الصفحة 1
الصفحة 1
Modern cryptography ; Vol.1 : A classical introduction to informational and mathematical principle
This book systematically explores the statistical characteristics of cryptographic systems, the computational complexity theory of cryptographic algorithms and the mathematical principles behind various encryption and decryption algorithms. The theory stems from technology. Based on Shannon's information theory, this book systematically introduces the information theory, statistical characteristics and computational complexity theory of public key cryptography, focusing on the three main algorithms of public key cryptography, RSA, discrete logarithm and elliptic curve cryptosystem.
High-Dynamic-Range (HDR) Vision : Microelectronics, Image Processing, Computer Graphics
This first comprehensive account of high-dynamic-range (HDR) vision focusses on HDR real-time, high-speed digital video recording and also systematically presents HDR video transmission and display. The power of the eye-like, logarithmic optoelectronic conversion concept is demonstrated in machine-vision, medical, automotive, surveillance and cinematic applications, and it is extended to HDR sub-retinal implants for the vision impaired. While the book conveys the overall picture of HDR vision, specific knowledge of microelectronics and image processing is not required. It provides a quantitative summary of the major issues to allow the assessment of the state of the art and a glimpse at future developments. Selected experts share their know-how and expectations in this rapidly evolving art related to the single most powerful of our senses.
Hierarchical Matrices : A Means to Efficiently Solve Elliptic Boundary Value Problems
Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients.
Entropy Methods for the Boltzmann Equation : Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001
Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these.
Elements for Physics : Quantities, Qualities, and Intrinsic Theories
While usual presentations of physical theories emphasize the notion of physical quantity, this book shows that there is much to gain when introducing the notion of physical quality. The usual physical quantities simply appear as coordinates over the manifolds representing the physical qualities. This allows to develop physical theories that have a degree of invariance much deeper than the usual one. It is shown that properly developed physical theories contain logarithms and exponentials of tensors: their conspicuous absence in usual theories suggests, in fact, that the fundamental invariance principle stated in this book is lacking in present-day mathematical physics. The book reviews and extends the theory if Lie groups, develops differential geometry, proposing compact definitions of torsion and of curvature, and adapts the usual notion of linear tangent application to the intrinsic point of view proposed for physics. As an illustration, two simple theories are studied with some detail, the theory of heat conduction and the theory of linear elastic media. The equations found differ quantitatively and qualitatively from those usually presented.
Elementary Functions : Algorithms and Implementation
This unique book provides concepts and background necessary to understand and build algorithms for computing the elementary functions—sine, cosine, tangent, exponentials, and logarithms. The author presents and structures the algorithms, hardware-oriented as well as software-oriented, and also discusses issues related to accurate floating-point implementation. The purpose is not to give "cookbook recipes" that allow one to implement a given function, but rather to provide the reader with tools necessary to build or adapt algorithms for their specific computing environment.
Compactifying Moduli Spaces for Abelian Varieties
This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
Algorithmic number theory ; 7th International Symposium, ANTS-VII, Berlin, Germany, July 23-28, 2006, Proceedings
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
Algebraic Analysis of Differential Equations : from Microlocal Analysis to Exponential Asymptotics Festschrift in Honor of Takahiro Kawai Editors
This volume contains 23 articles on algebraic analysis of differential equations and related topics, most of which were presented as papers at the international conference "Algebraic Analysis of Differential Equations – from Microlocal Analysis to Exponential Asymptotics" at Kyoto University in 2005. Microlocal analysis and exponential asymptotics are intimately connected and provide powerful tools that have been applied to linear and non-linear differential equations as well as many related fields such as real and complex analysis, integral transforms, spectral theory, inverse problems, integrable systems, and mathematical physics. The articles contained here present many new results and ideas, providing interested researchers and students with valuable suggestions and instructive guidance for their work.
A Course in Calculus and Real Analysis
Provides a self-contained and rigorous introduction to calculus of functions of one variable. The presentation and sequencing of topics emphasizes the structural development of calculus. At the same time, due importance is given to computational techniques and applications. The authors have strived to make a distinction between the intrinsic definition of a geometric notion and its analytic characterization. It highlight the fact that calculus provides a firm foundation to several concepts and results that are generally encountered in high school and accepted on faith. For example, one can find here a proof of the classical result that the ratio of the circumference of a circle to its diameter is the same for all circles. Also, this book helps get a clear understanding of the concept of an angle and the definitions of the logarithmic, exponential and trigonometric functions together with a proof of the fact that these are not algebraic functions. A number of topics that may have been inadequately covered in calculus courses and glossed over in real analysis courses are treated here in considerable detail. As such, this book provides a unified exposition of calculus and real analysis.
