+tdZ8L273ei6kcxpbAyCJzggDH8LZ4+hHpUl58KLTw58P11TxJczQazezxQ2lvERiMsRw4PU43E+mKAE0D49a7oehWul/2Xp1xHawrDC53o21QAN2DgnA7YrN1X4weO/FM6WlpcG1Mh2rBpcTKznGODkv+Rr12w/Z98HWoX7VJqF446+ZOEB/BQD+td9ovhbQfDkezR9JtLMlQpeKMb2Hu33j+JoA+ctB+CXjLxRIL3WJf7OSTlpL5medv+Adf++iK9V8PfAjwloximvkn1a5TBJuG2xFh3CL29mLfjXqVFAEccccMSxxIqRqMKqjAA9AKkrzm9+NngzT9XudNuLm6ElvI0cki25ZNw4IGOevHSum8P8AjPw74pZ10XVYbuREDvGuVdQe5UgGgCr8Q/E0nhHwNqOrQeX9qjQJAHI5kZgowD1xktj0U18+6d8fvG1krLcSWF+T0NzbbSP+/ZWvZ/ir8PdS8f2umW9lqUNpHaPI8iTBiJCwUKeO4w3/AH1Xhvj34R6n4F0iHU5b2G9tnlELmKMqY2IJGc9uMZ+nrQB7l4bvrr4sfDK7XWrQ6ct67Qhrc/fQFSHXdnHOR3+7UenfAvwPZWbwTWE967jma4uGDj6bNoH5VzXwB8anUNLl8LXjp51kvmWh6F4yfmX3wT+R9q9uoA+LEutV+G3j24Fm7R3On3DRENjEseejDkYZcfnX2Houpw61otjqluf3N3Akyj0DAHB9x0rx/wCP/gkXmmx+KrKIfaLbEV4FH34v4XPup4+h9q5X4RfFmy8KWb6HrzTrp5cyQXCgv5JOMqQOdvfjPOeOeACb44fDltKvZPFOlwounTlRdRpx5Up43Af3Tx+J965L4ffE/VPAUskMcQvtOlO57SSQqFb+8pwdp7Hg5r6W0Xxv4R8avPp2nalBqDGMmW2lhZdydD8rqNw5964XxL+z1oepSNPoV7LpcjHJhdfOi/DJDL+Z+lAD9H/aI8NXeE1SxvdPc/xACZBx6jDdf9muh8N33hPxF43u/FOj65a3dzJaJZG3MeyRMNncN2G54HTHHWvMj+zbq/lErr9iX3YAMLgbfXPr7Y/GsHU/gV4w0izuL7zNOmS1QykwXDBiAMkjco6fh0oA+rKjkdYkZ3YKiglmY4AHqa43wDPJo/wu0a61/U4yPsizGeZ8BY2G5FJJ5wpH5V4b8QPinrHjq9fQ9FjkTSpJdkcMKky3eDwWA5weDt/nQBZ+KvxduPEdxNouhTtFoyZSWVeGu/X6J6Dv39K6f4U/BtIktfEXiWJZHdUns7LnCZ+YNIPXp8vbv6DX+GPwbs9Ahh1bxDAlxqxw8cLfMltzx7M3Tnt29a9hoAAABgDArhfiH8SdN8BWUYlQ3OpXCMbe2Ujt/E/ouT+ODjpVP4h/FjS/BCvZW4F/rLLlbcH5IvQyHt64HJx2zmuV+HPw3vtc1W58ZePLRp724dZLa2uPp9507AAKFU9AOnSgB3w78BXviXVpvG/ji2866uHD2lpOpAA7OUPbGAoP1PavbqAABgDAooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAA0UGigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAOd8YeEtP8Z6BNpeoDbu5inVQXhYfxLn8j6ivF9Mk8YfA69KajbDUvDFxMN8sJJCHpuX+42McHg4wD3r6Kqte2VtqVlNZXkCT206FJInGQynqDQBleGfFmjeLtNN9o90ZolO2RWUq8bejA9P5VvEAjBGRXhOvfCnxD4Lvpde+HOoTpgEvYbtzY9FDZEgHPDc+mTXReAfjHp/iSRdJ1pI9L1lTsCyNtjmbphc/dbPG0/hnpQBm/EX4IWuuzTat4baOz1BgWktCNsUzeq/3GP5H25NeYeEvGnib4UatLp+o2E4tJGBmsLoMmMfxxk8An1GQePYj61rmvF3gjRfGunfZdXtyXTPk3EZ2yQk91P9DkUAM8IePNB8bWXn6VcgTqP3trLhZY/qO446jIrqK+S/GHwx8S/Du+XVNOmuLiyhO+PULUFHhP8AtAHK/XpXdeBfj4s8lvp3iyJI2ICDUYuFJx1kXtnuRx7CgD0fxP8ADDwz4u1iHVNWt5pLiNBGdk7KrqDkAgfU9Mda2dK8KeH9CtxDpmjWdsoHJSEbm+rHk/ia0rO8tr+0iu7O4iuLeVd0csTBlYeoI614nqPj/wCJXgvWp5/EejRXWirNtMkEWFCE8FHHfH978cGgD3SvMvEPxt8N+Gtfu9HvrLVXuLZwjtFCm0nAPG5wcc9cc12HhnxVo3i3Tvtuj3qXCgDzI+jxE9mU8j+RxxXlf7QPhL7Xp9n4isrJnuYX8i7eJckxn7hb6Hjp/F9KAOm8DfGDTfGN3qcMtoNNSyi85WmuQxlTJycYGMcdz1r518a67J408d32pW0csiXMojto8ZcoMKgwO5449Tik0f4eeLtcwbDQb10Jx5kieUn/AH0+B3r0/wCHHwV13T/FVrqviKC3gtLNvMWHzVkaR8ZXgAjAJ55ByOPWgD1r4d+Fz4Q8E2GkyKBdBTLckNuHmtycHpxwOPT8ateOPEq+EfB+oaztDyQpiJTnDSMcKD7ZNdHXz5+0V4luVvNP8NwSsts0IurhVPDksQgP02k49waAPEY4rzW9WEcSPPeXk3CqMl3Y/wCJr7e8PaPD4f8AD9hpNuB5dpCsWQMZIHJ/E5P4188/s/8AhePVPEt1rt1EkkOmIFgB5xM3Rseyhu3Ug9RX0zQAUUUUAFfM8o0HwP8AGzXdS8TSXGLed76wgtog3mtISyg84G0McZxzzkYwfpivnP8AaM0QQazpeuRQsPtMTW8zjGCyHK++cE8+iigDob+Tw98e9DWK1uZNN1rTTI0EEzg5DYySB95TtXkcj8efEIvBPiGfxVJ4bj02VtUicLJEBwgOPnJ6BcEHPTBFQeE59ct/Elk/hvzjqu/9ysIyW9QR3GM5zxjNfX96dRTRJ7zT7LT/APhJ3s1ykhCjfgZUsMkgHOBnBIAyOtAHmlrqvh/4D6ZbaTM76pq19Kst55J2+WmMA4OeB2HBbknHFcZ8QvhzpzaIPGvg65e90e4Jlnh+8YATywPXAPBB5XHJ9POPEcurz+ItQl14SjVWmY3IlGGD+mOw9AOMYxxXqfwHi8SNqczAt/wieyQXq3B/cltvG0HjdnGSOMZz2oAwfhp8LrjxhL/aupubPQIDmSU/KZ8dQhPGBjlu31zjvLf416Da+JE8NR6TAPCcYFmk+M8A7d5U8GP264568VY+NB8SN4Zhm8OzwP4VaLbOlggOF9Sw4MZ9uBjmvnEAsQACSeABQB6h8V/hu/hzUTrOixLPoN++6P7OCwgY/wAPHG05+U/h9eh8F/D+y8C6J/wnXjVTFPajzrLT3ba3mDlM/wC2SOF7dT0OOv8AhHbar4P8FPeeLNUSy0yZl+yW162w2wJI6sflDZB2/jxzXCfHXTfE6aomoXV+974dnfdaCMHy7cleFOOMkZwc8+3SgDY0zxdpPxps7rw14kittL1QuZNMuIhnH+yNx5b1GRuHTGK8l8Q+Cdb8OeJV0K6tGku5WAt/J+YTgnAK49fTqO9YllBdXN7DBYxTS3buBEkKkuWzxtA5zX174ZstYsfCVhZ63qVjL4sa3l+yyXWGkUkE7Sc7nxxuI9O+MkA80sLDT/gTov8Aa1/NFqPii/XyRZRz7UjiLAnsScFPvY68DoScnxn4Ms/HGkf8J14MQytcFpNTsN4LxSfeZgM9fUd8gjrXn3jiLxJF4puh4rMzaocbnkxhl6Arjjb6Y4rZ+Euua9pPjS1h0WGS5S6ZY7q3VCymLcMuQOm3ru7c+poAyvBHgjUvHOuLYWC+VCnzXF065SFeevqTjAHc+gyR7dZ+MfB3gW8t/hyry3enOjw3d+8w2xySEgq2AOOTkg/LnvzjR+I0D+CPAeoy+CdKt7T7VNtvp7RMGBcHLADp6ei5PSvlgnJyaAO8+JPw8u/A2sFog82j3LFrS5AzgdkY/wB4Dv36juBsfBjw7qkviJPFAuhp+j6YSbq5kO1ZFwcoOxGOp7cd8V0Pwj1C68b6Ld+CvENjLqGiRRB47g5BgKkFU3j6cd+o6cVB8Y9d1Lw7b2/gfS7CXTPD0cKhJQSftYwCQGPYE8jOSevWgDqfiM//AAtHwTJceDNbF5BYOz3VjGjK8+BkfKQGJHJAxg9uRXzUytGxVlKspwQRgg11PgPxtfeBvEC6jaASwyL5dxbscCVMg4z2Ixwe30Jr3eXwN4G1+9g+JMk0kOnvH9tngKYidhklmGM5yDkDqR78gGX8F9el8O+DA/inVrez027l26St1NtYhc+ZjPRMlce5PqKoeP7fX7r43eFGu41m0hr6A2AgG5SgdWkLD16knpgexrzb4meNT438UNdQB49Mtl8mziY4wvdiOgLH07ADtmut+DUms+LPG+n/ANpajdXFloFu80Ac7lQnCKmfoTjPZTigD6aooooAKr3VzFaWs1zO2yKFGkkbBOFAyTge1WKKAPg/Vr3+0tYvr8R+X9puJJtmc7dzE4z3616r+z3ol1d+L7nWVbZbWMBjbg/O78BfwAJ/AfUfQs3hjw/OrCbQ9NkD/eD2kZ3fXIp+keH9I0COVNJ063sllffIIIwu4++KANOsTxboMfifwvqOjPIYvtcJRZAM7G6qfpkDPtW3RQB8QWlzqvgXxgswXydR0y5wyNnaxU4KnplSPzBr7M0DWbTxDodnq9g++2uoxInqOxB9wQQfcV4v+0J4OQw23iy1GHUpa3SKgAIO4rISB1z8pJ/2fSvJfD3xC8VeFrVrXR9Ylt7djnymRJVB9g4IH4UAfZ1zawXltJbXUKTQSqUkjkUMrqeoIPUV8YeLvDV5pfjDWLO20u7jtobyVbdRC2PK3nYQccjbjB719geHJr+48M6ZPqbo99LaxvOyLtBcqCeOMVrUAfNP7O9io8banLPGyz29kQobIK5dQcj8K+lqjSGKN3dI0VnOWKqAW+vrTLq5gsrWW6upUhgiUvJJI2FVRyST2FAE9cF8RfHnh/w3oWoadeagrajPbPHHaQ/PJllwCw6KOc8446V5x43+P00kj2PhBfKTo1/OgLE/7CngD3P5DrWH8PPhJqHjWU634jlubfTpGLhif310xPJBYHC+569vWgDhvD+geI/Gd3baVpy3N1HEdo3MxhtlPUk9FH8+2TX0z4A+FekeBlS6Utd6uybZLp+i5AyqL2HHU8+/auu0bQ9N8PabHp+kWMVpapyI4x1PqSeSfc5NXJp4raFpppEiijUs7uwVVA6kk9BQBNXlXxI+Ka6O40DwsVv/ABBdHy18j959nJ4HABDP6L26n0PK+M/ipqfjHVB4T8CCZhO2x7yLKvIOp290Ud29Ae3XvPh58KtK8Expezt9t1mRMSXLj5YyeojHb03dT7ZxQBzXw6+EN1aauvijxfObnVCxmjt2O/a5/jkb+Jvbse5r2iiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAA0UGigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigArzb4gfCLR/GXnX1tt0/WSMi4UfJMeMCRfwxuHPPfpXpNFAHz/AOHviD4k+GMsPh7xxplxLYI22G9Vi7KnQYPR1GOBwQPwFe3aLrmmeINNj1DSr6K7tn6PGeh9COoPseadquj6drli9lqdjDd2r8mOVdwz6j0PuOa8m8RfDzXfA8sut/DO4ngDjN3pmfNDgdCisDuxluDyM8daAPZnRZUZHUMrDDKwyCPQ14/45+BOlaxDNfeG8adf8v8AZ85glODwB/ASccjj271o+C/jLpGswix8ROmj6xG4ieOfKpI3TIJ+77hsde9epAgjIORQB8g6X4h8dfCrUBbSx3lpCr/NZ3aFoJOedvbnn5lNe4eFvjF4V8W2yWOpmPT7ycbHtbr5onzxgORtIPocenNd5rOhaXr+nNYatYQ3lu3OyUdD6g9Qfcc14V4v/Z7uY5JbvwpdLNEeRY3LbXHssh4PPrj6mgDs9d+D0Ed8Nb8EXx0HVVyVVGPkPn1HO0ewBHtUvg7xf40TxOvhnxhoMnmsreVqdtERE21SxLH7vOMAjHOBjnjx/RfiF42+F97/AGJqUDvbw/8ALjeL90E9Y3HIHXGMr7V7f4T+MHhbxQsMDXi6fqEgwbW6O35vRX+63tyCfSgD0CvMviJ8XofAWtQ6WdGkvZpIFn3GcRKFJYcHaxPK+lem14h+0do1vJoGla5ki5hufsmAOGR1ZufoU/U0Adn8OviZafEFLxYtOuLK4tAhkVj5iENnGHAHPB4IHtnnHzP8QvEyeLvGt/q0Ue2B2EcIxglFGAT7nrR4Q8Q+KNH+3WPhnz2fUYxHNHDb+axAyARwSCNzcj1q5pfwr8aapeQQjQby2SVhumuU8tUGeSd2Dx1x1oA+h/g14fbw98OLAO2ZdQP29+eB5irtH/fIX8c16DVe0txaWUFuuAIo1jG0YHAxwKsUAeYeLPjh4a8OXFzZWyT6lfwsUZIRtjVx2Ln+gPStP4a/Ea38faXcSyQxWuoQSlXtVk3HZ1VxkDjqPqPcV81fEXwjJ4M8YXWmcm2f9/asTkmFidufcYIP0rqvht8PvHcGt6Z4i0+z+w26yKTNcuF3xN975PvEFT6c5GKAPqeuF+LegQ+IPh1qiSZ8yxjN9CdxGGjUk/XKlhj37da7qmSRrLG0bjKMCrD1BoA+efBev+DPh18PRrtvNb3/AIlvI9r24kBkRs8Ljqijgk9/fivOtJ+IuvaZ43fxW84ub6YkXAlHyyoQBtwOgAAxjpgV0msfCgJ8UbnwzDepYQ3MTXGnSXAJWXpiPPHP3hxnpWZ4R+FHiDxH4kk029s59Pt7SQLezTLt2D0TP3iQDjGR0PSgD1q48LeF/jVY2HimGaXTniYxX6xoA7lQCULHjIyMPg8Hp6cX8SPiVpsOiR+DvBHlw6UqbLi4gUoH55ReAeSMs38WfQnO34j+ImlfC2Sz8LeDILWeO1mLak0gLMXyAVLcZfjk84wB2xVHxz4L0Lxp4aXxp4FhVnXJvbKBdvux2cYcdwPvDkepAOQ+HHxLuvCM39l6gou/D9y224gkBfylbhmQe+eR0NelaZ8NPCPhK6l8d32qpdaEqC7sYHgACh8MnU/MeRtGBzj6Vyfw7+FFncaafFPjOQ2ekQZdbebMfmKP4nJwQp7Acn+e/afGXRtd8S3HhzVdOtf+ESugLW3dotpj6KrPk4C/QArwe1AHlnj7x1feN9emu3lni08MPs1m0pKRADGcdNxxkn3rt/hd8T4YrNPBvidRPpNyhtoZn+Yx7zgI2f4OTz247dMD4nfDabwjrEc2mQyT6JeMFtHDb2DkD5Djvnp6j3zXbeEvBGk/DXw2PG3jFVbUFUNaWMi/6qXqgAPWTj/gPJ7ZABqLo3hv4D2txrc8lxqupXZaGzjKeXhc5K55A7Zbv2HWvEdd8Z614g8Tf2/dXjpeowaBojt8kD7oXHTH6969c8N/EzTfiNDf+F/HSWtvDeEtaTofLWM9l3NnDDqrHryD6HzrxR8NNZ0Dxunh21t3vDdtmwcADzk689gRyDnpjPTmgD0qDVtH+OHhWPRbx0s/F1nCZIJHXCSMAMkEfwtxlcZHJAOKi1LXdJ+Cvhf/AIR/RHhu/FdwqveXGzcsZI6kn0/hX8SOeUms9G+B/h03EctnqPjO5CqomGfJVvvEKDkLgEZ6sfbilm0rTfjl4Zm1uyhSw8V2Q8uaJW+SfAyuc9j0B7EEHI5oA4D4dfEm88Ha/LLeNJdaZfPm+iJ3MxOf3gz/ABZPPqOPQjrdZ+DqeJ/ENtqvgy5tW8O6i295d3Fp3YBDhj7LjjocDmvNtB8Ga1r3ilfDsNpJFeq5WcSqVEAH3i/oB+pwBya90g8TeE/hC9j4NgmlvBcTl9Tui5H2csqruIH0Hyg5AB6mgDmfHfjWz8CeH18BeDpArRRgXuoxPh95+8AR/GccnPAOB04d4S1jTPip4Pj8GeJ74x6zbNnT7xzl5ODjJJ+ZgOCO4x35rlvib8MZvCr/ANtaXL9s0G6YNFKG3NFu5AY9wc8N3rN+G/gfWfF/iCKXTne0t7OVHmvgceVznCnu/oPzoA6Lw78EtafxZLa+IY1ttIsSJZ7oE+XcID0jbjqAck42jr2rpbr4z6ZoPi+w0fRIYj4Qs4/s0wji5Y8guhPUDg/7WD613Gt3elfELQdW8H6F4lY6laxASujcy7eCGOAGUnAYrxk/gfloaFqh13+xRYznU/M8n7NsO/d6Y/zxQB6147+DN3dXUmu+Clgv9NuyZRbQsqmPPJ2dAy56AcjpzXQ/s6aO1vpGt6jLGFd7pbXqdw2LlgR0/jH6026sNZ+Hvw50/wAHafqjS+ItZudsSIM+QjY8zZjkAd256sR7eoeDPC1t4O8M2+k27CR1zJPLjBllP3nP6D6AUAdFRRRQAUUUUAFYnirxJZ+EvDt1