Functional relations for elliptic polylogarithms

Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities

Amplitude recursions with an extra marked point

The recursive calculation of Selberg integrals by Aomoto and Terasoma using the Knizhnik-Zamolodchikov equation and the Drinfeld associator makes use of an auxiliary point and facilitates the recursive evaluation of string amplitudes at genus zero: open-string N-point amplitudes can be obtained from those at N-1 points. We establish a similar formalism at genus one, which allows the recursive calculation of genus-one Selberg integrals using an extra marked point in a differential equation of Knizhnik-Zamolodchikov-Bernard type. Hereby genus-one Selberg integrals are related to genus-zero Selberg integrals. Accordingly, N-point open-string amplitudes at genus one can be obtained from (N+2)-point open-string amplitudes at tree level. The construction is related to and in accordance with various recent results in intersection theory and string theory

MEASURING THE SENSITIVITY OF TURKISH AND ROMANIAN STOCK MARKETS TO EUROPEAN STOCK MARKETS: A COMPARATIVE ANALYSIS

Since the process of globalization accelerates all over the world, trade and economic relations among countries become very intensive and the stock markets in these countries started to integrate to each other quickly. As a result of this, world wide stocBeta Coefficient, Istanbul Stock Exchange (ISE,) Bucharest Stock Exchange (BSE), ISE100 Index, BET10 Index, FTS Eurofirst 300 Index

Elliptic multiple polylogarithms in open string theory

In dieser Dissertation wird eine Methode zur Berechnung der genus-eins Korrekturen von offenen Strings zu Feldtheorie-Amplituden konstruiert. Hierzu werden Vektoren von Integralen definiert, die ein elliptisches Knizhnik-Zamolodchikov-Bernard (KZB) System auf dem punktierten Torus erfüllen, und die entsprechenden Matrizen aus dem KZB System berechnet. Der elliptische KZB Assoziator erzeugt eine Relation zwischen zwei regulierten Randwerten dieser Vektoren. Die Randwerte enthalten die genus-null und genus-eins Korrekturen. Das führt zu einer Rekursion im Genus und der Anzahl externer Zustände, die einzig algebraische Operationen der bekannten Matrizen aus dem KZB System umfasst. Geometrisch werden zwei externe Zustände der genus-null Weltfläche der offenen Strings zu einer genus-eins Weltfläche zusammengeklebt. Die Herleitung dieser genus-eins Rekursion und die Berechnung der relevanten Matrizen wird durch eine graphische Methode erleichtert, mit der die Kombinatorik strukturiert werden kann. Sie wurde durch eine erneute Untersuchung der auf Genus null bekannten Rekursion entwickelt, bei welcher der Drinfeld Assoziator Korrekturen offener Strings auf Genus null auf solche mit einem zusätzlichen externen Zustand abbildet. Diese genus-null Rekursion umfasst ebenfalls ausschliesslich Matrixoperationen und basiert auf einem Vektor von Integralen, der eine Knizhnik-Zamolodchikov (KZ) Gleichung erfüllt. Die in der Rekursion gebrauchten Matrizen aus der KZ Gleichung werden als Darstellungen einer Zopfgruppe identifiziert und rekursiv berechnet. Der elliptische KZB Assoziator ist die Erzeugendenreihe der elliptischen Multiplen Zeta-Werte. Die Konstruktion der genus-eins Rekursion benötigt verschiedene Eigenschaften dieser Werte und ihren definierenden Funktionen, den elliptischen Multiplen Polylogarithmen. So werden Relationen verschiedener Klassen von elliptischen Polylogarithmen und Funktionalrelationen erzeugt durch elliptische Funktionen hergeleitet.In this thesis, a method to calculate the genus-one, open-string corrections to the field-theory amplitudes is constructed. For this purpose, vectors of integrals satisfying an elliptic Knizhnik-Zamolodchikov-Bernard (KZB) system on the punctured torus are defined and the matrices from the KZB system are calculated. The elliptic KZB associator is used to relate two regularised boundary values of these vectors. The boundary values are shown to contain the open-string corrections at genus zero and genus one. This yields a recursion in the genus and the number of external states, solely involving algebraic operations on the known matrices from the KZB system. Geometrically, two external states of the genus-zero, open-string worldsheet are glued together to form a genus-one, open-string worldsheet. The derivation of this genus-one recursion and the calculation of the relevant matrices is facilitated by a graphical method to structure the combinatorics involved. It is motivated by the reinvestigation of the recursion in the number of external states known at genus zero, where the Drinfeld associator maps the genus-zero, open-string corrections to the corrections with one more external state. This genus-zero recursion also involves matrix operations only and is based on a vector of integrals satisfying a Knizhnik-Zamolodchikov (KZ) equation. The matrices in the KZ equation and used in the recursion are shown to be braid matrices and a recursive method for their calculation is provided. The elliptic KZB associator is the generating series of elliptic multiple zeta values. The construction of the genus-one recursion requires various properties of these values and their defining functions, the elliptic multiple polylogarithms. Thus, the third part of this thesis consists of an analysis of elliptic multiple polylogarithms, which in particular leads to relations among different classes of elliptic polylogarithms and functional relations generated by elliptic functions

