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2013 (14)

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Book
The mathematical works of Isaac Barrow
Authors: ---
ISBN: 1139568035 Year: 2013 Publisher: Cambridge : Cambridge University Press,

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The Cambridge polymath Isaac Barrow (1630-77) gained recognition as a theologian, classicist and mathematician. This one-volume collection of his mathematical writings, dutifully edited by one of his successors as Master of Trinity College, William Whewell (1794-1866), was first published in 1860. Containing significant contributions to the field, the work consists chiefly of the lectures on mathematics, optics and geometry that Barrow gave in his position as Lucasian Professor of Mathematics between 1663 and 1669. It includes the first general statement of the fundamental theorem of calculus as well as Barrow's 'differential triangle'. Not only did he precede Isaac Newton in the Lucasian chair, but his works were also to be found in the library of Gottfried Leibniz. However, rather than considering arid questions of priority, scholars can see in these Latin texts the status of advanced mathematics just before the great revolution of Newton and Leibniz.


Book
Elliptic Curves, Hilbert Modular Forms and Galois Deformations
Authors: --- --- --- --- --- et al.
ISBN: 3034806175 3034806183 Year: 2013 Publisher: Basel : Springer Basel : Imprint: Birkhäuser,

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The notes in this volume correspond to advanced courses held at the Centre de Recerca Matemàtica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year. The notes by Laurent Berger provide an introduction to p-adic Galois representations and Fontaine rings, which are especially useful for describing many local deformation rings at p that arise naturally in Galois deformation theory. The notes by Gebhard Böckle offer a comprehensive course on Galois deformation theory, starting from the foundational results of Mazur and discussing in detail the theory of pseudo-representations and their deformations, local deformations at places l ≠ p and local deformations at p which are flat. In the last section,the results of Böckle and Kisin on presentations of global deformation rings over local ones are discussed. The notes by Mladen Dimitrov present the basics of the arithmetic theory of Hilbert modular forms and varieties, with an emphasis on the study of the images of the attached Galois representations, on modularity lifting theorems over totally real number fields, and on the cohomology of Hilbert modular varieties with integral coefficients.  The notes by Lassina Dembélé and John Voight describe methods for performing explicit computations in spaces of Hilbert modular forms. These methods depend on the Jacquet-Langlands correspondence and on computations in spaces of quaternionic modular forms, both for the case of definite and indefinite quaternion algebras. Several examples are given, and applications to modularity of Galois representations are discussed.  The notes by Tim Dokchitser describe the proof, obtained by the author in a joint project with Vladimir Dokchitser, of the parity conjecture for elliptic curves over number fields under the assumption of finiteness of the Tate-Shafarevich group. The statement of the Birch and Swinnerton-Dyer conjecture is included, as well as a detailed study of local and global root numbers of elliptic curves and their classification.


Book
What Does Variation in Survey Design Reveal about the Nature of Measurement Errors in Household Consumption?
Authors: --- --- ---
Year: 2013 Publisher: Washington, D.C., The World Bank,

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This paper uses data from eight different consumption questionnaires randomly assigned to 4,000 households in Tanzania to obtain evidence on the nature of measurement errors in estimates of household consumption. While there are no validation data, the design of one questionnaire and the resources put into its implementation make it likely to be substantially more accurate than the others. Comparing regressions using data from this benchmark design with results from the other questionnaires shows that errors have a negative correlation with the true value of consumption, creating a non-classical measurement error problem for which conventional statistical corrections may be ineffective.


Book
Constant mean curvature surfaces with boundary
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ISBN: 3642396259 3642396267 Year: 2013 Publisher: Heidelberg, Germany : Springer,

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The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate two different media, or for capillary phenomena. Further, as most techniques used in the theory of CMC surfaces not only involve geometric methods but also PDE and complex analysis, the theory is also of great interest for many other mathematical fields.   While minimal surfaces and CMC surfaces in general have already been treated in the literature, the present work is the first to present a comprehensive study of “compact surfaces with boundaries,” narrowing its focus to a geometric view. Basic issues include the discussion whether the symmetries of the curve inherit to the surface; the possible values of the mean curvature, area and volume; stability; the circular boundary case; and the existence of the Plateau problem in the non-parametric case. The exposition provides an outlook on recent research but also a set of techniques that allows the results to be expanded to other ambient spaces. Throughout the text, numerous illustrations clarify the results and their proofs.   The book is intended for graduate students and researchers in the field of differential geometry and especially theory of surfaces, including geometric analysis and geometric PDEs. It guides readers up to the state-of-the-art of the theory and introduces them to interesting open problems.


Book
Space-Filling Curves : An Introduction with Applications in Scientific Computing
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ISBN: 9783642310454 3642310451 364231046X Year: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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­The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings. ­The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.


Book
Lecture Notes on Mean Curvature Flow: Barriers and Singular Perturbations
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ISBN: 8876424288 8876424296 Year: 2013 Publisher: Pisa : Scuola Normale Superiore : Imprint: Edizioni della Normale,

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The aim of the book is to study some aspects of geometric evolutions, such as mean curvature flow and anisotropic mean curvature flow of hypersurfaces. We analyze the origin of such flows and their geometric and variational nature. Some of the most important aspects of mean curvature flow are described, such as the comparison principle and its use in the definition of suitable weak solutions. The anisotropic evolutions, which can be considered as a generalization of mean curvature flow, are studied from the view point of Finsler geometry. Concerning singular perturbations, we discuss the convergence of the Allen–Cahn (or Ginsburg–Landau) type equations to (possibly anisotropic) mean curvature flow before the onset of singularities in the limit problem. We study such kinds of asymptotic problems also in the static case, showing convergence to prescribed curvature-type problems.


Book
Deformations of Surface Singularities
Authors: ---
ISBN: 3642391303 3642391311 Year: 2013 Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer,

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The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry.  This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several open problems. Recently several connections were established with low dimensional topology, symplectic geometry and theory of Stein fillings. This created an intense mathematical activity with spectacular bridges between the two areas. The theory of deformation of singularities is the key object in these connections. .


Book
Elliptic curves and arithmetic invariants
Author:
ISBN: 1489990925 1461466563 1461466571 Year: 2013 Publisher: New York : Springer,

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This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics.   This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties.  Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader.  Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory.  Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.


Book
Drinfeld moduli schemes and automorphic forms : the theory of elliptic modules with applications
Author:
ISSN: 21918198 ISBN: 1461458870 1461458889 1283945908 Year: 2013 Publisher: New York : Springer,

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Drinfeld Moduli Schemes and Automorphic Forms: The Theory of Elliptic Modules with Applications is based on the author’s original work establishing the correspondence between ell-adic rank r Galois representations and automorphic representations of GL(r) over a function field, in the local case, and, in the global case, under a restriction at a single place. It develops Drinfeld’s theory of elliptic modules, their moduli schemes and covering schemes, the simple trace formula, the fixed point formula, as well as the congruence relations and a "simple" converse theorem, not yet published anywhere. This version, based on a recent course taught by the author at The Ohio State University, is updated with references to research that has extended and developed the original work. The use of the theory of elliptic modules in the present work makes it accessible to graduate students, and it will serve as a valuable resource to facilitate an entrance to this fascinating area of mathematics.


Book
Introduction to global optimization exploiting space-filling curves
Authors: --- ---
ISBN: 1461480418 1461480426 Year: 2013 Publisher: New York : Springer,

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Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful . .

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