rN6rvFAB8keNzsTgAZ9zW3Xh37RmqzR6PpGjRB9tzO07kLwdgwBnPqxOMdh6UAaWm/tE+FrpcX9lqNk+eyLKv5g5/SvVrG+ttT0+3vrOVZba4QSRSL0ZSMg18IS281vKEnhkiY87XUqcfjX3dYWNvpmn29jaRrFb28axxovRVAwKAOW+JPg258d+F10q2v0snW4Wfc6Flk2qw2nB6ZYHPPTpXiF/+z14vtV3W1xpl2N2AsczI2PU7lA/WvqKigCjpNtJZ6PZWk7B5oLeON2BJBZVAJBPuKvVzPijx34e8HQ51fUUjmKlktk+eV/oo6fU4FeDeK/jp4h8QkWXh+CTSoWJGYW8yeT/AIFj5f8AgPPvQB6948+LOi+CFFuANQ1NhxbQyABPd252/TBNeCal4k8b/FzVhp0Ebzx53pZWw2Qxf7TEn3PLHvXS+C/gTquuiLU/Etw1hbSneYMFriTn+LPCZ98n2FfQGg+GtI8M2RtNHsIbSI8t5a8ucAZY9SeKAPNPBPwH0rRvJvvETrqV8p3eQB/o6cdCCMufc4HtXsVFeT+PPjRZeHbptH0KBdV1Y/LuRsxRMeg4yXb/AGR+fagD0HxB4i0zwvpUuo6rdRwQRqSoLANIwBO1AT8zHHSvBtT17xd8bNUGl6LbSad4dSQiSVshCOOZWHBb0QevfrV3R/hh4s+IeqQ6749u5re2/htWGyXbn7oTGIx+vt3r3LSNG0/QtLh07S7WO2tYVwkaD9SepJ7k8mgDD8D/AA/0fwNYGLT1aW5lUC4u5fvykZ7dFHPQfjk811tFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAAaKDRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFAHH+Lfhp4Y8ZKZNQsTFdn/AJe7XCS/icEN+INebXv/AAmHwUltxZzya74VdsuksfzQHuoIJK8Dg/d68Zr3mmlQylWAIIwQe9AHJ+D/AIjeHfGqbdMuyl0q7ntJxtlX8OjD3BNddXkPjP4H2GrXL6t4ZuRpOp7g4jHywFuORtGUPfIyPbvXPf8ACwPiD8NJ7ex8YaaNT08fKt4GJaTvxL0JHPDDPH40Aez+IPDOj+KNPax1iwiuof4SwwyH1Vhyp+leE+M/2f8AULWZrrwpN9stzkm0nYLKn0Y8N+OD9a9l8KeP/D3jOBG0u+X7SVLNaSkLMgHXK55HuMiupoA+SNB+J/jXwLqKWF9LcTw2xEcun34OVUdgT8ynHTt04Nez2Pj34e/Eyyi03VfKWTcsgtNQOz94Bj5Gzgnkjg5PpXc6z4a0TxFEI9X0u0vAFKq00QLKD/dbqPwNeO+Kf2dY55jP4X1FLdWPNrfFiq/7rqCfwIP1oA9m0fRdJ0KzFvpFhbWdufmxAgUN7kjr9TWnXykLr4l/CKZDN9oXTw2xUlbz7V/Yc/Ln22mu00X9pC3kmCa3obwocZltJd+P+Atj+dAHvNFc/wCH/GXh7xSB/Y2qwXUnl+Y0IbEirxyUPIwSB0710FAHNaz4G8Pa94itNb1SwW5vLWPy4/MJKbQSwynQ4JPX1+ldKAAMDgUUUAFFFFAHnnxX8Ez+LNGhvdNlmi1rS901mYTguTglc5GD8owex+tY+h+M7z4jeDZtE0zVpdH8W20AM++LG9l4OD/CCcZI+Zc9K9brwf4s+C9Y0PxAPHnhMTxSoDLffZ25jIxl9vdSM7hyOCTwTQB4VrNlf6drF3Z6pHJHfRSkTCU5bd3JPfPXPfOa9T+Bmna1Y6rP4lluDY+GoIpPtskrbY58KcADvtJzntjHeu30nRfD/wAbtF0/xFqlrLaX1lO1tdC3KgTlQrYJIyVwRjuMkV5/8UviZBrMEfhnw5FNYaNZs0UqgCMT7SABtHRBgkA9cjIGKAOv+MMGp+M/Ctv4g8O6pDe+G7aNpJoICVbcDy5H8WPQ4K9cda+da7b4fePrzwTq53Dz9JuiEvbRhlXToWAP8QGfr0NexJ4I8A+G5Y/iQZ5hpIRbu2tNgZA78rgYznJGFONp78UAL8ILjUNB8Dtc+ML2C10iSWP+zBfOqlc5zjd0B+XA7YJ4Fef/ABssfFkfiJrzWpjc6PI5+wSQnEKKRwuOzYHOevODXN/ELx/qHjrWWllkZNNhY/ZLXgBB0y2OrHufy4rt/hp4+g1ywHgDxdi5srxPs1nO4yyseFQn6/dPUHA+gB4zbwTXU6QW8UksznCJGpZmPoAK+tPBupajo/hXTNE8Wava2viO6jcWSTMrSKgGE3DgFh6Z56ZznHGzeHNB+BOnSa68j6xrdyzQWAlTy1TjJOAT0GMnqegxk14f4i8R6l4o1qXVdUn8y5kwBgYVFHRVHYCgDS8eaJ4i0bxPcr4mDSX1wxl+09UnH95Tgce3GOmBUHgu78S2fiSCTwqLhtTIKhIV3bl7hgeNvTrxXqfhrxRafFzQJPB3iuaOLV1w+m3oQhncA8kZwW65HAI9xmrd1daX8B/D8mn2hW/8V6gnmGZoyESPJCn/AHQQcDqTnPGKAPQvFUeu2vg68v8AwzpVonii5iiF60CJ5oO35sH+Jl6KCT7Zr5DuJJ5bmSS5eR52Y+Y0hJYnvnPOa6bwx4/1vw54rbXlupbiWeTdeJI/FwCeQ3v6HtXp3irwXpnxXgh8UeB5oVvZWWO/s5GEe08/Ow7N29GAyOc5AKHwh8cy6kE8Ba5Zyalpd2hihwu4wrjJVsc7OpznK/Tp0HxS1O3+Gfg+Dwt4X0+axj1AMXvVLcDPzAPnJc9Dnop47Yo6xq+l/BXw2ND0KS1uvFM6/wClXZjBaIHnJ9QP4VJ9yDVPwL47tPHdgfBPjv8A0s3BP2O+YgPv5wC3Zv7p79DQB5Doms6hoOs22p6ZM0V5A4ZCOd3sR3B6Ed6+utDiOo6LZeLtR8PQx+JvsLFkEZSTOD8gzkjPvkjdivMPC3w2tvhml74v8ZyQTDTjm0htz5gZs/Kw3AfNnG3pg8nGK499c8S/Fz4g/Y7C8urG1uvk8hZm8uCBRyWC4B79epIFAHefCix1bxp4zvPiHrhGE3W9nGAQAcbTs9FVSR7liete51naHo9l4f0a00nTovKtLVAkanr6kn1JJJJ9Sa0aACiiigAooooAKYyK5UsoJU5GR0PrT6inmitoWmnlSKJBlndgqqPcmgClqmgaRrbQNqmm2t4YG3RGeINsPtmtKvLfE3x18KaG7QaeZdXuV6/ZiFiB9DIev/AQwryPV/jX431+aS10+ZbGO4bZHDYxZk54ADnLZOeowc9MUAfSOu+L/D/hqPfrGrW1pnO1Wbc5x1woyT+VeEeLf2gdWvppbXw1bpYW2Sq3MqiSZxnqAflXI7YPXrVXwv8AA3xJ4jmkvvEly+mJIxcmX97cSseSSM8e+459q9h8I/CTwz4QmS7gge8v1H/Hzd4YqfVRjCn3HPvQB4P4V+EnivxpdLf36y2VlM2+S9vMmSTJ5KqfmYn1OB719D+EPh54d8FBm0u1Y3boEkuZm3SMPT0UE84AH6V11Z+q6zp2h2bXeqX1vZwL/HM4UH6Z6n2FAGhXO+KfGOieD9Ne71W8WNtpaO3VgZZj6Kvf69PU15drXxg1rxXd/wBi/DrS7iS4YnfeSxgkL6gH5VGe7fkDWh4b+Cf2i7Gr+O9Sl1m+YAiAysyL3wzE5b6DA+tAHMy+K/H3xcuf7P0C2l0nQ5cxTzKCUxnJ3S4BzjjavXv1r0rwD8LNH8DQCcqt9qzfeu5EwU9kHO0e/U/pXcW1rBZ20dtbQpDDEoSOONQqoo6AAdBU9ABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUABooNFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABVe7s7a/tZLa8t4riCQYeKVAysPcHg1YooA8Y8WfA6ITjV/BF1JpWpREusAlZUJ/2H6of0+lULLxp8TvAyMvi7w/PqtgBn7TEVLx+5ePIx1+8AfcV7tRQByfhX4h+GvGCIml6gn2srua0lGyVfXg9evUZFdZXn3iP4P8AhPXx50NkdKvQSyXGn4jIbsSv3Tz7A+4rlIrT4u+AottvLbeJ9Oj+7G5LyqvtnD5x2BYDigD2W5toLy3e3uoI54ZBteOVAysPQg8GuF1v4MeCNbDMNLOnzEf6yxfy8f8AAeU/Ss3QPjl4dvWFrrsdxoeoD5ZI7mMmMN/vAZH/AAICvTLa6t7y3S4tZ4p4XGUkicMrD2I4NAHzNrPwD8W6VdtJos1vqMYbMTJMIZQO2QxAB+jHpWfbeO/iZ8Ppvs+pNe+UWwItViaRWx/dc84/3WxX1hUNxbQXcJhuYY5om6pIgZT+BoA8S0f9o/TpY0TWNEuIJSwDPauHTHdsHBH05+ten6P4+8Ka+kP9n69YySTHakDzCOUn02Nhv0rC1r4MeCNadpP7LNhKSSXsZPL/APHeVH5V5lq/7OWrRTSvo+sWk8OcxpdBo3x6EgEE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},
{
"title": "kolbe2018hubbard_DIA_0002",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105244802",
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"caption": "Darstellung einer Heisenberg-Kette mit Übernächster-Nachbar-Wechselwirkung und sieben Plätzen",
"kind": "Abbildung",
"refnum": "1.1",
"height": "323",
"width": "1297",
"top_left_x": "383",
"top_left_y": "459"
},
{
"title": "kolbe2018hubbard_DIA_0003",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105245825",
"modified": "20260602105245825",
"page": "016",
"latex_code": "",
"canonical_uri": 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pnHFR2dv04roLS16cV7NSrqZJEUFl7VfjseOlaNtaZxxV2VbaytzPdSpDEOrOwH+eeK4Z1rFpGP9g9qiex46VpyazpcEfmTm6gi6edNZTJH/AN9FMfrV4QRXECzQOksTDKuhyCPrWccQm7XCxyE1ljPFZNzZ9eK7a5s+vFYt3a9eK6qdViaOIu7XqcHNepfBbxy9peL4S1Ob9zMSbF2P3W5Yx/Q8kD1yOcgDhLy368VhTGW0uI7iBzHLE4kR1OCGByD+fI9MCt61KGIpOnP5eok7M+0880tYXg/xBH4o8J6dq6YDXEY81R0WRSVcf99A1u18dODhJwlujo31CvmT41aodS+I72oLeXp9vHBg9CTlycf8CA99v0r6br488XN5nxD8RNgZ/tOdcgAcCRh2A/x9+tevksU60pPojOo7IbYx9K6SyhHFYdio4rp7FRxXs1ZWM0bFlADitS5mTTNOkvHt7idYwP3dvHvkYkgYC/jUNig44rpbGPp1znOc15VaTLRx8Gi6140niOr2baZocZV/sTNumucHI8w/wqOuOv6EZHhXwrd3Wif21oMkVvq1teXEexx+6uIt/wBxwPTnH/6se02duGAGPz5rlPhXbbvBtw2B/wAhK57f7ZrzJTfMaGTpeq3Oo3EllqGh3um3kcZdzKu6FuQPkkHB6068tuvFdrewAZwOeea5u+jxmuyhN21IaONvYAM1zl7D1rr75OtczfKOa9SjIhnI30Y5r6Z+EurNqvw20tpGDS2wa1bH+wcL/wCO7a+br5RzXoHw28Yar4Z8Jyw6b4eOrrNfyu5+2rB5eI4sfeU7s57elZZ1KMcG6kujX4lUYylPlirtn0TRXkv/AAtrxR/0T7/ytRf/ABFH/C2vFH/RPv8AytRf/EV8i8Zh19tHd9Ur/wArPWqK8l/4W14o/wCiff8Alai/+Io/4W14o/6J9/5Wov8A4il9dw/86D6nX/kZ61RXkv8AwtrxR/0T7/ytRf8AxFH/AAtrxR/0T7/ytRf/ABFH13D/AM6D6nX/AJGetUV5L/wtrxR/0T7/AMrUX/xFH/C2vFH/AET7/wArUX/xFH13D/zoPqdf+RnrVFeS/wDC2vFH/RPv/K1F/wDEUf8AC2vFH/RPv/K1F/8AEUfXcP8AzoPqdf8AkZ61RXkv/C2vFH/RPv8AytRf/EUf8La8Uf8ARPv/ACtRf/EUfXcP/OhfVK/8rO48dH/i33iXjn+yrrp/1yauX+DJz8J9E/7b/wDo+Sua8S/E3xFqHhXV7OfwR9mhuLKeJ5v7Xjfy1aMgttC5bAOcV0nwY/5JPon/AG3/APR8lcuNqwqUk4O+q/UXsp03aasd5RRRmvH6F+ZxPxFtdNtfDd5qLWsf2+QpHHMOHzkc5HsDWt4R0K20nRLKTyAt9JAhmlOS5JGSM/56VgfEI/2nrXh7QF5W4uBLKB2Xhc/kXrt7m8hs40eXzCCcKIonkP5KCao9au5RwFKmndzcn8k0kvnZlij+dZmh61b69Zy3NtHJGkc7RYkABJXr36VJcapHHqA0+GNp7vy/NMSsF2JnGTkg/lmkec6FRTdNqzXTsX/50Vl6frtvfajc6a0clvfW4DSQy45U/wASkHBH+NalBNSnKlLlmrPf5M8u+LIH/CS+AG4yNZTnp0ePivYK8W+Nd1JY6h4MvIoPPlg1LzY4t4TzGUoQu7oMkdav/wDC2vFH/RPv/K1F/wDEV7WFr06VCKnK2/5mKoVKjfIrnrVFeS/8La8Uf9E+/wDK1F/8RR/wtrxR/wBE+/8AK1F/8RW/13D/AM6K+p1/5GetUV5L/wALa8Uf9E+/8rUX/wARR/wtrxR/0T7/AMrUX/xFH13D/wA6D6nX/kZ61RXkv/C2vFH/AET7/wArUX/xFH/C2vFH/RPv/K1F/wDEUfXcP/Og+p1/5GetUV5L/wALa8Uf9E+/8rUX/wARR/wtrxR/0T7/AMrUX/xFH13D/wA6D6nX/kZ61RXkv/C2vFH/AET7/wArUX/xFH/C2vFH/RPv/K1F/wDEUfXcP/Og+p1/5GetUV5L/wALa8Uf9E+/8rUX/wARR/wtrxR/0T7/AMrUX/xFP67h7fGhfVK/8jMv9oPVWSy0XR4/uyyvcye2wBV/9Cb8QK8gsYxxXTfFLWrvxBr+k3l7Y/YZW04brUXAm8siaUfeHByFU/l6Vg2IHFfb5fyrBwceqv8AecFRNTaZu2UPSujsoAcVi2KjiumsUHFZ1pAjUs7bpxWRf2uur8RNKNvpoutM8oqZGHyxMSd7DB4YDA6HI4HU11NjHnFdJZQAgDt6flj8scV5VeTa0NEjOfTY5IWSSNWRl2sGAwR6H2ryb4SGWZddtkZnsIZlaDOcLu3A4/AL/k16X40S/wBVurTwho8vkXF/G019dDrb2obaSPd2JUfQ+vF7TPC+m+GNJTTdNh8uFMsSTlpGPVmPc+/6YGK5lO81Ydjnbu2xniufvYAM12d9GBmuavl68V6VKTIZx97COa5q+j61118o5rmb5RzXq0Zmb2PWv2f9UaTTdZ0hyT5EyXCZPZxtP5bB+dez186fAed4/Hl/Du+STTmJX3WSPH8zX0XXzuawUcU7dbM3g7oK+PfFg2fEHxEOCf7TuD8rA/8ALVvT9fTp1r7Cr5j+NGmPp3xIluTuKX8EdwOMAFRsbH/fAPrz9MdGSzSrSj3RNTY5+wI4rprAjiuSsX6c10ljKOOa9mstWZo7CwccV0thIOK46xmHHNdBZ3OMc15NaLNEdrZTBcc1yvwpuQvgy4XP/MSuv/RhrQgvMAYNcr8NbsR+FZ1z/wAv9wfzc1586fvIo7m9lBzzXNX7jmr11eZB5rDvLjrzXVSg0SzIv261zF+RzW5ezA55rm76XrzXqUYkMwb4jmuw8EeE/FniLwmZvDGp2NmI7+ZbgXYPz/u4tu35G/2s9O1cRfP972619LfCPSm0r4caaJFxJdbrp/cOflP/AHwFrLOFCWE5JdX+Wv52LozlCXNB6nn/APwrH4r/APQyaH+R/wDjFH/Csfiv/wBDJof5H/4xXvNFfI/U6F/gR2fWq+3Mzwb/AIVj8V/+hk0P8j/8Yo/4Vj8V/wDoZND/ACP/AMYr3mij6nQ/kQvrVf8AmZ4N/wAKx+K//QyaH+R/+MUf8Kx+K/8A0Mmh/kf/AIxXvNFH1Oh/Ig+tV/5meDf8Kx+K/wD0Mmh/kf8A4xR/wrH4r/8AQyaH+R/+MV7zRR9TofyIPrVf+Zng3/Csfiv/ANDJof5H/wCMUf8ACsfiv/0Mmh/kf/jFe80UfU6H8iD61X/mZ4N/wrH4r/8AQyaH+R/+MUf8Kx+K/wD0Mmh/kf8A4xXvNFH1PD3+BD+tVv5j521/4efEux8Oapd3/iDR5bKG0lluI487mRUJYD9yOSB6iu++DH/JJ9E/7b/+j5K6rx2f+Le+Jf8AsFXX/opq5X4M8fCfRP8Atv8A+j5K5MbShSorkVtf0YlVnOV5u53bMEQsewziuf8ACfiabxLb3Nw+nSWkKSBYWds+aD+A5H9a6Gsl9Ah8hraG8vbe0bObaGXanPUA43KOvAIHNeQjroul7OUai1bVn23v9+hyul/8VB8Ur3U0+ez02LyIpBypc8EA9D1f8q9A75PJqtYafaaXaJa2UCQQL0RB39T6067vI7KISSpOwJxiGB5T+SAmnua4rEfWKsVTWiSS9F/wbv5nM/D7nRL3k/8AIQm6/UVu3Fnbw3rapFp32i/8sRbo9ocoecfMQOveud8CzPaWFxaXVnfQTS3ksiCS0kUbSRgltuB+JrTW5vrHxHfvqV2w0t0T7KghJRDgbiWAODnPWg6MZCTxVR38/VaaGb4dSO58YarqF6wt9WMaxfYT96KHjnPRs4ByvHPWuxrjLe0n1f4iLrdvHJFp9pa+R5joUE7HdjAPJA3denArs6T2MMwac4Wf2Vp2tpb5fqeQ/HG3ubu58IW1lIkd3NqJjgd/uq5KBS3B4yfSqf8AwrH4r/8AQyaH+R/+MVsfFr/kZPAH/YaT/wBDjr2GvawlCnUopzjc8721SDtB2PBv+FY/Ff8A6GTQ/wAj/wDGKP8AhWPxX/6GTQ/yP/xiveaK6PqdD+RB9ar/AMzPBv8AhWPxX/6GTQ/yP/xij/hWPxX/AOhk0P8AI/8AxiveaKPqdD+RB9ar/wAzPBv+FY/Ff/oZND/I/wDxij/hWPxX/wChk0P8j/8AGK95oo+p0P5EH1qv/Mzwb/hWPxX/AOhk0P8AI/8Axij/AIVj8V/+hk0P8j/8Yr3mij6nQ/kQfWq/8zPBv+FY/Ff/AKGTQ/yP/wAYo/4Vj8V/+hk0P8j/APGK95oo+p0P5EH1qv8AzM8G/wCFY/Ff/oZND/I//GKP+FY/Ff8A6GTQ/wAj/wDGK95oo+p0P5ENYuv/ADs+UfiLpGsaJq2jWmu3ENzqA0797PB9x/38xGPlXopUHisiwPSvV/2g9MZrbRNYQfLHJJbSH/eG5R/461eQ2Mg45r7fAOLwkFHorfd/wDgqNubbOusCOK6ewYcVyFjKOOa6OxmHHNZVkCOxsHHFdLZTAY5rirO5xjmt22vMAc15dWDLRe0Z1bxh4ju2UlwttbIT/CioWwPT5pGz71evZgc81wfhz4k2viLxDfaRFZzwtahmSWTkOFYLkgcg8jHXiuiubzIPNc0Kd3oVcq37jnmuZv261q3lwDnmuevphzzXpUoslmJfkc1zN+RzW9fSjnmuavn6816lGJnLY7z4ERM/j2+mx8iac43dsmSPA/Q19F14t+z/AKYyafrWqsOJpkt0OP7gLH/0MflXtNfPZtNSxTS6WNYbBXl3xv8ADT6v4Rj1WBN1xpTtI2O8LcPx7YU/QGvUajliSaN4pEV43BVlYZBB6g1y4es6NVVF0LaurHxlZTdOa6GzuMY5pfiF4Nm8EeJGjiDNpd0xktJOwGeUPqyk4+mDWPaXXTJx9RX16lGtBTjszmejsdtaXPTmtu2u+nNcTbXfTmtWC9xjmuOpSuWmdnFfYHWsjwrbz6No8ltclQ7XM0gwc8FiRVGO+461Ib7A6iuV4e8rjubs15weaybq7BzzVGS+461nT3nXmtYUrCuPvLnrzXP3s455qW6u855rEu7nPTntxXfSp2JZe8P6JN4q8U2GjQll+0SDzHHVIxy5/AA496+vYII7aCOCFFjiiUIiLwFUDAH0xivNPg/4Gfw5pDaxqEW3U79FIRhzDFwQvsT1P0HpXqFfP5pilWqckdomsFZBRRRXllhRRRQAUUUUAFFFFABRRRQAUUUUAVNRsItU0u70+4GYbqF4ZMf3WUqf0NeR/CHV5dEkvvh9rIEOqaZK7QAniaMncdvr13eu1s/wmvZ64bx38M9O8Z+XepPJp+t24H2e/hJ3DByAwGMjPORgg9D2rHEUVWg4MqLszqhyMijFeUKvxs0OJbVbPRtdCjAuXcBiPfc0efqRn3NL/bPxv/6E7RP+/wAn/wAkV5Dy+t6mntEerYpe/wD9f/PHtXlH9s/G/wD6E7RP+/yf/JFH9s/G/wD6E7RP+/yf/JFL+z639MHNNWZ6tj+WKXHTPUfp/n9K8o/tn43/APQnaJ/3+T/5Io/tn43/APQnaJ/3+T/5Io/s+t/TD2kb3Wh6tj/D6f5/Cj8frXlP9s/G/wD6E7RP+/yf/JFMn8OfFfxrGLPXb3T9A01+LiOzbfI6+nDMSPbeB9aay+tfUftEQ3Vx/wALG+NOmW1gvmaR4Xczz3K/daXIOAehG9FGO4VyM9/bq5/wn4O0nwXpH9m6RCVjLB5JZG3SSvjBZj+HQYHtXQV7VOmqcVBGLd3cKKKKsQUUUUAFFFFABRRRQAUUUUAFFFFNAc5448ODxV4P1DSRgTSx7oWP8MinK/qMH2Jr5MtmeCZ4pVKSRsVdWHKkdQa+1cV8+/GjwO+mai3irTYj9juWH2xFH+qlJxv+jHAJ7N/vCvayfFKD9jLZmc49Ti7KfpzXQWlz05ribO56c1uW1305r2KlMyTO2trvpzWpDe4A5rjIL3pzV+K+461wzo30LTOlh+yW80s8NtBFNMcyyJGoaQ/7R7/jSy3uQea5/wC38daikvuOtZqilsguaNzd8HmsW7uRzzUU97nPNZFzd9ea6qdITZHe3HXmsCfzLmdIIEaSWVgiIo5ZicAD3zVi7uc559f0616Z8F/BDX9+PFeoR4tbdiLJWH+skzgyfQcgf7XutdNWrHDUnUfQSV2ev+DfD6+F/CWnaT8pkhizMw/ikY7nP5k49sVv0mKWvjpzc5Xe50WsFFFFR5gZHiLw5p/inRZtL1OLzIJOVYcNG3ZlPYjP9DwTXy94u8F6t4F1Mw3iebZu2Le8jUhJOcgHsrgdQfwyOa+uKqX+nWuqWclnfW8VxayDDxSLuVvw/r1Fd+Cx08M7bx7ESgnqfH8F7yBnmtKG9969G8VfAlkaS58KXeFPzfYblv0R/wCjf99V5bq2g6/4ckZNX0q6tQDjzGTMZ+jjKn8DX0VLEUK6vGRk00a6X3HWnG+461y633vT/t/v+XNbexFc6CS+461Rmvc5+b/61ZQunmkWOJWkkb7qoCSfwFddoPwu8X+IXR2sDp1qTgzXv7vAHXCH5uexxj3qZOnS1m7DV3scpPdF2Crksx2gAck+mK9k+GPwplhuIdf8SwlZV2va2T/wH+F5B6jsO3euz8G/CvQ/CLJdFft+pgf8fUyAbT/sLyF+vJ967gLwRxivFxuac8XTo6LuaRh3ECYp9FFeJ6GgUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAJiloooAKKKKACiiigApMUtFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVBc2kF5ay21zEksEqFJI3GQykYIP4VPRQt7h5HzL8Q/hfe+EbmXUtKSS50NmzwCz22f4W/wBn0b6ZweTxNtedOa+zHiDoUYKynIZSOCD2ryvxd8D9L1aR7zQJl0u6PJgK5gc+w6p/wHj2r6DCZqpRUK+/cxlT7HjUF705q7Hf8dar6z4H8V+G3b7fpFwYVyfPgHmxkDvlen44NYKX3+1XrJQnrB3IudV9u460x7/jrXO/b+cZ59Kja+z0an7GwXNqa9461mXN515rZ0TwN4r8SOv2HSZ1hOP39wPKjAPfLdf+A5Nev+EPglpmkSJea9Kmp3g5EIXECH6dX/4Fx7Vz1sXQw6u3d+RSi2ef/Dz4YXni24j1LVkktdFUhlBG17oDsvovq3vxzyPpCC2itbeO3gjSKGJQiRoNqqoGAAOwAFOWJUUKoAUYwAOBjpUlfNYvFzxMrz27GsYJBRRRXL5lBRRRQAUUUUAN2/l6UFQwwQCD1B706imtxpXMW68IeG76XzLrQNLmk/vSWkZP54zVZPAHhFCSPDWlHJz81qjfzFdHRXRGc/5n94uVFKy0nT9Mj2WFha2qf3YIVjH/AI6BVzb7n86Wisp3b1bC1gooorPrYAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiijqAmKzb/AMOaLqj77/SLC6f+/PbI5/MjNadFNVJxejBpHOf8IB4Q37/+Ea0rOMY+ypj8sYq/YeHNF0tt2n6RYWrf3oLdEP5gZrUoreFSc73k/vFZDcHFOoormveTGFFFFMAooooA/9k=",
"caption": "Ein Sketch zu dem Phänomen der Frustration.",
"kind": "Abbildung",
"refnum": "2.1",
"height": "310",
"width": "511",
"top_left_x": "776",
"top_left_y": "1027"
},
{
"title": "kolbe2018hubbard_DIA_0004",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105246359",
"modified": "20260602105246359",
"page": "017",
"latex_code": "",
"canonical_uri": 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"caption": "Eine lineare Heisenberg-Kette mit N Plätzen.",
"kind": "Abbildung",
"refnum": "3.1",
"height": "113",
"width": "1367",
"top_left_x": "356",
"top_left_y": "1320"
},
{
"title": "kolbe2018hubbard_DIA_0005",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105247145",
"modified": "20260602105247145",
"page": "019",
"latex_code": "",
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RpX1a0Te6/pEccSQxJFGqpGgCqqjAAHYCqGq6munIiIiy3k2RDCXC7iOpJPRRxk+47kA6dYGr+C9C12+N5qViZ5ygTd58i4A7YVgMUTvb3UTh3S9pevt/W/9bEGk2lppV+JJ7lbzV9SciWdcdApOAM/Kg2gD3I/DpRWDo/gvQNBvje6bYCC4KlN/nSN8p6jDMR2reAwAKKaajqi8ZVhUqc0JNqy3/rtZIWiiirOQKKKKACiiigAooooAKKKKACiiigLXM/WtHtdd0ybT71SYZB1U4ZT2IPY1VgsteS3S2fU7QqowbgWx8xh64LbQ3vyPatqipcU3c3hiJxSjur316PQxr/WINO1LTtKnhuLiS/LIrKgZRtAyX6evYevSuY8bCPwydL1HRIo7a5lvFhkghUIlyhDEhl4BxgYPv1rtbzT4b4L5wYMh3RvG5RkPTIYc/wCI4qonh+0+3w31w013cQZ8lriQuIiepVeFB98Z96icJSVkdWExFKi4yavZPmXSW/y7IXXdL/trQ7rTRcyW3nqF82PqvIPqOuPUdaq+D7OTTvD0Vk9y9yttLJEkrjBYK5H5ZBx7YrZnheWCSNZWiLqQHTque496W2to7S2jt4V2xRqFRfQCqUfeT7HOsQ1QdJu65r2+QlxbRXdtJb3EayQyqUkRujKRgiuc0zRNc8P2Y0/TrqzurFMiEXQZHiHXblc7hyfSupopuCbuTTrzhB09Gn32/roZFlpEy3o1DUblbq8VSsQVNkUIPUIuTycDJJyfarmoXiabptzeSq7R28TSMFGSQBnj3q3TJEEisjKGRhgg9CO4o5dGluTKrzyTnt2/yMI2ul+JtGj1Gay8gzw70lljCTQ8cMG6gjqMGqPw61e/1nwlHcagzPKkrxLKx5kUdz75yPwrVl8N2ktu9qZrtbRxhrdZ2CEdx6hfYHFaVraQWVtHbW0SRQxrtREGABUKMnK77HZUxNP2EqS1u015Kz0v8/wJxRQOlFbHnBRRRSAKKKKACiiigAooooAKKKKAEIzWJe6Aza2Na064W2vjEIZg6bo50ByAwBBBHZgfbkVuUUpRUtzSnWnTvy9VZ+hn2sGpCcy3l3E6YIWCGLaPqWJJJ7cYHPSsyzfVrU3FxcaUJLiZt0ji5GMDO1V9gPzJJ78dHVW9sIdQgMNwZRGeoimeIngjBKkEjnp0qeS+prCvduMtna/ojkvhjPcN4PtI2tisGZSs3mAknzG4x1//AFVP4q8PyXetaZrkOpTQS2ckaJAoyrkyAevGd2DwcjHStvSvDunaIu3TopYo+f3RuJGQZOeFZiAc98Zq3NYpcXUE0jMwgyyR5+XcRjd9QCR+NZwp/uoxkddXGx+uyxFPRNt/f0LK/dHOaw/EHhxdYltbyCc2upWb77e5ChseqsO6n0/+vW4Mgc0tayimkmcFKtOlPni9f60/Qwmt/El0vkzXWnWqH701uju5/wB0N8qn67q0bDToNNtRb24O3JZmc5Z2JyWY9yecmrlFCgkOVZyXKrJeXcxNUj1CTUrXy7MXFpCvmFRME3S54yD2XqPcj0rmmvb4/FONhpuZl0jAi89eV837wP8ASu+IJJ9KxP8AhENI+3fbtl39q27fO+3z78emd/T26VFSnzWZ2YTF04qSqLeLX3m4OgpaQDAxS1qeb3CiiigAooooAKKKKACiiigAooooAKjlhSeJ4pFDxuCrKehB6g1JRRa6sxptO6Oe07Q9R0S2Nlpt7btZBiYUuYmZoQTnGQw3DJOBxjpmna1dy6R4fc3FvJq7yOInjVFXf5h24xjGOcY57ZPU1v1DcW0d1DJDNGkkbjaysOCPQ1Dh7rSOqOJ5qsZVddbvu/n/AFqc746jgHgTUxIqqqQgxrjowI2gY6c4xitXRXuZvD2nyXm5bl7WMyk8HcVGc+hzUTeHbSZovtTz3aQsHjiuJS6KR0OD97/gWcVrAHHP6UlH323sOdeP1eNJatNu/wAlp+GpyPg7w/J4a1DU7H+0pb2JlimzIvKMS+R1POApP1rrsE9Dg1WtLFLRZQrM7SuXkdzlmJ/wAAHsKt04QUYqJniq7rVXUb3/AMrHL23hy+0O+u5tCntvst3IZpLK5DBEkPVkZemcdCKuppF7fTxzazcxSJEweO0t0KxBgchmJ5cg8joO+MgGtuijk7Fyxc5PmdnJaXtrtYaf1rH0O/GoyajONNa0ZbpojI2Mz7Pl3evbHP4VskZrPn0eCWeSZJbi3eXmTyJSoc4xkjpnH8QwfenLVozoyjGLUnZvr89fvOb8KvIPGviuGHJsBNEw64ExXL4/HrXajpVPT9MtdLt/Is4VijLFzgklmPViTySe5PWrYzjnrSpxcY2ZeLrRrVXKK0sl62Vr/PcWiiirOUKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACs3W9Ftdf017G73BCQ6Ohw8bjoynsRWlRQ0mrMqE5QkpRdmtmY0VlrogW3fUrQBeDOtsfMYeuC20N78j2q9e3SafptxdSsWW3iaRiepwM1brO1bQ7HW4hDfxyyxYwY1nkRW5B5CsAeg61LXum6qRqVF7TRX1svvGadpyx+H4LC7RZN0ASdT0dmHz5+pJ/OuL8K/abTVl8I3XmMNJuXuo3YHEkG07P/HnB/D2r0G1tUtLZYI2kZFzgyytI34sxJP4mmixt11B75YlFy8YiaTuVBJA/M1Eqd7NG9LG8kKsJaqW3k+/3XLH41x48PPYfECPWItSlk+3FkktSDhUEZyc55G4J2HWuxqqLFBqEl4zM8jIEUN0RRyQPqeT9B6Vc4qVjDD13R57dU19//B1LIFc9qPhuZtdTXdKuY7a/8sRzLIm6OdePvYwQeOvsK6EDAA6+9LRKPMrMihWlRleHVW+XVGC+nazqQMWoXVva2xGHjsixeQem9sbR9Bn3FbUMEcEKQxIqRooVVUcKB2FSUUKKQp1ZTiotJLtb8TJ8RMf7FngQkSXWLZCOoMhCZ/DcT+FO1vRoNa0G50qQBY5oyin+4w+6fwIH5Umo+HtO1a5jnvUnkeNg0e26lQIw6EBWAB9+taMcXlRLGCxVQFBZixIHqTyfqaXLd6mqrezhB037ybf5W+6xxHgbULrV3jS+jdLrR4Gs5iwPMrNg/iFjX/vo13Y6VWt7C3tJriWCJUe5k82Uj+NsAZ/ICrI4FKlFxjZ7jxleNaq5wVl2/P8AEKKKK0OQKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKAP/Z",
"caption": "Lineare Hubbard-Kette mit N Plätzen.",
"kind": "Abbildung",
"refnum": "3.2",
"height": "163",