A note on the Drinfeld associator for genus-zero superstring amplitudes in twisted de Rham theory

The string corrections of tree-level open-string amplitudes can be described by Selberg integrals satisfying a Knizhnik-Zamolodchikov (KZ) equation. This allows for a recursion of the $\alpha'$-expansion of tree-level string corrections in the number of external states using the Drinfeld associator. While the feasibility of this recursion is well-known, we provide a mathematical description in terms of twisted de Rham theory and intersection numbers of twisted forms. In particular, this leads to purely combinatorial expressions for the matrix representation of the Lie algebra generators appearing in the KZ equation in terms of directed graphs. This, in turn, admits efficient algorithms for symbolic and numerical computations using adjacency matrices of directed graphs and is a crucial step towards analogous recursions and algorithms at higher genera

Long-term disease-free survival of patients with primary cardiac lymphoma treated with systemic chemotherapy and radiotherapy

Primary cardiac lymphoma (PCL) is a rare disease entity with only a few reported cases in Korea. In this paper, we report a case of PCL in a 59-year-old man presenting with chest pain. Diffuse large B-cell lymphoma was diagnosed through a cardiac catheterization-assisted percutaneous endomyocardial biopsy, and there was no evidence of extracardiac involvement of the lymphoma.The patient had a complete clinical response after systemic chemotherapy with a rituximab, cyclophosphamide, doxorubicin, vincristine, and prednisolone (R-CHOP) regimen and additional post-chemotherapeutic radiation therapy. The patient experienced a long-term disease-free survival of over 4 years. However, he received coronary artery bypass graft surgery due to an acute myocardial infarction that occurred 3 years after the completion of the radiation therapy. Although the addition of radiation therapy to the treatment is thought to decrease the risk of relapse in patients with PCL, a careful and thorough consideration of the potential complications of radiation therapy, particularly with respect to cardiac complications, should be considered

Conservation Initiatives/Assessments in Rock-Carved Churches Specific to the Göreme Saklı Church

Cappadocia contains historical, documentary, aesthetic, artistic, symbolic, social, economic, religious and spiritual values. Many structures and places produced by the rock carving technique have been destroyed and/or are on the way to extinction because of intense destruction in the historical process. Rock-carved churches, unique in their religious, artistic, and cultural values, are among the most affected. In this study, the current status of the Saklı Church, the examination of its historical development, the architectural documentation studies with the monasteries in its immediate vicinity, the structural deterioration, and the reasons for the preservation of the rock-hewn churches in the Göreme Valley, and the current conservation strategies and practices in the rock churches were evaluated. Preservation proposals have been developed so that the cultural heritage can be safely transferred to the future. As a result, the status and deterioration of the Saklı Church have been documented with various architectural representation methods, and conservation proposals have been developed