Modular forms

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  • The theory of automorphic functions in one complex variable was created during the second half of the nineteenth and the beginning of the twentieth centuries. Important contributions are due to such illustrious mathematicians as F. Klein, P. Koebe and H. Poincare. Two sources may be traced: the uniformization theory of algebraic functions, and certain topics in number theory. Automorphic functions with respect to groups with compact quotient space on the one hand and elliptic modular functions on the other are examples of these two aspects.

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  • One way of characterising texts is in terms of the discourse structures on which they appear to be built. Each type of text, or genre, e.g. the sports report, the recipe, the sermon, the proverb, will have associated with it a characteristic organisation of units. In this paper, a general model of the structure of one text type, the story, is described. This model forms the basis of a program which combines the general story structure principles with rules goveming a particular sub-genre, the Old French epic, in order to generate story summaries. INTRODUCTION Over the last twelve years,...

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  • The paper describes work on applying a general purpose natural language processing system to transfer-based interactive translation. Transfer takes place at the level of Quasi Logical Form (QLF), a contextually sensitive logical form representation which is deep enough for dealing with cross-linguistic differences. Theoretical arguments and experimental results are presented to support the claim that this framework has good properties in terms of modularity, compositionality, reversibility and monotonicity. ...

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  • This grammar formalism, a high degree of modularity between syntax and semantics. There is a syntax rule compiler (compiling into Prolog) which takes care of the building of analysis structures and the interface to a clearly separated semantic interpretation component dealing with scoping and the construction of logical forms. The whole system can work in either a one-pass mode or a two-pass mode. [n the one-pass mode, logical forms are built directly during parsing through interleaved calls to semantics, added automatically by the rule compiler. ...

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  • We introduce new modulus scaling techniques for transforming a class of primes into special forms which enables efficient arithmetic. The scaling technique may be used to improve multiplication and inversion in finite fields. We present an efficient inversion algorithm that utilizes the structure of scaled modulus.

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  • Articles in this volume are based on talks given at the Gauss-Dirichlet Conference held in Göttingen on June 20-24, 2005. The conference commemorated the 150th anniversary of the death of C.-F. Gauss and the 200th anniversary of the birth of J.-L. Dirichlet. The volume begins with a definitive summary of the life and work of Dirichlet and continues with thirteen papers by leading experts on research topics of current interest in number theory that were directly influenced by Gauss and Dirichlet.

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  • Annals of Mathematics This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...

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  • Chapter 1 - Genetics: The study of biological information. This chapter includes contents: DNA - The fundamental information molecule of life, proteins: the functional molecules of life processes, complex systems and molecular interactions, molecular similarities of all life-forms, the modular construction of genomes, modern genetic techniques, human genetics.

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  • Abstract Neural architectures have been proposed to navigate mobile robots within several environment definitions. In this paper a new neural modular constructive approach to navigate mobile robots in unknown environments is presented. The problem, in its basic form, consists of defining and executing a trajectory to a predefined goal while avoiding all obstacles, in an unknown environment. Some crucial issues arise when trying to solve this problem, such as an overflow of sensorial information and conflicting objectives.

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  • English for Business Communication is a short course for people in or preparing for work who need to improve their English in these key areas: socialising, telephoning, presenting, taking part in meetings and negotiating. With its modular approach it is easy to fit into any teaching programme. As the title suggests, the focus is on developing speaking skills in the contexts of day-to-day dealings with customers, clients and suppliers of services or goods. Great emphasis is also placed on developing listening skills.

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  • This fast-moving guide introduces web application development with Haskell and Yesod, a potent language/framework combination that supports high-performing applications that are modular, type-safe, and concise. You’ll work with several samples to explore the way Yesod handles widgets, forms, persistence, and RESTful content. You also get an introduction to various Haskell tools to supplement your basic knowledge of the language.

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  • Let Γ be a principal congruence subgroup of SLn (Z) and let σ be an Γ irreducible unitary representation of SO(n). Let Ncus (λ, σ) be the counting function of the eigenvalues of the Casimir operator acting in the space of cusp forms for Γ which transform under SO(n) according to σ. In this paper we Γ prove that the counting function Ncus (λ, σ) satisfies Weyl’s law. Especially, this implies that there exist infinitely many cusp forms for the full modular group SLn (Z). Contents 1. Preliminaries 2. Heat kernel estimates 3. Estimations of the discrete spectrum 4....

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  • ADC’s TrueNet® Category 6 patch panels, patch cords, modular jacks, and cable form an end-to-end channel optimized to preserve signal amplitude and deliver zero bit error performance in Gigabit Ethernet applications. TrueNet patch panels are manufactured in 24-port (1RU) or 48-port (2RU) configurations to provide high-density modular patching solutions for all high-density applications where space is limited.

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  • ADC’s FlexDSX® Multifunction Product Solutions provide maximum flexibility while eliminating the need to support multiple DSX-1, DSX-3, Fiber and Ethernet panels, particularly valuable in a small to medium size application. Designed to meet your requirements, one FlexDSX® panel is capable of housing all forms of multimedia services, including fiber, coax, and twisted pair connectivity. Ultimate flexibility is provided with the mix and match modularity of FlexDSX modules.

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  • In writing this book we have kept in mind our aim of providing a concise account of the main issues which presently characterise our system of administrative justice. The book is intended as a text for undergraduates taking a modular course in administrative law and indeed its origins lie in our own experience of teaching and adapting such a course here at Sheffield. Inevitably we owe a considerable debt to past and present colleagues whose work has formed the basis of much of our thinking in this text.

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  • This paper describes a modular connectionist model of the acquisition of receptive inflectional morphology. The model takes inputs in the form of phones one at a time and outputs the associated roots and inflections. Simulations using artificial language stimuli demonstrate the capacity of the model to learn suffixation, prefixation, infixation, circumfixation, mutation, template, and deletion rules.

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  • We present a program for segmenting texts according to the separate events they describe. A modular architecture is described that allows us to examine the contributions made by particular aspects of natural language to event structuring. This is applied in the context of terrorist news articles, and a technique is suggested for evaluating the resulting segmentations. We also examine the usefulness of various heuristics in forming these segmentations.

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  • The paper presents the state of elaboration of the natural language information retrieval system DIALOG. Its aim is an automatic, conversational extraction of facts from a given text. Actually it is real medical text on gastroenterology, which was prepared by a team of specialists. The system has a modular structure. The first, and in fact very important module is the language analysis module. Its task is to ensure the transition of a medical text from its natural form, i.e. rentences formed by physicians, into a formal ~ogical notation. ...

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  • The formal architecture of Lexical Functional Grammar offers a particular formal device, the structural correspondence, for modularizing the mapping between the surface forms of a language and representations of their underlying meanings. This approach works well when the structural discrepancies between form and meaning representations are finitely bounded, but there are some phenomena in natural language, e.g. adverbs in English, where this restriction does not hold.

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