"width": "1374",
"top_left_x": "342",
"top_left_y": "1763"
},
{
"title": "kolbe2018hubbard_DIA_0006",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105247965",
"modified": "20260602105247965",
"page": "020",
"latex_code": "```\nfunction spin_state_generator(N)\n\n x=collect(1:N)\n\n states=[]\n\n for j in 0:2^N-1\n\n stat=copy(digits!(x,j,2))\n\n push!(states, stat)\n\n end\n\n return (states)\n\nend\n```",
"canonical_uri": 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"height": "437",
"width": "1388",
"top_left_x": "342",
"top_left_y": "1352"
},
{
"title": "kolbe2018hubbard_DIA_0007",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105248886",
"modified": "20260602105248886",
"page": "020",
"latex_code": "```\nfunction SpinPlus(i,state)\n\n zustand=copy(state)\n\n if(state==0)\n\n zustand=0\n\n else\n\n if(zustand[i]==0)\n\n zustand=0\n\n elseif(zustand[i]==1)\n\n zustand[i]=0\n\n end\n```",
"canonical_uri": 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"height": "426",
"width": "1388",
"top_left_x": "342",
"top_left_y": "2142"
},
{
"title": "kolbe2018hubbard_DIA_0008",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105249697",
"modified": "20260602105249697",
"page": "021",
"latex_code": "```\n end\n\n return zustand\n\nend\n```",
"canonical_uri": 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"height": "147",
"width": "1388",
"top_left_x": "342",
"top_left_y": "233"
},
{
"title": "kolbe2018hubbard_DIA_0009",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105250377",
"modified": "20260602105250377",
"page": "022",
"latex_code": "```\nfunction fermion_state_generator(N)\n\n x=collect(1:N)\n\n states=[]\n\n for j in 0:4^N-1\n\n stat=copy(digits!(x, j,4))\n\n push!(states, stat)\n\n end\n\n return states\n\nend\n```",
"canonical_uri": 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"height": "405",
"width": "1390",
"top_left_x": "342",
"top_left_y": "1224"
},
{
"title": "kolbe2018hubbard_DIA_0010",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105250937",
"modified": "20260602105250937",
"page": "022",
"latex_code": "```\nfunction CupDagger(i, vec)\n\n #0=0 2=up 1=down 3= updown\n\n states=copy (vec)\n\n if states==0\n\n return 0\n\n else\n\n if(states[i]==0)\n\n states[i]=2\n\n elseif(states[i]==1)\n\n states[i]=3\n\n else\n\n return 0\n\n end\n\n end\n\n return states\n```",
"canonical_uri": 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"height": "630",
"width": "1392",
"top_left_x": "340",
"top_left_y": "1918"
},
{
"title": "kolbe2018hubbard_DIA_0011",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105251510",
"modified": "20260602105251510",
"page": "023",
"latex_code": "```\nend\n```",
"canonical_uri": 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"height": "70",
"width": "1378",
"top_left_x": "356",
"top_left_y": "230"
},
{
"title": "kolbe2018hubbard_DIA_0012",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105252264",
"modified": "20260602105252264",
"page": "028",
"latex_code": "",
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FABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFVr6+tNNtXu725it7eMZeWVwiqPck4rnvGvjiw8H2sQkja81K4yLSwiOHlbpkn+FR3Y/rXkdzZ6v4rvF1DxTdfaHDZisIuLa39MLn5mHqc9e9c2JxNOgvfevY6KGGqVvh0Xc7TUvjRpxZofDWk3esupx55/cW+f99hk49lrmrr4g/EC+3lJdI0xW+75Fu0rge+84P5VYj0wIiqqgKowFHQewFD2AHavFqZtVk/c0PXp5ZTWs9TDbxX8Q16+MGz2/wCJZb4/LFWrb4k+PtPVQ95pepYPzfabUxMR9YyB+lSz2XB4rMuLXGeKhZniL7lvL6NtjttI+N9mZFi8R6NdaZk4+0wt9oh+p2gMv5GvTNL1XT9YsVvdNvILu2fpLA4Zc+mR39q+bZoRyCAR6YqnYT6l4a1H+0vD141jc9ZIwMwzj+66dPx6jtzXo4fMoy0qfeefXy9x1gz6ryPWiuI8A/EWx8ZQNbSxix1qAfv7Jmzkf30P8S/y79ie2HSvUi01dannPR2FooopiCiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAy9f1/S/DOlvqesXa2tohALtkkk9AAOSfYDsa8Y8ZfF34f+LNIn0e+0zVp4SSYrlIYwY3AIDplwe/fGQcGu/+K3gO68e+HbazsbqGC7trgTR+fkRuMEEEgEjg5BAPTHfI8wsP2bdTmgDaj4itbaX+5BbtMAPqSn8qAOG07xhYz6Dc6Jrqy3MAUi2n2AsBj5cjJwR65Pp25xfBAU/EDw2D93+1LYHn/pqteoX/AOzdq0UJOn+ILK4cHhbiFoRj6jf/ACrz+48IeI/B3jOwtbi1ibUY5UuYUjnRwwVgQxwcquR3ArCnRp0OaS0T18jepVqVrRau1959gapq2n6NYPe6neQWlsmN0kzhVz6c9T7da841H4zwSt5fhrQrrU1zj7VcH7PD9RuBZvyFcc+k32v3yan4muzqN4OUiYfubcH+GNOn4nk4rYTTsADYAPYV52IzZRfLSVzuoZa5K9RlO68e/EO+RgL3StNz0+y2pkYD6yEj9Kzz4r+Iajnxi2f+wZbkflitp9PwOlUp7PAPFcH9pV297Hb/AGfRS+Eba/Ezx5YFPOk0rU0X73nQNC7D2KHAP4V1ekfG3Sp5Eg8Q6bdaLIxx55xPb57ZdRkZ9147muDntip6VnTQggqVBB4IPceldFHNKi0lZmNXLqf2bo+mLG+tdRtI7uyuYbm3lGY5YZA6sPYjirOc18saPqWseD743vh268oM26WylJMFx9Vz8re4I7epr3vwP480zxrp7vbhra/gA+1WUp+eI+v+0p7MPxxXs0cRCtG8Tya1CVJ2Z1lFFFbGIUUUUAFNcgAZxjvmnV518X9fnsPD1todhMY9Q1uQ26uvVIQAZXB+hA/4F7UpSUU5PoOMXJ8qOJ8R68/xD8QNHDI//CL2EpWKMHi9lHBkJ7oD0HfGeprds7EED5QPoKzNFsYbS1ht4ECxRqFUDt/nr+NddYwj5eK+UxFeeJqt9Oh9NQoxw9Nd+pHFYDb0pXsgB0rooLRTHnAqC5gAB4FavCWjcyWKvKxylxajB4rIurfrxXV3UYAbPAFYMzQ3EXmQSJJGc4ZGBBxx1FcUoOLO2MlJHL3UGM8VlTJya6O7j61iXCYY0ReopIxbqCOWJ45VDIRyCOo9P8/WvQfhH43ms76Lwdq87SRsD/ZdxIcnA6wk+w+6T2GPQVw8y1lXscuwS20jR3MLiWCRDhkkU5Ug9ua9XBYiVNpdDzcXRVRXW59dL3pa5zwL4lXxZ4QsNXKhJpE2ToONsqkq/HYZGRnnBFdHmvf66Hh2a0YUVja74q0Lw2ITrGqW1mZc+Wsr4L4IBwPbIrVgmjuIUmhkSSJ1DJIhBDgjIII6igCSiikPagAbp2xXEa18WvBWhXklpda0kk6Eq8dujy7SOCCVBAPtmuT8fa3qvi/xpF4A8OXclpCi79XvIxyiEZKZHbB5HcsFPQ11Phz4e+GfDNnHFZ6ZBLMo5u7mNZJWOME7iDt6dBxXFisdTw75d2XCDkZ//C+PAY/5f7r/AMBH/wAKP+F8+A/+f+6/8BH/AMK63+zLD/nxtvwhUD+VH9l2H/Plbf8Afpf8K4/7XX8pfsmcl/wvnwH/AM/91/4CP/hR/wAL58B/8/8Adf8AgI/+Fdb/AGXYf8+Vt/36X/Cj+y7D/nytv+/S/wCFL+11/KHsmcl/wvnwH/z/AN1/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zdh/z5W3/fpf8ACl/suw/58bb/AL9L/hR/a6/lD2TOR/4Xz4D/AOf+6/8AAR/8KP8AhfPgP/n/ALr/AMBH/wAK63+zLDOPsVt/36X/AAo/suw/58rb/v0v+FH9rr+UXszkv+F8+A/+f+6/8BH/AMKP+F8+A/8An/uv/AR/8K63+y7D/nytv+/S/wCFH9l2H/Plbf8Afpf8KP7XX8o/ZM5E/HfwG2B9vuev/Po/+FdV4b8c+GvFm5dF1aG5lUbmhOUkA6Z2MAcZ74xUh0vTyMGxtSDwcxCuF8X/AAq03UYzqfh1Bo2t2wMkEln+6V3HQMBjGf7wwRnnPSrp5tCTtKNhOkz1iiuC+FfjSbxXoE1tqatHrmluLe+R12sTyA5HYnDAj1U9Miu9r1009tjNhRRWbreu6X4fslvNXvobO3LiMPK2Msew9+v5GgRpUVU03UbLVrGK+0+6iurWUZSWJwytzg8j34q0T70AR3M8VtbyTzyLHFEpd3cgBVAySSenAPNeCahq9z8Q9fXVZ96aJaSY0y1YcSEcGd1PUnt6D3yT1fxg1t5orDwhaSMkupHz70qcFbVTyPX52wM+xFZWl2yRIkaKFRRhQB0HT+leTmeLdOKpw36np5dhlUbqS6F+zscgcfT6VqxWHy9KnsYQccVuw2gMecV5NDDe0Vz1K+I9m7I5qWyAHSs64tODxXWXEAA6delc7fX2nwSmGa9to5D0R5VB/ImprYdxeiHSrqW5z11b9eKxLqDGeK6m4VJFDIQysMqQcg/SsS7jHNc+qZvujnZo8E1l3trFcwPFMu5G4IrbnX5jWdMtdNKbTvHcwqxTVmem/CTx5cXzN4V1y483UIELWdzIebmIdQSerqPxI57En1oHOa+R5ZrrT7q31Swby76ykE0Dj1HY+oI4x3zX1J4a1y28S+HbHWbT/U3cIkC5zsPRlJ9QQQfcGvpcNW9rD0Pn8RR9nPQ1aKKxNY8XeH9AuobbVtYtLOeUApHNKASCcZx2HB5PHBroOc26KRenFLQAU1yAuSQFAySe1K3avEvFF/qPxP8AHNx4P0m7ms/D+mkrqtxFx5r5+578ggDoSGbBAFRUqRpx5p7DSuzsNS+MvgXTLhoH1pbh1+99mieVf++gNp/A1S/4Xx4DH/L/AHX/AICv/hWxofgjw34etI4LDSLYMq4M0sYeVz6s55z/AJHHFav9mWB/5cbb/v0v+FeTLN4p2jE0VJnJf8L58B/8/wDdf+Aj/wCFH/C+fAf/AD/3X/gI/wDhXW/2XYf8+Vt/36X/AAo/suw/58rb/v0v+FL+11/KP2TOS/4Xz4D/AOf+6/8AAR/8KP8AhfPgP/n/ALr/AMBH/wAK63+y7D/nytv+/S/4Uf2XYf8APjbf9+l/wo/tdfyh7I5L/hfPgP8A5/7r/wABH/wo/wCF8+A/+f8Auv8AwEf/AArrRplgellbf9+l/wAKP7MsP+fK2/79L/hR/a6/lD2RyX/C+fAf/P8A3X/gI/8AhR/wvnwH/wA/91/4CP8A4V1v9mWH/Plbf9+l/wAKP7LsP+fK2/79L/hR/a6/lD2RyX/C+fAf/P8A3X/gI/8AhQPjv4CZhnULkc9TaPx+ldb/AGXYf8+Vt/36X/CkfSdOeNkfT7V1YYKtCpB+oo/tdL7IeyH+HPF3h/xVC8uiapBd7AN6LlXX03K2GH4itzIPSvHfGPwwjiV/EHgoNpOt2w3rFafu0mx1UKOAT27HoRzkdp8OPGcfjbwrFqBXy72FvIvIsY2ygDJHscgj8u1elhsTDER5omcouJ11FFFdBIUVk674l0Xw3DFLrOpW9kkrbYzK+Nx9h3xWha3UF7axXVrPHPbzKHjljYMrqehBHUUATdKp6pqNppGm3Go30ohtbaNpJJD0AH659B61bJHHIrx/4s6udW1zT/CELZtVAvdSweGXOI4zj1ILEegBqKk1Ti5PoXTg5yUV1OdF3feNtcHiLVldbccaZZN92CI4+Zh0LsOSfp2AA6uzscgcfnVLToRheB/n/OPwrqbGAHHFfKTqzxVVyf8ASPpYU44enyoqpYfL0pslmADkV06Wi+XnAqlcQjB4FbTwfKjGGKu7HJ3NqOeKx7q368V0N5qGnRytE99arIOqGZQR+GazbpFIyCDnpjvXFKEovVHZGaktGctdQYzxWXMntXQ3UY5NYs68mqgxSWhiXtqs6YyUcEMkinDIw6MD2INe1fCjx5L4jspdF1eQHWrBQWc/8vEXQSY9egPYZHrivIJVqnDqVz4e1qx8QWRPn2ModlHHmRHh0P1XIr2MDiHB8r2PKxtBSXMtz60FLVbTr231PTba/tG321zEs0TYxlGAIP5EVYNe3e6PHForDvfF3h7TtZi0i81e0hv5WVUgaQBst90H0z2z1zW2OaAFoopr9M+lADJ54reB55pUiijUu7uwVVUckknoK4O++NXgSxuGhOsGdl4Jt4Hdf++gMH8K4q/kvPjJ4yvNPgvbq18HaWwSRoTj7XIDnI7HPUZzgAHq1ek6V4R8PaLbLb2GjWUSqNpPlBmbH95jy31J71wYrMKdB8trs0jTb1MH/hfHgMf8v91/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zdh0+w23H/AExX/Cj+y7D/AJ8rb/v0v+Fcn9rr+Qr2TOS/4Xz4D/5/7r/wEf8Awo/4Xz4D/wCf+6/8BH/wrrf7LsP+fK2/79L/AIUf2XYf8+Vt/wB+l/wo/tdfyh7JnJf8L58B/wDP/df+Aj/4Uf8AC+fAf/P/AHX/AICP/hXW/wBl2H/Pjbf9+l/wo/szT/8Anytv+/S/4Uf2uv5Q9kzkv+F8+A/+f+6/8BH/AMKP+F8+A/8An/uv/AR/8K646XYDrY23/fpf8KP7LsP+fG2/79L/AIUf2uv5Q9kzkf8AhfPgP/n/ALr/AMBH/wAKP+F8+A/+f+6/8BH/AMK63+y7D/nytv8Av0v+FH9l2H/Plbf9+l/wo/tdfyB7JnJp8dvATuAdRuEH95rSTA/IZrtNB8S6N4ls2u9G1GC7hUgMY25Q+jKeR+NVJtG0ueJoptNs5I2GGV4FYH6gjmvMvGPw+l8MSS+LvAkkmnahajzJrOAnypkHLBV