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Automorphic Forms and Lie Superalgebras
Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26.The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course.
Automorphic forms and even unimodular lattices : Kneser neighbors of niemeier lattices
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices.It explains how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations.
Automatic Differentiation : Applications, Theory, and Implementations
This collection covers the state of the art in automatic differentiation theory and practice. Practitioners and students will learn about advances in automatic differentiation techniques and strategies for the implementation of robust and powerful tools. Computational scientists and engineers will benefit from the discussion of applications, which provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.
Attractivity and bifurcation for nonautonomous dynamical systems
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity.
Asymptotics for Dissipative Nonlinear Equations
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Asymptotic Theory of Statistics and Probability
An encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics.
Assessment of cancer screening : A primer
Provides an in-depth look at the many aspects of cancer screening and its assessment, including screening phenomena, performance measures, population-level outcomes, research designs, and other important and timely topics.
Aspects of mathematical modelling : Applications in science, medicine, economics and management
The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management. The reader will find some review papers outlining current research directions in hot topics such as pattern formation and applications to medicine, and more targeted research papers on current developments in the various disciplines included.
Aspects of Mathematical Finance
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.
Aspects of Brownian motion
Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum.
Artinian Modules over Group Rings
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Artificial neural networks - ICANN 2008 ; 18th International Conference, Prague, Czech Republic, September 3-6, 2008, Proceedings, Part II
This two volume set LNCS 5163 and LNCS 5164 constitutes the refereed proceedings of the 18th International Conference on Artificial Neural Networks, ICANN 2008, held in Prague Czech Republic, in September 2008.
Artificial neural networks - ICANN 2008 ; 18th International Conference, Prague, Czech Republic, September 3-6, 2008, Proceedings, Part I
This two volume set LNCS 5163 and LNCS 5164 constitutes the refereed proceedings of the 18th International Conference on Artificial Neural Networks, ICANN 2008, held in Prague Czech Republic, in September 2008.
Arnolds Problems
Arnold's Problems contains mathematical problems.The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world.The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them).
Aritmetica, crittografia e codici = Arithmetic, cryptography and codes
The basic techniques of algebra and number theory useful in recent applications to cryptography and codes are developed, with the aim of being elementary and self-sufficient. The emphasis is on computational problems. This part of the volume can be useful as a textbook for a first course in algebra for mathematicians, computer scientists or engineers. Important applications of algebra and geometry to cryptography and codes are then illustrated. Both, cryptography and codes have significant applications in daily life which are illustrated here. Cryptography is developed in detail in much of its classic and current aspects, and both private and public key cryptography are developed. Cryptography with the use of elliptic curves on finite fields is also illustrated. A chapter introducing the subject is dedicated to linear codes.
Aritmetica : Un approccio computazionale = Arithmetic : A computational approach
Intended to be a contribution to the algorithmic re-reading of some classic topics of elementary number theory and an invitation to more demanding reading, according to the indications provided by the bibliography annexed to it.
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Arithmetic and geometry around hypergeometric functions : Lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session.
Arakelov Geometry and Diophantine Applications
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry.The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research.
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