/DJU8EDgZHO1DNKdSVmrClTaVz27NFc/4K8U2vjHwva6zagJ5o2yxZz5Ug4Zf8PUEHvXQV6vn3MgoozisXXPFmg+HJII9Y1a1snmyY1lfBYDvj096QG1QSB1NRwyJNGssbq6MAQynIIPQg+lPJ96EBl+I9dsfDWg3esai5W2tk3MF+8x6BV9ySAPrXiNlHf8AiPWZPEmuZ+3TjbDb5ytnH2RAe+MEn1J/HX+I+rN4h8cwaBGc6fowWe5APElywyin12qc/UnNW9OhHy8e3NeJmmKafsY/M9jLsMpL2svkW7SxyAcfh6VpLYDb0q3YwA44rYFoojzgVwUcLzq7O2tiVB2Ry8tmADxWZc2vXiusuYQAeBWNdRjnisa1LkNqNXnOTurfrxWNcw4JrpLmSCSeSCOaNpoxl41YFlB9R2rHu4+tY6rc00exgTJ171l3du7PHNDK8F1AwkguIzho3ByCCPcVtTLyaz5l4NddGbi00ctWmpKzPcvhl44PjDRXivtsetWJEd4gGN/XbIvs2PwOe2K7mvlPQ9el8I+LLHXomKwK4hvlUZ327EBjjvjgj3Ar6pjZWQMjBlYZDA5yPWvpaFb2sOY+frUnTnysfRSGsNvF/h4a8NDOsWf9pklRbeYN+4dj6H2PNbGRu0UgpaACq97e22n2kl3eXMVvbxLukllcKqj1JNSTypBC8srBI0BZmJwAByTXhNpa3vxq8RXWo39zdW3hCym2WlqpKm5YfxHsD6nsDtHOTWdWrGlBzlsNR5nY7W6+OHgK1naIatJMQcFobaQr+eOfwqH/AIXz4D/5/wC6/wDAR/8ACui0/wAMaFpVuILDR7K3iHZIFy31OMk/U1b/ALLsP+fK2/79L/hXlPN43aUTVUmcl/wvnwH/AM/91/4CP/hR/wAL58B/8/8Adf8AgI/+Fdb/AGXYf8+Vt/36X/Cj+y7D/nytv+/S/wCFL+11/KHsmcl/wvnwH/z/AN1/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zdh/z5W3/fpf8ACj+y7D/nxtv+/S/4Uf2uv5Q9kcl/wvnwH/z/AN1/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zdh/z5W3/fpf8ACj+y7D/nytv+/S/4Uf2uv5Q9kcl/wvnwH/z/AN1/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zlh/z5W3/fpf8ACj+y7D/nytv+/S/4Uf2uv5Q9kzkv+F8+A/8An/uv/AR/8Kcnx18BSOAdTuIx/ea0kIH5Amur/suw/wCfK2/79L/hUVxoek3ULQ3OlWU8TdUkt0YH8CP8/wAxZul9kPZM09G1vTNfsRe6VfQXdsTt3xNnB9COoPsea0K8K8V+Erv4cXbeMvBLywQROrahpqktE8eecA87euR1UHIIxx7F4e1uy8R6FZ6vp7FrW6jDpnqD0Kn3BBB9wa9ShXhWjzQMpJp2Zp0UUVsIKKxNV8X+HtE1GHT9T1i0tbuYZSKWQBiOgJ9Ae2euDjpW0KAFrA8Y+KbTwh4dm1W5UyuD5VvAv3p5WztQfXGT6AE9q3WPTkYrwrxfqreK/iLNGG3aboJNvEvZ7o8yN/wHhefT3rGvVVGm5y6f0jWjTdWagippNhe3+oTa5rcguNXvDmVj92Je0aDsoHH+PWuutbEbRkZxx0qtp8IyOOK6eytw2OK+WvPEVOaf9eR9Jyxw8FGPQorYjH3ahmswB92upNooTOBWVdGFZhAZEErDcqbhuI9celb1MJZaGNPFXZy9za9eKxrq368V1l1GCDWBdmLzTGHXzNu7bnnHrj05rhaaZ2Jo5m6hwTWZMmM1vXcfWsidetaQepE0Y0gubW9g1HTp2ttStXEkE69QR2I7gjgg+vfoforwB4zt/Gnh1bwKIb6E+VeW2eY5B/Q9Qf8AA18/TKPer3gjxC3hLx1Z3jPt0/UGW0vh2G44ST2wep9C3rXuYCu/gkePjaKtzxPp6imoMDnrSmvWPLFyMZorDtfF3h+91x9GtdXtJtSj3BrdJAWBU4YfUc5HXg+lba96AFooqpql/baVplzqN5II7a1jaaVyM4VRk/pQr9AE1PU7DSLF77UbuG1tY+XlmcKo9Bk9z6Vwc3xz8AwSlF1SeUD+JLWTH6gVxuh6Dd/F7VJvFHiaW5TQEmZdO01XKqyA4JJH5EjlmB5AAFerWvh/RrGAQWmk2MEQ6JHbqo/l/nNebiMzp0pcsVc0jTb1OY/4Xz4D/wCf+6/8BH/wo/4Xz4D/AOf+6/8AAR/8K63+y7D/AJ8rb/v0v+FH9l2H/Plbf9+l/wAK5/7XX8pXsmcl/wAL58B/8/8Adf8AgI/+FH/C+fAf/P8A3X/gI/8AhXW/2XYf8+Vt/wB+l/wo/suw/wCfK2/79L/hR/a6/lD2RyX/AAvnwH/z/wB1/wCAj/4Uf8L58B/8/wDdf+Aj/wCFdb/Zmnj/AJcrb/v0v+FH9l2H/Plbf9+l/wAKP7XX8oeyOS/4Xz4D/wCf+6/8BH/wo/4Xz4D/AOf+6/8AAR/8K67+y7D/AJ8bb/v0v+FJ/Zdh/wA+Vt/36X/Cj+11/KHsmcl/wvnwH/z/AN1/4CP/AIUf8L58B/8AP/df+Aj/AOFdb/Zdh/z5W3/fpf8ACj+y7D/nytv+/S/4Uf2uv5A9kzlofjn4BnlCNqs8QP8AE9rJj9Aa7vTdTsNXsUvtOu4bq1k5SWFwyn1GR3HpWPdeH9GvoDDd6VYzxHqklurD+X+cV5VrWh3fwf1eHxP4ZluX8PSShNS01nLqqk4BBP6E8g4GSGNdGHzKnVkotWZMqbWp7zRVTTL+21TTbbULOTzLa5iWaJ8YyrDI47Vbr0jMKMjGaRu1Ylx4v8PWeux6Nc6vaRalIVVLZpBuLMcKv1PYdeaANyikBFI54o16Acv498Xx+ENCE8UYuNSun8ixtv8AnpKR1P8AsjqT/jXlWhaPKk02oX832rVbt/Mublhyx9B6AdAPSk1PVf8AhMfHV7rAcvp1kTZ6cOqkA/vJB2+Zs4PoB6V0+nwjjIA7V8/meLcpeyhstz3MvwyjH2stye2sPlHFXhYDHStGytwcDArSktVVO1c9PCc0bs6KmJ5XY5SazAB4rLurXrxXV3MQGT2rntRu7K2cxz3UET/3ZJAp/I1zVKLi9Eb06qa1Zzl1b9eKxbiLDGunuQjruRgynkEHINYl3H1rJPU0ZhTJgGqMd1faLqsGtaRKIdRtjuUkfLIO6MO4I/z3rUmXrVCYYzXbh6soO6OSvTjNWZ9H+EPFFl4u8OwatZkrv+SaFyN0Mo+8je44+oIPet6vnL4X+IT4a8dx2MjldP1phCwJ4S5/gYf733fxHpX0Yv6V9LSqKpBTR89UpunJwYtFFFaECGvBfGN8dY+K+ou2fJ0q3is4u43MPMcj3yQte9GvmqCUy+JfElwzbjLrNyQ3+yHwMe2BXBmU3HD6dTtwEFKvdnYaeRxnrXT2T4xXH2Mv3ea6G1nwBzXzUJcsrs+hmuaNkdTFcAJisjxGNXuNP2aJd29tdbwS9whddvcYFEdz8vWke4z3r0PrS5Tg+rO54z8So/FOk6Rbyal4mNytzIYjBbwiFAACeSOW/Gtn4dH/AIoKz/35f/QzVT41vv0TTf8Ar5P/AKCam+Hj48C2Y/25P/QzWmIkp4NT7v8AVkUIuGLlHsjau+9Yd0OTWvdP1rGuGyxryUekzOmHJqhKO3rV+Y1QlNdlM5p6novwK1Uwanr2gvKNj7L+BPr8sh/PZXsOp6jaaTptxf6hcLBa28ZklkY4CqP1z9OT2r5m8IeK7HwX40XV7/zDbmylhdYgCz8qygA8dQO49c8c4HxA+JmrePLsJKDaaXE26GzRsjP95z/E36AdB1z9JQlzUlJngVo2qNFDx74qm8ceMbjVBG6xNiC1hxkrGPujHqSScepr6y8CaTc6F4G0bTbzP2mC1QSKTnYxGSv4E4/CvlrwO114Z16HWbzwfqGrGAb7WPDxIj9n/wBW27Hb0PPpXrf/AAvXXAP+Sc6gc/8ATw//AMZp+2pfzL7yfY1P5X9x7ZSH614n/wAL31z/AKJxqH/gQ/8A8ZoPx21s9fhzqHp/x8P/APGaPbU/5l94exqfyv7i18JYhNr3jnU3/wBdPq8kbeoVWY4B9Mt+leofXk+teU/A+5a9sPEl3JC0Lz6o8jRt1QkZ2n6V6tXzWYO+Jk/Q1hpFBRRRXGWFFFFAwqhqbakiGWxmso40Ql/tETN0HbBGP1q/XPeOL/8As7wdqMoOHePyl+rHb+gJNNK7N8LTdStCCV7tL79Cn4P1/W/Etsb6dLKC0WQx7VRyz4A5GTgDn3rrR0FYXg3T/wCzfCOnW5XDGISsPd/m/qB+FbtOdrmmPnB4ifsklFOy9FfUKKKKk4woxmigdaAPMPDCGx/aN8Swx4WC601ZzGvQt+5yT75L/wDfVewr06189+IPFN14Q+OupajaaNNq0jabHCYIWKkAhDuyFb0A6d62P+F7a4P+ac6gf+3h/wD4zX1mHqxVGHNJLT/I5/Zzk9Ez22vFf2jdFub3w5pWrwhnh0+Z0nUDosgUBj7AoB/wKmf8L31z/onGof8AgQ//AMZqC9+NOp6lZTWV58M72a2nQxyxvO5DqeCD+5rX29L+ZfeHsan8r+45r4F+P7fQb+bw7qkqpZ30nmW8zn5Y5sYIPswAH1HvX0sMAZxgdua+GNV0y5tZ5rj+yb2xs2kPli5RiUB6KXKjcfwr1T4dfHGfQ4IdJ8Tedd2SELFeJ80sI6YYfxqPXqPfitISjL4XciUXH4kaWp3p1n4k+I9RZmZIbj+z4Aw+4sQw2PYvuNdFpxHFefeE7lrnS1u5MeZczSzPjgbmc5ruLKX7vNfJ46bnXm+zsfTYOChQil11Ovs5AMVsR3H7vHtXL21xgDmtBLrjrWlDEcqsRXoczuec/F/xxd6XqtloltJPDbyoJ7uS3fy5XQsQEVsHb9084q3a+CfBur6Bb3NtpOIrqFZEd3bzclQcls/e/HHFbHibwjofimeC41K3ZpoV2q8blCV64PqOauiOCzs4ra3jWK3hjEcaL/CoGAK1xOKj7OKp/F1M6GGl7Rua93oeC3dxqXw98VXFjbXLS2isG8tj8ksZ55HY9s+1enm5jvbSK6jJKTIJBn3Ga8u8ZXEnifx5PFp6ebgi3j28g7eCeO2SefSvSYbcWGmW1mG3CCJYt3rgAZ/rVZhGPs6bfxW1/wCCTgpS9pUitY30KNx941mzVoXDZY1nSmuGmdtQoyda9Y+A2pltG1nQndj/AGfdiWLPRY5QSAP+BK5/GvJ5etaPgnx3ZeAvEuq3l/HLJDc6euyKIfNJKJAFGT0GCxJ9B3OBXs4CTU7HkY2N43Po7xDr+n+GdFuNV1OcRW8Ck9RudscKoPVj2FfG+vatf+OfGlxfLCz3mo3CpDDGckZwqID7AAZq5448e6x471QTXjeXbISLeyiJ2Rgn0/iY9z+gGBWr8P7278Fau+rXPgrUdUu1Urblt8Sw5+8QPLbJxx2wCfXj1ZTjH4nY82MJS+FXPqvQNPfSPD2m6bJJ5j2lrFA0n94ogUn8SM/jWjXiZ+OuuL/zTnUP/AiT/wCM0n/C99c/6JxqH/gQ/wD8ZqHXpfzL7y/Y1P5X9x7VI2yNm67QTivHPgNDu8FXt/K2+5u9QkeSQj5jhVHJ+uT+NVpPjprbxsp+HWoKCCM/aHOP/INX/gR/yTo8f8vsv8lrgzOpGWHfK76jhCUZe8rHptFFFfOmwUUUUAFH6+1FFCDzMfXrvVNPsrm+tZbIW1vCZWS4jcscDJGQ2PpwKp+E9W1nXtPh1K8SygtpdwEcaPvOCRnJbHY9jVT4lX/2TwhLEhPmXUiQqB1I+8f0XH410GiWP9maHY2XGYYFRsd2xyfxOTV6ch6c4wp4FTcVzSlZadEtfxZf7f4dKKKKg8wKKKKTAP59K80+GEY0/wCKPxAsIuIWnjnCjgAkueB/wP8AQV6XXg48bXngv4t+L5rPw/caw1y8SssMhXywFHJwjdc+3SvWyqXLUk29LGdROSSR9FCg+1eJ/wDC9tcH/NONR/8AAh//AIzR/wAL31z/AKJxqH/gQ/8A8Zr3Pb0v5l95n7Gp/K/uMz9o7Rbt30bWkDNaIr2z4ziNidyk/Ubv++RTPgP4+ggjbwjqUwj3O0thI5wCT96L0Bzlh7k+1WNa+L194g0e60vUfhnfzWtymx0Nw/4EfueCDgg9iM14Ze6de6fKss1jeWcbOfKM8bKR3AzgAkewFONWm3ZSX3ilSqJXaZ915559a+crC/OueIda19nD/br1xE4/54odkY/ACl8GfHi5ttGfSvEQknnWFlttQHLbtp2iXPJ5x8/J9QetUfCirDoViq8AxK358/1Nefms2qKXdnflsE6zfZHfaeR8uK6eykC4rj7GbGK3ra44HNeBSnySue3Uhzo6dbj5OPwNeL/Gfxhfafq1jo1q0kdo8QuLjy3KGYFiNm4cgfLzj1FeoLde4HuaytY0jSNb8ptSsLe6MOfLMqAlPbPp7V6kMXFNOSuedLCyd1E5yw8J+FdW8NWk0egQQR3dusigrmRNwB+/ncT1715L4W1m90PxUmlw3EkllJdG2aLJwctt3Adj34r0nxF8RtO0vT547C1uXmRTHEGtWjjQ9s5A4HBwK5DwR4TX7QNbvbqCd1JMccUokw2PvMw4yPSqpO1OpKts9kKorzhGn8S3O4u+cnjnmsW4HzGta6f731Oax52yxrx49D1JX2KEo61nzKCGB6YOavymqMnJ56V20jjqHtXwO1N7vwE2nSkmTSruS1BY5JTh1P5Pj/gNdZ4w8Wad4O8PT6tqDghPlihDANM56Kvv/IAntXgHgj4iWPw/PiNruGW5muvs7WtunALhX3MW/hH3cnk8jA644PxV4u1rx1rgu9RkLuTst7aIHZECR8qr6njJ5J4r6WErwUmeBONpuKIYYtT8ceMtijzdQ1W7LN12gs2SfZQOfYD2r7ejUIgXOcDGT3r5R+HetXfgK5nvW8C6hqOoyjYk7M8QiTuFHlNyTnJz0wOOc+hj47a4P+ac6h/4EP8A/Gan29L+ZfeHsan8r+49trH8V3b2Hg/W72Mnfb2E8q4ODlY2I5/CvKv+F765/wBE41D/AMCH/wDjNZ3iH4z6xq3hrVdPl8BX1rHc2csLztO5EQZCpY5hHTOeoo9tTe0l94OlU/lf3HV/BW1it/hfp0iIA9xJNJIR3YSMv8lH5V6BXC/Bv/klGif9t/8A0fJXdV8tim3Xn6v8zaOwUUUVzlBRRRQAHkHPSue8Tapq+iafd6nBJYNawhSI5Y33noMZDY/SuhrhvibcSPpmn6TCf31/dKgHqB/9dlqoJN6nbltJVcTCnJXTevotX+BveGr3VtT06C/v1tIoriHfHFCrBgD90kk45H0rb47d+celRW1ulpaxW8QxHEgRR6ADA/Spal7nPXnGdRyirJhRRRQZBQeVI6gjkUUfpjkmi9gZ5v8AA9Vsn8YaTEALe01hxGB0HVf5IK9br5q8M/EG/wDBfijxhDZ+GbnWBc6rKzNDIyeXh34OEbrn26V1H/C99c/6JxqH/gQ//wAZr7CNWCiuaS6dfI51Tm9Ume2E180/tE6NeQeK7DWCrNZXFqIFcZISRCcqfTIYH3+b0rqv+F765/0TjUP/AAIf/wCM1j+J/ihd+LtBuNI1P4a6iYZBuV1uH3ROPuup8jgg/wCB4JFP29L+ZfeHsan8r+42fgT4/gv9KTwnfyhL60BNmWP+uiznaM/xL6f3cf3TXss9xFa20txK4WKJDI7HoABkn8hXwvJb6no1zBPLBeWMyMHhkdGiYEcgqeCCD3HSvXbL44PqXgbV9E16JhqcthNBDexDCyMyEfOP4T06cE+laRkmrxZDTTs0M8MzzX8U+rXQ/wBJ1O4ku5e+NzHAHtjGK7rTyOK4nQwsFhbQrwI41UD0wBXWWU2Mc18fiJOdSUvM+roQUKaj5HX2cgUCtT7TlcVzNvccDmrq3OR3rpo4jljY5atDmdy5cSAg1w/jfxOnh7TGMKedfzqwt4QM5wMliP7qjk1ta3rtro2lT395IVhjGcDksewHue3+FcLJp91NoWueIdYTGqXlhMEi7WsOwkIM9z3PqapOM3zy2FaUVyx3OO+GdxNd69qlxcyNLNLEHd2PLEt3ru7vp71578Lmxqt/7wDp/vV31y/WlmKtiH8vyHl7vQWvf8zJnHzGs6YVoTNyaz5jXPTOioZt1EssMkb42uCDmvoL4R6u+r/DfS2nbNxaKbOX2MZ2j6/LtP414A/Jx19vWt/wZ8UbLwB4Z1eyNu93qE9+89vCBtQbkQFnbqBkdB+nWvcy+W6PGx0dme1fELxzY+BvDkl7MySX0oKWdtnmV8dcf3RwSfoOpFfLfgfT9R8UfEXS0iMk1w94tzcTE52gPvdyfz+pIHes/XNd1rxprrXl8817ezcRxxoTtXqERR0A5/meea734d+Kbv4f21wY/AOo31/cH57pnePCdlC+Uce/PPFehKpCPxOxwxpzl8KufUi8ClrxIfHbXB/zTjUP/Ah//jNH/C99c/6JxqH/AIEP/wDGaSr0v5l94/Y1P5X9x6B8T7o2fwz8QSgnmzePj/b+X8uaz/hrZpY/DfQIo1ChrRZSB6v85/VjXmXjP4vat4g8H6lpdx4HvbCK5iCNcyTuVj+YHJBiUdvWvVvAf/JP/D3/AGD4P/QBXlZrNSpR5XfUunGUZPmVjoaKKK8I1CiiigYUd/5/SijuOO9Amcp4r1vWfDenyairadJB5iokTxOGOffdj1rZ0WXVLiySfU/sqtIisscCsCmRkhsk+1cn4/zqes+H9BGW8+fzZQP7vA/lv/Ku+AAAAAAHTH+fTFW0lFHqYmMIYSl7q5pX1t0TsvyYUUUVB5YUUUUgIrq2jvbSe1mQPFNGY3Q9Cp4Neffs8XUlx8N543bK2+oyxRj0Uoj/AM3Nejf/AKq+cPhh8StR8G+GbjT7Pwnd6vHLdtMZ4pWUKSiLtwI27KD1717eUzUVNt22/UyqRcnZI+oqRucV4n/wvfXP+icah/4EP/8AGaP+F762f+acah/4EP8A/Ga9f29L+ZfeR7Gp/K/uPP8A48aLdaf8Rp9QlUm31KKOSJ9vGURUZfqNoP0YV6v8F/H9v4h8OwaFdy41fT4tm1us0S8Kw9wMA/TPeuF8bfEO88c+HpNLvvh1qUbg+ZBcJO5aGQdGH7nkdiO4J6HBHkcbar4d1K3ukW7069iIeJyrRuMdxn/PUU1VpydlJP5idOcVdpo+2PEOqroXhvU9VcbvsdtJMATjcVUkD8TxXgPhOJotIt5JWZ558zyu3Vnc7jn3yaj1P40f8JT8NtR0PUYmttbmjjiSeJf3U48xA3TlCV3cdOvqBV/T2CgY/lXl5xNqMY9/0PSyuCcpSOw08jiuktJQoFcjYzYxzW3BcYA5rxaFTkZ69WHOjpDcArjNeFfGXTr/AFnxjpNrpkDzXX2NnVEYA8MckZNeufasLnNeb+LdTbT/AIn6Lcpa3F3J9ikjWGBcsxbIHXgDkEmvWo4jmmeZVocsNTz+08L/ABBuyIWOowxE8tcXRVR/49n8ga7vw74Sh8NwSyyTG5v5x++mbPTrgf4nrV3UNe8VQ2rXbeHLYoi7/JW93ygf984/AfrVLRfGWn+Jo3W33w3K8tA/Jx6g9x/nAzXNiK1arBuyUetv1OihSpUpJXbfS/6Fi75ye/rWNMOTWrdPnPasiU8muCB2PYozCsrUIBcWc0WASykL9e364rUmNUZTjnOOvNd1F2aZx1Ve6PpXwFrZ8Q+BNG1R5PMlmtlErn+KRfkc/wDfStWF8VviBbeC/DkkMEobWbyMpaxo3zRg8GU+gHb1PHqR5T4c+L8HgnwB/Y1tatdaslzP5SvxFChbILEcnkk4H5ivLb2+1jxVrc17dNc6hqM53SFE3McdgF6ADA4GAOK+k5ly3Z4HK72R0/wf0e71n4l6W0KnZaP9rnfH3UT/ABbaB9a+v1xk18zeAPG154B0Z7S3+HmoXN3O2+4u2kZDL/dGPJOFHYZPUnvXXf8AC9tbH/NOdQ/8CH/+M1Htqf8AMvvK9jU/lf3Httef/GyV4vhNrJjcqWMKkg9jMmf0rkv+F765/wBE41D/AMCH/wDjNc14/wDitqnijwXfaTdeC7zTYZjGWupJmZU2urDgxr1xjr3pqtTeikvvB0qi1cX9x7N4St47TwfotvEoVI7GEAD/AHBz9T1rZrL8N/8AIraQP+nKH/0WtalfIVH77+f5m62CiiioGFFFFAw9+nuK43xV4h1zw1BDMP7OuBPP5UcQjkDcgnn5uf8A69dlXA+JP+Jt8R9B0r70dqPtMnpn73P/AHwB/wACqoWvqehlcITr/vI80Um38lc7PT11AQZ1FrYyntboVA/MnNW6PxzRUt3ZwSlzycrWuFFFFBIVi+L7WO98Ga3bSgbZLGYcjOPkJB/A8/hW1WX4k/5FbVx/05Tf+i2q6btOPqgexj/BSeSb4TaKZGLFfOQZOeBM+B+A4/Cu/r5t8AfFbVPC/gux0m18F3mpQwmQrdRzMqvudmPAjbpnHXtXS/8AC99c/wCicah/4EP/APGa+v8AbU+sl95zKlUa0i/uPbGNfHnxc0i80f4lasbkuUu5TdQSkY3o/Ixj+6cr/wABr1f/AIXtrZ/5pzqH/gQ//wAZrkPH/jS78f6Qltc/D3ULa8gO63u1kdzHn7wI8oZU+meoFL29L+ZfeP2NT+V/ceu/Cv4gWvjTw7HHNMq6zaRhLuJjy+OPNX1U9/Q8emdr4ga0fD/gLWtSjcpNHbMkTDqJH+RD/wB9MK+PNPvtY8J61De2rXGn6hAdyb0KsPYqRyCM5ByDXqviD4vW/jjwZb6Lc2httUlvrcTImWhljDZJB6jkDg+vU81UprlckSo+8ky34dtFsNNtrVQB5aAMfVu5/E12tgQAK4+wkAwM9K6Wym4HNfGzblNy76n1kIpRUTrbSUKAavtcblP0rnYLjAHNPvNQFrYT3HB8qNn59hn+ld9LE6KJw1aGrZ5n498calq/iqPwj4buPIYyiG4uozhi56gMPuqvOSOeOo5rXTwF4e0jTJcaYmoXCozNLcDzHlYA9AeBk9hXkPgjVVsvGsOqXYeaQeY4VBl5JHUgAepJb9a9W1LU/GVvayXp0/SmjRd7WqSyNMoHYNjBI9B+Ga6sZGUHGEH/AMEwwklJSnJa/kcR8O9TurjV9QtRD5NkUMwhQsUifcAAuScZBP5e1dldDrVXw/4ssPEcMnkRC3u1+aWHjnPcHv8AXr09qnun4wOmM15+Mk3Wd42O/DJKno7mVMOTWfMKvynrVCapphUMnUw62rTQuyTwETRuv3lZTkEe+a+sNB1RNb0DT9VjXat5bRzhT1G5QcfrXyvMAysp6EEfhXv/AMG7mS6+FOiNKcuiyxH6LK6j9AK97L5e649jxcdH3lLud1RRRXoHCIelfMSHyPEPiG35Ah1i6QD28wkV9OmvnTxxZnR/ijrERG2K/SO+gHqSNr/juU1w5jDnoPyOzAztWXmXLOfAXmtq2usY5rkYJ9pxnjNacF3wOa+XaPo07nVJd8dacbv3rAW796g1DW7bS7Nrq7lKQqQCQpbr7ClZvRDulqzmvi9N5mkaeD2uD/6Cam8BSbPBdqDxh5P/AEM1zHjvxLp2u2FrDYTNI0cpcgxsuBjHepfDHinTdL8PQ2lzcMkyFiyiNzwWz1Ax3r15wf1GMOz/AMzy4zX1xz7r/I7e5mznmsqV8k077WlzAk0ZJRxuUkYyKrSScmvNjF31PQk1bQglaqUp64qeV6qO2eOvp9a66cTlmyfQPCCeOvFUejNcG3AtZZvOC7thBUAkdxk47VzHi7wZrXgbVltdTiKhvmt7qIkxygd1PYjjI4I9ORXsnwK003PiLXdbZW2W8CWMb9mLHe/4jan51674k8O6b4p0WfStVtxNbyjg9GjbsynsR/8AWPGa+hoR5aSR4VaV6jZ8u+ENT8XeL9WXSbLxFY2t2UzGt8gXzcDkAiNiWwM8816B/wAKy+K5/wCZm0Q9u/8A8Yrx7xJoWpeAvGUuntMy3VnIslvcJxuHVHH6cdjkdq+v/B2tv4j8IaXrEiBJbq3V5FHQN0bHtkHHtUPB0L35EX9arpW5meRf8Ky+K/8A0Muh/r/8Yo/4Vn8V15/4SXRP1/8AjFe80ho+p4f+RB9br/zM8W+BsE9tp3iOC5dHuItTZJWToXCgMRwOM57V6vXl/wAInWPU/G1ix/fQazIzj0BZgP8A0A16hXz2PjbESXoVB3jcKKKK4ygoPTPpRRnHOcUAVl1Cze+ksUu4Wu4xueEON69Oq9e4/MVxfxGY39zoegxnJvLkM+D/AAjj8vmJ/CtW20H+x/EOoatFYPez3RJjkWYDywcZQqxAxnnIzxT9P8PXM/iJ/EOsOjXgXZbQRtuWBfdsDceT2/PNaR01PXw6oYWr7eMrqMbrzla2no9TpFUKqqo2qBgAdBS0f4daKze55L3YUUUUCCgdaKB1H16UJ6jPCPE+h6/r/wActRtPDt5a2l4unRyPJc/dMYCAj7rc5K9q0f8AhWXxWPTxLof6/wDxitfw7J5/7Sev7R8tvpKxswOQT+5P9f0r2EV9RQw1KdGDqRu7L8jFYirDSMrHg/8AwrL4r/8AQy6H+v8A8Ypr/Db4qQo0knifQlRQSzEkADHOT5PAxXvdeQftB+JbjSfCdno9s7Rtq0jiVh3ij2llz2yWX8AR3rX6nQ/kQ/rddfaZ4HrnijWrvz9NuNXS9tVkxvhjCJKAeCPlU49sCuo+Hnwg1Xxmseo3bnT9GP8Ay3YZkmHcRj/2Y8em7BFT/Bv4dx+M9Yk1LU036RYMA8Z/5byEZCfQcE/UDvX1PFGsKCNUVEUBVVRgKB0AraFOFNWpqxjUqTnrN3PljwuHttJigmG2WF5InX+6Q7DBrr7SfGOawtZszo3j3xFpjZ2/bTdRcYBSYbxj1xkj8KsW9xtxzXy2NpuNafqfSYOopUo+h11vdYHWryXXvXLQXfA5q4t3kY3da5LHVc3WuuDz2zXDeJ9fvtVu38P+H2zcNxdXYOFgU9Rkd+vvwcDPIzfG/jKXSo/7OsWZLuVAzS/88lPp7/yrz2x8WaxpdqLayuUhiyScQoSSe5JGSfevTwmDco+1uvK55+KxUVL2aTsenabo2meD9JmuADJIkRkmnKjcQOw9Pp79asC9S7tYbiPcEljDqGGDgjNeVXnivXNUtntLi8LxyYUosaru/ICvSEIitoowchUCjn0FZ4uhKCUpu8mXhq0ZtqCtFCSvmqMrVPJJ1qlK+aypxNJsgkNS+G/Ab/EHxFqFml2bU22niWOXbuTzDIAqsPQjd05HB5xiq0jcZzivVvgJprfZtf1plO24uUtYsr/DEpyQfQl//Ha9bARvO55mMl7ljwTxD4d1rwTrpstSia2u4T5kMsbfK4zw6N3/AM5weK67wZc+M/HN/LY6d4l0+3u413iG7jCNIo6ldsTDj0r6O8Y+D9N8Z6FLpmoIFY5ME4GXhk7Mv9R3FfIbx6v4D8ZlA3kappdxwwOVJHceqsPzB969KpRp1XepG5wU61SmrQlY9l/4Vl8VsceJND/I/wDxil/4Vl8V/wDoZdD/AF/+MV7XouoprGiWOpxKyx3lvHcIp6gOoYD8jV6s/qeH/kRf1qv/ADM8Ek+GnxVWNmbxJohABJAz/wDGa2/gP/yTk46C9l5/Ba9dlUtC6jqVIrx34CzK/gG4hxteDUJUdT1ztQ/1/SuLMKEKWHfs0lqgVapUl77uepUUUV8+aBRRRQMPyqtBqFnc3M1vBdwyTwH95Gjgsh9x26GrOcetcppOhyeGrrUJrTTnu7i6dmE6zhRtJLAHccqR0yA2ePoGopo3oU6c4y5n7y2Rl+L/APia+OvD2jDmONvtMi9iM5wfwQ/nXf1zmieHJbXV7rXdUljm1O5G0CLJSBP7q5AJ4GM/pXRnr0H4VUnc3xtWDjTo03dQVm+7e9vy+QUUUVBwBRRRQgYV4BP4c8T+Iviz4uj8NahZWcsTxmY3Q4YFRjHyN6H0r3/pn2rzX4bOLr4tfEC5i5jSWGFiP7wLL/NGr08qhGc5Rkrq36kSnKFpRdmYf/Csviuf+Zl0P06H/wCMUn/Csviv/wBDLof6/wDxiveRQT617X1PD/yIX1uv/Mz5/u/h98TtPs5ry78V6DDbwxtJJKxIVFAySf3HoK8e1fxNrGrRm1vtR+0W6NkeWgVXweuAoJHH8Ve2/tFeJbi1s9O8OW7lIbpTcXJH8SqcIv0zk/UCub+CHw3g8QXD+I9YhWWwtpNlvA4yJpR1Zh3VfToSfYg1HC0YtSjFJilia0laUnYy/BvwZ1jxDo8ms6iWsrIQtLBEy/vbnjK4H8Knjk8nPAqx4dn3aNZNn/liuceoGP6V9RgdcjvXyzbWTaFqWp6E4ZTp15JCgbq0edyN+INceawvRT7M6stnaq13R11pcdOa2ILrgc1yFvcbcc1qQ3fA5r51o95M6dbsYznB9e9YuoeN9D0/Uhp93qEaXPAK4ZlXPTJxgGmrd/7WK8q8XeHpE8Ty385l/s25k3vPGm8x+oIHTnpXRhaNOpJxqMwxNWpTipU1ueyXcqSo0ciq6sNpV+QRjoc9q8GvLqbwx4wvDprmNIpztT+EoTkKR6YNejP410KK0DpqCsqrgKFO5uOmPevOoNPuvE+vT3flPHayzF3kxgBM9B6nFduAjyc/tfhS/E5MbLn5PZ7/ANXPTmulmgjkXhXQMM+hFUJX61I7hVCjACgAAVTlevOUbvQ7nJ2IZmqk59ankeqkjcHpXXTic02XfDPw4m+IMmvNbXf2a7sBbiEyD93IWD7lYjkH5V5GcenPHE3+n6z4L8RG3u45bHUrU7lIP5MD0Knn1Br6R+BOnGDwXdao686leySRtjrGmEXP4h/zroviH4CsvHegPayqkWoQgtZ3RHMbeh9VPf8AMcgV9HTivZpM8CbvNs8J8FReOPHi3K6V4m0qGe3OXt7pAj7T/EAsRBXJxweD6ZGeu/4Vl8V/+hl0P9f/AIxXjmg6vqPgXxpDeBXju9PuTHcw55YAlXjPbnkfWvtqNg6Bx0bmsfqWH25Ea/W6+/Mzwj/hWXxX/wChl0P9f/jFZ2vfD34mWHh3U7u/8QaPLZwWksk6Rg7mjCEsB+5HOM9xX0VWH4yge68D6/bx/fl024RfqY2FH1OgteRA8VXejkzjvg5z8KdFJ/6b/wDo+Su6rgfgvKsnwr0lVILRvOrAdj5rtz+BFd9XzWLX7+fq/wAy4/CkgooornGFH5fWikZQyspJGQRkdR9PegdrkFpf2d+0q2t1DO0TbJBG4bYfQ46Hj9K4nUf+Jz8WrC0PzRabB5rr6Pjdn/x5K0dC0S48K6fNZ2GlCed25nM6iNwPuk55HBPygEcnmrvhzw2dIlur+9nFzql426eVRhFGSdqD0/8ArVorRbaPWg6GFlUq05X0cY+d93910dBRR/Siszx/IKKKKBhR6fWigHkc+/FAM+dtB8K+L/EXinxdJ4Y1Sws44dVlWYXWcsS74xhG9D6fjXR/8Ky+K/8A0Muh/r/8Yre+CeJ77xtfR8wT6w/lsO/LH/2YV63X1iwtGa55QV3b8jJYmrBckZaI8F/4Vl8V/wDoZdD/AF/+MVS1bwT8R9C0q41PUvFugwWluu95GBOPYDyOSTwAOScV9DHkYr5z/aJ8SXUus2Ph2JytnFCLuQA8SSMSBn2UKf8Avo0/qWH6wQ/rdf8AnZ5JqviPVdaSNNQvGlSM5RQiqoPqQoGT+Fd3pnwa1Y+DNS8S6yxsltrOS4gsiv719qlsvn7g9jk/Tv1fwL+HEE8Ufi/VoBKAxGnQuAQCpwZSPUEELnoQT12ke8XlnHqGnXNjcLuhuImhceqsMH+ZreFOMIqEFZGUpuUueTufN2lXAeztnUkq0akfTAro7S46c1xWiia1tmsLkBbmyke1mUHO10JUj9K3ra5xjmvkcRTcako+Z9PRmpU4yOuguuOtXFuxjJ5xzzXMRXWAOatLd981hY23OSufGWiap4pabWb3yrPTZCtpbtE7ebIOsrYBHHYVc1vx94dvNFvreHUt8k1vIijyJBlipA5IxW80kTH/AFUfJ7qDz+VcZ4n8TaO2m6jpySD7UY2jCiFuG+uK76bp1ZxSi9PuOOanTjJtrU5XwNrFjo19dy38/kpJEFB2s3OfQA16F9uivLaO4gffFIoZWxjI+hFebeENUs9JvLmS9bYjxgKdhbnPsK7yK7iubaOeE5idcrxj/wCvWuZKLrOSRjgJNUrNhM3NUJWqeV6pyPXPTidE5EEhzwemau+Hvhdc+PdB1bVtOvEivra8aBI5R8kwCISM/wAJGfQ5z26jMnkVI3dzhVUkn2r334OaU+m/DayllTbPqEkl7IB33n5T/wB8KtezgI+82eVjpaJHy0TrHhTXpInE1hqNuTHJGy8j1BzkMMYPfsRXo/g3TfHnjvT5bvSfE+ko0L7JoLhQsiHsSFhIwQODk5wa9c+KPw3tvG2ivPbxKmt2yE2so48wDnymz2J6E9CfTIPzt8NfEV54Y8f6dPCSI55ltbmI5w0bMFIx6g4I9wK7KmHpVHecbnJCvVpq0JWR6l/wrL4r/wDQy6H+v/xil/4Vl8V/+hl0P9f/AIxXvAGM0tR9Sw/8iK+t1/5mfNXi/wABfEXSvCmoX2sa7pFxp8MYaaKEHewyBxmId8dxXsPgP/kn/h4f9Q6D/wBAFSfFSBrj4YeIY1zkWhfj0Uhj+gNVvh1cLdfDnw/ImCBZRxkg55UbT+orzczpQp0oqmrK41VnUlebuzpqKKK8QsKKKKAYhYKCSQABkk+lQWd9aahCZrO5iuIQxUtEwYA4zjI78ii/tRfaddWZdkE8TRlhn5cjGfrzXO6Vpt94e0X+zdL0lFuMktPJcAxFiMF+PmPbjb0qlG51UqNKpBu+t193VmXYf8Tn4t3tyfmh0uDylxyN/Q498tJ+Vd9WH4Z8OR+H7SXdMbi9uW8y5uSOXb29uT+Zrcom7mmPrwq1Ixpv3YJRXnbr83cKKKKk4QooooAPfp7jrXzR8N/B/jbxD4duLvw3q+m2dml20bx3OdxkCISf9W3GCvf14r6VkkSKJpHICKCWJ6AAcmvOf2doXj+HV07DCy6lI6e48uNf5qa9jKqcKimpK60/UzlOdOV4uxg/8Ky+K/8A0Muh/r/8YpP+FZfFf/oZdD/X/wCMV71SHpx1r1fqeH/kQfW6/wDMz5x8R+FviJ4U0SfWNV8VaIltCBhVBLyMeioPJ5Y/h3JIGa8l1DWdU8Q3MAvriS6kUbIlCAHnsAo6nj36da9G+PniW51HxwdE3slnpiIAh4DyOoYuf+AsF/A+tdv8EPhtDp+l2/ivVIRJf3Kb7KJxkQRno49GYcg9gfc1UMNRpu8YpMmeIq1FaUnY89n+D+p6F8Pr3xVrMhguoFjkhsEXLAGRATIe3yknaOemSORW3aS4IOePUd/evefFWknXfCWr6UMB7u1kijz/AHivyn88V83aJeG40u3kYneE2vnqGHB/WvPzeF4xl2O/K52lJHa2lxjHNa8N3wOa5G3ucY5rShusd68Bo9tM6ZbvpzXJnx/oUniZdLCy/alk8hLnyl27s425+9yeK0Bd8da87utLstC8Yy6vqEM0llJL9ohnTlYpCckOADxnOK6cNTpz54zeqWhz4mc4cvItD1GacdGx9PavAtJnew8ZxGElcXfl4HdS20j8q9Hv/HWjW9q0kN2J5cfu44wcn07cVxfhbQrqTUF1S8Ro40YugcYLv6464GetdmCXsqVSVTS/46HLi/3lSmqetv8AM9BuZc5x9KzpW61LJIOcGqUr158I9Ttm90QStVKQ/T8asSNVC8nENtLKeQqkkevFdtKN7HJUla5raX8JL/xb4Mk8R6Rchrw3UwFpKQomUNwVb+Fs5GDge4xzwNpe6r4Z1OUQtNZXqZiljkTBBzyrKw/nX158NtHfQ/hzodk6sJfswmlVhgh5CZGB+hbH4Vynxj+G0HiXR5tc06EJrNnGWbav/HzGoyVP+0ACQfbHcEfQ8kXG0ldHg8zjLmW5wHhLQfiD400UappPijR/L3FJIphtkjYdmAhIBxg/St3/AIVl8V/+hl0P9f8A4xXB/BXxHcaJ8RLK1Rj9l1L/AEWZB0JIOxvqDj8Ca+tR1NY/UsP/ACo2+t1/5meD/wDCsviv/wBDLof6/wDxiuc8c+B/H+i+ELy+13WtKutOjMYkigzvJLqFx+6XuR3FfTleefG9S3wl1jHQNAT/AN/kH9accHQUk1FIHiqz0cmbvhvH/CLaRg8fYocf98CtOsnwvKk3hLRpUIKPYwkH2KA1rV8nO/M7lrsgoooqRhTJZI4YXmlkWOKNSzuxwFA6knsKfWfrmmf2xot1YCTy2mTCv/dPUGgumoucVN2V1f0uWrW7t763We0njmiYna8bBgccdRXD+EiNW8feIdZ+/HE32aJuox04/BP/AB6ta3sdS0/QU0fRdMSyIUqbia4DomerDB3Mc+oHvxxWl4d0C28O6Utlbs0jE75ZW6yOQMnHYe3ar0SaPRjKnhaVVQd3L3V6Xvd+qsjW/pxRRRUHl7aBRRRQAVmeI+fC+rD1spun+4a06yPFUyW/g/W5pDhEsJy2P9w1UPiQO1tTw3wN4H8f614Qs7/Qta0q106QyCOKfO8EOwbP7pu4Pc10f/Csviv/ANDLof6//GK7f4IKV+EujZGMmcj6ec9ehV9ZLCUHJtxTM1iq6VlI8F/4Vl8V/wDoZdD/AF/+MVg+LdC+IHgrRjqereKNG8ssFjiiG6SRvRQYQDxX0uf518j/ABl8S3OvfEO+tpGZbbTnNpBGwxtK/fbHuwP4YpfUsP8AyIPrddfaZx9zeat4n1SEStLfX0mIoo0Tk88BVUfyr0DUPhLf+EPC1p4j1a5QXYvoFa0jG5Yoyedzd2zjgcD1OePUvg78NYPC+kQ61qEO/WruMN8w/wCPVGGQo/2iMZPvjsc9T8StIfWvhzrdpGrGVbczxBRk74yJAAPcrj8a25EqfJFWMuduSlLU8dtJsYyfc89Dit21ucY5rjtOvFubWCcHiRA36Vs29zjHNfHzi02j6qElJI62G74HNGoSNdaXd2yn5poXQfUqRWHFd8dasi7OOv0+tQtNS2k9GeN/DyJJPHNh5i7lQu4U+oQ4r26ecOrAkHdwf8/lXk+pabN4W8YJrltA8untIzsUXPlhgQwPpjJx9K6O98daOLJ5obwSyFfkjCndnsMV6mPTxFSNWGzX6s83BWoxlCe9/wBEeeeFp3tfF9t5eQGkaMgdwQR/9f8ACvT7iXNcL4P0O4S9GqXkbRomfLDDlmI5OPYGuwkk7kjNTmM4zrJLovxux4CMoUm33/REMrVRlarEj1SkesacTacivKeDnpg1778F4ni+FGjGRSGk86Tn0aZyP0r531KZorKUoCXI2oAMnJ4H86+sPC+lf2H4W0vSiQWs7WOFiO7BQCfzzXtZfHRs8jGy1SNaiiivQOEQ15Z8a9Bkm0Wz8S2sbNPpLkTKg5a3fAf/AL5OD7DJr1So54UnheKVFeN1KurDIYHggg9RUyipLlY4tp3R8vQXCyIroQVIBUj0q5HP6GmeK/DE/gHxD/Z7B20e5Ytp85zhQTzExP8AEO3qD+ApJNnAzk181icM6U3E+hoYhVIJo2VuiB1p/wBq461kiYetO873rl5GmdPNfc0Guagebd16VVM3HWo2l96tKRLcexK8tVZJKa0vvUDyVpCHcylPsI7ZqjeXIt7d3xuboqgZ3N2H51PJIACSQAM5z9DXc/CTwZL4h1eLxRfRsNLsXzYI4/4+Jhx5mP7qnp79+DXfhqDnJdjjr1lBHq3w28Mv4U8E2dhcLi9lzcXZ/wCmr8kH1wML/wABrrCM/SkXgmlyPWvb0Wh47d9TkvFnw58N+M7mC51aydriEbRLE5RmXOdpI6j9Rk10mnWFtplhBY2cKw2sEaxxRrnCqBjFWqKACmtnHAzTqKAPEvGMN38MfiH/AMJlaQSTaBqrCPU40X/VPn734n5gT33DjcK9J0TXdM8Q6al/pN5Hc27Dqp5X2Yfwn2Nb9xDHcQvDNEssUilHRlBDKRyCPevM9Q+BfhyfUXvtKvNS0aZjnbZTYQE9cAjI+gbHtXn4zARrtSTtLqXCdjvqK86/4UgpP/I6+I//AAIo/wCFIL/0O3iP/wACK4v7Hl/N+BftT0WivOv+FIL/ANDt4j/8CKP+FIL/ANDt4j/8CKX9jy/nD2p6LRXnX/CkF/6HbxH/AOBFH/CkF/6HbxH/AOBFH9jy/nD2p6LRXnX/AApBf+h28R/+BFH/AApBf+h28R/+BFH9jy/nD2p6LRXnX/CkF/6HbxH/AOBFH/CkF/6HbxH/AOBFP+x5fzh7U9FrkfHHxB0jwXYP58yzak6E29khyzN2Lf3Vzjk++M1jn4IJgg+NPEbA9Qbit3wp8JPC/hG7F9bW8t7fg5W5vXDsh65UABQffGfetKWU2leUrg6pR+EfhS/0nS73xBrpkbXNbfz51cYaJMkquOxOckduBgba9JFIowOT1p1ewklojEK57xb4L0XxrYw2ms2zSCF98UsbbXjPfB9DjBH07gEdDRTAyfDnh3TPC2kJpmk2q29srF9oJJZj1JJ5J+vbA6AVqmlooA8Z+NmhNbT6f4wiTMcQFlfjH/LJmyjn2DHB9crXBRS8ZJznv6/5Oa+mNS0+11bTriwvYhLbXEbRyxn+JSMGvmTWtCvfBPiB9Bv9zwHJsLojieP0/wB5eAR9O2CfLzHDc/7yJ6OBr8n7tl+Ocip1uj36VjrNwKlE3vXhOmz2VO5q/au9Ne5J7/rWf53vTTMPWmlPZMG49UWZJc9Tn61Xkl9Tk+tRNN71XeX3q1FvdktpbIdJJVV3pXkqtLKsas8hARfvZ6Y7g10wh2MJy7kdy07+XBaI0l3cOIYI0+80jHAx75r6l8G+Ho/CnhLTtFiKt9lixI69HkJJdvxYmvK/g54Imu7uLxlqkLLGqkabDIvJyMGYj3HC+3Poa9wHU17mGpKnA8bEVeeQjjI/CuO8SfDDwr4r1ZdU1TT3a7G0O8UhTzQOgbHXgYz1xxnGK7Oiug5yK3hjggjhijWKKNQqIowFAHAA7D2qWiigBDntXhupPP8ACD4iXOoSJK/hPXpC8jKpb7NNyeg9CTx3U4GSte51XvbK21C0ktLu3iuLeVdrxTIGVh7g9azq041IOEtmNOzuZOmanY6xYRXunXMVzbSLuR4iCP8A630/rmrdee3HwH8Pi7e50jU9X0kuf9Xb3AKr9Mjd/wCPUz/hSKnj/hNfEY/7eK8eWUO+krGqqnotFedf8KQX/odvEf8A4EUf8KQX/odvEf8A4EVP9jy/nD2p6LRXnX/CkF/6HbxH/wCBFH/CkF/6HbxH/wCBFH9jy/nD2p6LRXnX/CkF/wCh28R/+BFH/CkF/wCh28R/+BFH9jy/nD2p6LRXnX/CkF/6HbxH/wCBFH/CkF/6HbxH/wCBFH9jy/nD2p6LR/OvOv8AhSC/9Dt4j/8AAikPwPiZSknjPxE8bcMpuOoo/seX84e1Lfj74j2PhW0ksLF1u9fmHl29rCN+xm6F8fXO3qSB7kanwr8HT+EvDDtqDl9X1GT7Ves3JViOEJ745yfUntU/hD4Y+GvBcnn6dayTXpGDdXTB5APbgBfwAzx6V2Q/H8a9TC4WOHjZGcp8wtIaWiuok5jxb4C0HxqLU6zaySPbMTG8UhRtp6qSOoOB+Va+i6PY6DpUGmabbLbWduuyONfT1PqT1JPJJJNaFGQKAENeF/GDQn0nxTa+JYk22eoqtpeEDhZlH7tz9V+X/gPvXuuR61l+ItDsvEuhXekX65t7mMoxH3lPUMvuCAR9KipBTg4vqXTm4SUkfOUcuRk+vSrcc5HrWRd2OoeG9auNB1ZSLuDmObB23Ef8Lj8MD2PHapkmr5ivh3Tm4vdH0VGuqkFJGwt0fWnG64rKE3HWl84etc/IzfnLUq27vveCJn/vbBn86Y0vHB4qsZveo2lq7SfxEXivhJZJfeqkklNeWoHfNbQgZSmI7ZNVxa3OrX1ro9iu68v5RBGMZC56scdgMk+mM0lxcJBC8sjbUXqT/nr/AJ5r2L4O+BprFG8VavCUvbpNllbuvNvD/eI7M36D64Ho4Shzy5nscOJrcqaW56fomlwaJotlpVsD5NnCkCEjlgoAyfc4yfrV1hkUowPalyPWvZe55JxGr/CrwnrfiIa3e6bvuzIskiq5EcpAwN69D2z69++e1QYGMEAcDNOBB6GikAU11DDBGQeCKdRQB4Np94fgz41u9H1Pzh4V1JzcWVzsLCB+4OPQcHHP3T3r2C0u7e+to7m0njngkG5JInDKw9QR1+tWtX0iw1vT5LHUrSK6tZBh45FyPYj0PuOfpXm8nwH0WG4kk0nW9b0tZDlooLgbR6Y4z+ZNebisuhXk6kXZmkallY9E69KK86/4Uip/5nXxH/4EUf8ACkF/6HbxH/4EVyf2PL+Yr2p6LRXnX/CkF/6HbxH/AOBFH/CkF/6HbxH/AOBFL+x5fzh7U9Forzr/AIUgv/Q7eI//AAIo/wCFIL/0O3iP/wACKP7Hl/OHtT0WivOv+FIL/wBDt4j/APAij/hSC/8AQ7eI/wDwIo/seX84e1PRaK86/wCFIL/0O3iP/wACKP8AhSC/9Dt4j/8AAin/AGPL+cPanov/AOuvNviH8RYrCCTw54cka+8R3f7hEt8v5BPUk/3/AEA6Hk8DBe/wMtpkMVz4v8Qzwvw8bTjBH4g/yrrfCXw98PeC0b+ybL/SGXa91Od8rj03dh7AAVtQypQlepK4nV0D4c+EE8FeDrbSyQ10xM1246NKwGcewACj/dzXWU1Rj/PWnV65kIa5HxX8N/DfjK8gvNXtJHuYV2CSKQozL1CtjqASa6+igCvYWVtp1jDZWcCQW0CBI4kGFVRwAKnOe1LRQB8+fFHRX8O+Pf7RVSun62obcOAlwgCkH03Dafc59KwY5vT/APUa+gvGXhe18YeGrnSLljGz/PBOFyYZR91x9D1HcEjvXzc63mlajcaRq0fk6jaHbIpPDr2dT3U9fxryMxw137SJ62AxFl7ORtRzkd6nW6PrWOsuDg5z0xUomxXjOmeqpmqbrjrUT3Gaoed700ze9KMZLYJSi9yy8vXnNVpJPp+VRtN71XeX3rVRb3Zk5LoLI9VnfrSu+apXV0kEe9snnAUclj6D3/z71006d9EYzmkrst6dpE/ibxBYaBbbt15IBM6/8s4R99j+HT1OBX1lawRWttHbQIEhhQRxovRVAwBXnPwl8CS+HNMl1jVYyus6go3xsObaLqI/Yngt74HavSxnJzXu0KapwseJWqOpIDyQK4pvhV4TbxUPEf8AZzfbvOM5XeTG0h/iKnjrz9a7aitjIRRiloooQFe+s4NQsbiyuYxJb3ETRSof4kYYI/I14f4W1t/hVr9z4N8TSyLpDyGTTb90+QK3JB9ByMjsS3Y17uay9d8PaV4l09rDV7KO6t2OcOOVPqrDlT7gg1lWoRrQ5JjTs7iQzR3EKTQyJJG4BV0bKt7gjqKfXnI+A2lWzv8A2X4j12whY5MUU4x+gH60v/CkF/6HbxH/AOBFeQ8nd3aRqqqPRaK86/4Ugv8A0O3iP/wIo/4Ugv8A0O3iP/wIqf7Hl/OHtT0WivOv+FIL/wBDt4j/APAij/hSC/8AQ7eI/wDwIo/seX84e1PRaK86/wCFIL/0O3iP/wACKP8AhSC/9Dt4j/8AAij+x5fzh7U9Forzr/hSC/8AQ7eI/wDwIo/4Ugv/AEO3iP8A8CKP7Hl/OHtT0Wj/APXXnX/CkF/6HbxH/wCBFMk+BNlcp5V74s8Q3MB+9G045/MEU/7Hl1kHtSj8Q/HB1jd4L8IuL/V79vs88kAykKHhgWHfnBPQDOe1em+EPDkHhLwvY6LbvvW3T55MY3uTlmx2ySeOw4qDwp4J0LwbZtb6PYiN5CDLO53SyY9WPP4DAGTiuiFethsPHDw5Ymcpc2otI3bgn6UtFbknF+IPhf4W8T65Hq+p6ezXYAWQxylFlxjG/HXAGM+nXtXX28MdvAkMMaxxIoVEQYVQOgA9KlooAQ9q+bvG2it4W+IN7bBGWx1Ute2jEcbzzIgPThucDoGHrX0jwa5T4heDY/Gnht7NXSG/gbzrO4Yf6uQdM/7J6Hr64JArKvSVaDia0ajpTUjwyOb3681aScjvWFFPcQ3E1lfwNbahbSGK4t36o39QeoPOfU1bWbgHPFfMVKLi7H0VOspK5si6OOtDXOQQfyrLE3HWl873rLkaNOdMsbLdG3JBEreqoBTXlJ6nP1qsZveo2l96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"caption": "Eine Schematische Darstellung einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung.",
"kind": "Abbildung",
"refnum": "5.3",
"height": "383",
"width": "1589",
"top_left_x": "244",
"top_left_y": "625"
},
{
"title": "kolbe2018hubbard_DIA_0013",
"text": "<$image source={{!!canonical_uri}} width={{!!width}} height={{!!height}}/>",
"type": "text/vnd.tiddlywiki",
"tags": "diagram kolbe2018hubbard",
"created": "20260602105253247",
"modified": "20260602105253247",
"page": "031",
"latex_code": "",
"canonical_uri": 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"caption": "Ein Sketch einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung und sechs Plätzen.",
"kind": "Abbildung",
"refnum": "5.6",
"height": "113",
"width": "1370",
"top_left_x": "360",
"top_left_y": "1233"
},
{
"title": "kolbe2018hubbard_FN0001",
"text": "In der Quantenmechanik kann man zwei Größen gleichzeitig messen wenn die Observablen die Vertauschungsrelationen erfüllen.",
"type": "text/vnd.tiddlywiki",
"tags": "footnote kolbe2018hubbard",
"created": "20260602105254109",
"modified": "20260602105254109",
"refnum": "1",
"anchor": "{ }^{1}",
"page": "009"
},
{
"title": "kolbe2018hubbard_FN0002",
"text": "nach Nolting (2009), S. 22\n\\({ }^{3}\\) Zwei identische Fermionen können nicht im gleichen Zustand existieren.",
"type": "text/vnd.tiddlywiki",
"tags": "footnote kolbe2018hubbard",
"created": "20260602105254109",
"modified": "20260602105254109",
"refnum": "2",
"anchor": "{ }^{2}",
"page": "014"
},
{
"title": "kolbe2018hubbard_FN0001",
"text": "Ein regelmäßiges Punktgitter, dass mit einem Gittervektor \\(R=n_{1} a_{1}+n_{2} a_{2}+n_{3} a_{3}\\) vollständig beschrieben werden kann.",
"type": "text/vnd.tiddlywiki",
"tags": "footnote kolbe2018hubbard",
"created": "20260602105254109",
"modified": "20260602105254109",
"refnum": "1",
"anchor": "{ }^{1}",
"page": "017"
},
{
"title": "kolbe2018hubbard_FN0002",
"text": "Wenn sich zwei Unter-Gitter bilden, spricht man von einer Überstruktur. In Legierungen können sich bei niedriger Temperatur Überstrukturen bilden. Die Überstruktur von \\(C u Z n\\) bildet z.B. ein sc-Gitter mit zweiatomiger Basis[4].",
"type": "text/vnd.tiddlywiki",
"tags": "footnote kolbe2018hubbard",
"created": "20260602105254109",
"modified": "20260602105254109",
"refnum": "2",
"anchor": "{ }^{2}",
"page": "018"
},
{
"title": "kolbe2018hubbard_LI0001",
"text": "Lineare Operatoren",
"type": "text/vnd.tiddlywiki",
"tags": "listitem kolbe2018hubbard",
"created": "20260602105254109",
"modified": "20260602105254109",
"marker": "-",
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"title": "kolbe2018hubbard_LI0002",
"text": "Antilineare Operatoren",
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"title": "kolbe2018hubbard_LI0003",
"text": "Selbstadjungierte Operatoren",
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"title": "kolbe2018hubbard_LI0004",
"text": "Hermitescher Operatoren",
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"title": "kolbe2018hubbard_LI0005",
"text": "Unitäre Operatoren",
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"title": "kolbe2018hubbard_TOC01",
"text": "* 1 Einleitung ..... 1\n* 1 Einleitung\n* ..... 1\n* 2 Grundlagen der Quanten-Mechanik ..... 2\n* 2 Grundlagen der Quanten-Mechanik\n* ..... 2\n* 2.1 Hilbertraum und Eigenschaften von Operatoren ..... 2\n* 2.1 Hilbertraum und Eigenschaften von Operatoren\n* ..... 2\n* 2.2 Drehimpulsoperator ..... 3\n* 2.2 Drehimpulsoperator\n* ..... 3\n* 2.3 Der Spin ..... 5\n* 2.3 Der Spin\n* ..... 5\n* 2.4 Spin-Korrelation ..... 6\n* 2.4 Spin-Korrelation\n* ..... 6\n* 2.5 Vielteilchen-Systeme ..... 7\n* 2.5 Vielteilchen-Systeme\n* ..... 7\n* 2.5.1 Der Hilbertraum ..... 7\n* 2.5.1 Der Hilbertraum\n* ..... 7\n* 2.5.2 Operatoren ..... 7\n* 2.5.2 Operatoren\n* ..... 7\n* 2.6 Zweite Quantisierung ..... 7\n* 2.6 Zweite Quantisierung\n* ..... 7\n* 2.6.1 Hilbertraum ..... 8\n* 2.6.1 Hilbertraum\n* ..... 8\n* 2.6.2 Vielteilchenwellenfunktion ..... 8\n* 2.6.2 Vielteilchenwellenfunktion\n* ..... 8\n* 2.6.3 Der Fockraum ..... 9\n* 2.6.3 Der Fockraum\n* ..... 9\n* 2.6.4 Erzeugungs- und Vernichtungsoperatoren ..... 9\n* 2.6.4 Erzeugungs- und Vernichtungsoperatoren\n* ..... 9\n* 2.7 Die Geometrische Frustration ..... 11\n* 2.7 Die Geometrische Frustration\n* ..... 11\n* 3 Einführung in die theoretischen Modelle ..... 12\n* 3 Einführung in die theoretischen Modelle\n* ..... 12\n* 3.1 Das Heisenberg-Modell ..... 12\n* 3.1 Das Heisenberg-Modell\n* ..... 12\n* 3.2 Das Hubbard-Modell ..... 14\n* 3.2 Das Hubbard-Modell\n* ..... 14\n* 4 Implementierung der Modelle ..... 15\n* 4 Implementierung der Modelle\n* ..... 15\n* 4.1 Das Heisenberg-Modell ..... 15\n* 4.1 Das Heisenberg-Modell\n* ..... 15\n* 4.1.1 Korrelationsfunktion ..... 16\n* 4.1.1 Korrelationsfunktion\n* ..... 16\n* 4.2 Das Hubbard-Modell ..... 17\n* 4.2 Das Hubbard-Modell\n* ..... 17\n* 4.2.1 Korrelationsfunktion ..... 20\n* 4.2.1 Korrelationsfunktion\n* ..... 20\n* 5 Ergebnisse der numerischen Analyse ..... 21\n* 5 Ergebnisse der numerischen Analyse\n* ..... 21\n* 5.1 Das Heisenberg-Modell ..... 21\n* 5.1 Das Heisenberg-Modell\n* ..... 21\n* 5.1.1 Nächste-Nachbar Wechselwirkung ..... 21\n* 5.1.1 Nächste-Nachbar Wechselwirkung\n* ..... 21\n* 5.1.2 Über-Nächste-Nachbar Wechselwirkung ..... 23\n* 5.1.2 Über-Nächste-Nachbar Wechselwirkung\n* ..... 23\n* 5.1.3 Störstellen ..... 26\n* 5.1.3 Störstellen\n* ..... 26\n* 5.2 Das Hubbard-Modell ..... 30\n* 5.2 Das Hubbard-Modell\n* ..... 30\n* 5.2.1 Nächste-Nachbar Hopping ..... 30\n* 5.2.1 Nächste-Nachbar Hopping\n* ..... 30\n* 5.2.2 Über-Nächste-Nachbar Hopping ..... 31\n* 5.2.2 Über-Nächste-Nachbar Hopping\n* ..... 31\n* 5.2.3 Störstellen ..... 33\n* 5.2.3 Störstellen\n* ..... 33\n* 6 Fazit und Ausblick ..... 36\n* 6 Fazit und Ausblick\n* ..... 36\n* Literaturverzeichnis ..... 37\n* Literaturverzeichnis\n* ..... 37\n* 1.1 Darstellung einer Heisenberg-Kette mit Übernächster-Nachbar-Wechselwirkung und sieben Plätzen ..... 1\n* 1.1 Darstellung einer Heisenberg-Kette mit Übernächster-Nachbar-Wechselwirkung\n* und sieben Plätzen\n* ..... 1\n* 2.1 Ein Sketch zu dem Phänomen der Frustration. ..... 11\n* 2.1 Ein Sketch zu dem Phänomen der Frustration.\n* ..... 11\n* 3.1 Eine lineare Heisenberg-Kette mit N Plätzen. ..... 12\n* 3.1 Eine lineare Heisenberg-Kette mit N Plätzen.\n* ..... 12\n* 3.2 Lineare Hubbard-Kette mit N Plätzen. ..... 14\n* 3.2 Lineare Hubbard-Kette mit N Plätzen.\n* ..... 14\n* 5.1 Eindimensionale Heisenbergkette mit Nächster-Nachbar Wechselwirkung ..... 21\n* 5.1 Eindimensionale Heisenbergkette mit Nächster-Nachbar Wechselwirkung\n* ..... 21\n* 5.2 Eindimensionale Heisenbergkette mit \\(N=10\\) Gitterplätzen und Nächster-Nachbar Wechselwirkung ..... 22\n* 5.2 Eindimensionale Heisenbergkette mit \\(N=10\\) Gitterplätzen und Nächster-Nachbar\n* Wechselwirkung\n* ..... 22\n* 5.3 Eine Schematische Darstellung einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung. ..... 23\n* 5.3 Eine Schematische Darstellung einer Heisenberg-Kette mit Über-nächster Nachbar\n* Wechselwirkung.\n* ..... 23\n* 5.4 Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächste-Nachbar Wechselwirkung. ..... 24\n* 5.4 Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächste-Nachbar\n* Wechselwirkung.\n* ..... 24\n* 5.5 Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächster-Nachbar Wechselwirkung. ..... 25\n* 5.5 Eine Heisenberg-Kette mit \\(N=10\\) Gitterplätzen und Über-Nächster-Nachbar\n* Wechselwirkung.\n* ..... 25\n* 5.6 Ein Sketch einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung und sechs Plätzen. ..... 26\n* 5.6 Ein Sketch einer Heisenberg-Kette mit Über-nächster Nachbar Wechselwirkung\n* und sechs Plätzen.\n* ..... 26\n* 5.7 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\) ..... 27\n* 5.7 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\)\n* ..... 27\n* 5.8 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\) ..... 28\n* 5.8 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1,10)\\)\n* ..... 28\n* 5.9 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1, N)\\). ..... 29\n* 5.9 Heisenberg-Kette mit Störstelle an den Gitterplätzen \\(j=(1, N)\\).\n* ..... 29\n* 5.10 Eindimensionale Hubbard-kette mit \\(N=6\\) Gitterplätzen ..... 30\n* 5.10 Eindimensionale Hubbard-kette mit \\(N=6\\) Gitterplätzen\n* ..... 30\n* 5.11 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\) ..... 31\n* 5.11 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\)\n* ..... 31\n* 5.12 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\) ..... 32\n* 5.12 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und \\(t^{\\prime}=0.5\\)\n* ..... 32\n* 5.13 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und Über-Nächster-Nachbar Hopping mit \\(t^{\\prime}=0.5\\) ..... 33\n* 5.13 Hubbard-Kette mit \\(N=6\\) Gitterplätzen und Über-Nächster-Nachbar Hopping\n* mit \\(t^{\\prime}=0.5\\)\n* ..... 33\n* 5.14 Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\) ..... 34\n* 5.14 Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\)\n* ..... 34\n* 5.15 Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\) ..... 35\n* 5.15 Hubbard-Kette mit, Störstellen an beiden Enden, \\(N=6\\) Gitterplätzen und \\(U=1\\)\n* ..... 35",
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"text": "! kolbe2018hubbard\n\n* Total Pages: 42\n* Total Sections: 38\n* Total Paragraphs: 134\n* Total Equations: 61\n* Total Formulas: 238\n\n!! Top-level Sections\n\n<$list filter=\"[tag[section]kolbe2018hubbard]!has[parent_section]] [tag[section]parent_section[kolbe2018hubbard]]\" variable=\"sec\">\n * <$link to=<>><>\n\n",
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