الصفحة 11
الصفحة 11
Cyclotomic Fields and Zeta Values
Cyclotomic fields have always occupied a central place in number theory, and the so called "main conjecture" on cyclotomic fields is arguably the deepest and most beautiful theorem known about them. It is also the simplest example of a vast array of subsequent, unproven "main conjectures'' in modern arithmetic geometry involving the arithmetic behaviour of motives over p-adic Lie extensions of number fields. These main conjectures are concerned with what one might loosely call the exact formulae of number theory which conjecturally link the special values of zeta and L-functions to purely arithmetic expressions.
Cycle Spaces of Flag Domains : A Complex Geometric Viewpoint
This monograph, divided into four parts, presents a comprehensive treatment and systematic examination of cycle spaces of flag domains. Assuming only a basic familiarity with the concepts of Lie theory and geometry, this work presents a complete structure theory for these cycle spaces, as well as their applications to harmonic analysis and algebraic geometry.
Cryptography and coding ; 11th IMA International Conference, Cirencester, UK, December 18-20, 2007, Proceedings
This book presented signatures, boolean functions, block cipher cryptanalysis, side channels, linear complexity, public key encryption, curves, and RSA implementation.
Cryptography and coding ; 10th IMA International Conference, Cirencester, UK, December 19-21, 2005, Proceedings
Constitutes the refereed proceedings of the 10th IMA International Conference on Cryptography and Coding, held in Cirencester, UK, in December 2005. This book features papers that are organized in topical sections on coding theory, signatures and signcryption, symmetric cryptography, side channels, algebraic cryptanalysis, and more.
Cours doptique : Simulations et exercices résolus avec Maple, Matlab, Mathematica, Mathcad = Optics course: Simulations and exercises solved with Maple, Matlab, Mathematica, Mathcad
Intended for students at the L and M levels of the university as well as for engineers wishing to study certain subjects in greater depth. It covers all the themes of a traditional optics course, from geometric optics to holography, interference, diffraction, coherence and the use of the Fourier transform for spectroscopy. The presentation is developed from mathematical models deriving from typical situations and fundamental examples which are presented in the form of computer programs ready to be implemented. These programs are also available on the CD accompanying the book, for each of the following scientific programming environments: Matlab, Maple, Mathematica and Mathcad. Thus, the reader will be able to modify the parameters of the examples proposed to adapt them to new situations.
Courbes algébriques planes = Plane Algebraic Curves
Resulting from a master's course at the University of Paris VII, this text is re-edited as it appeared in 1978. Various tools are introduced in connection with Bézout's theorem necessary for the development of the notion of the multiplicity of intersection of two algebraic curves in the complex projective plane. Starting from elementary notions on affine and projective algebraic subsets, we define the intersection multiplicities and interpret their sum in terms of the resultant of two polynomials. The local study is a pretext for the introduction of formal or convergent series rings; it culminates in Puiseux's theorem, the convergence of which is reduced by splits to that of the theorem of implicit functions. Various figures illuminate the text: we "see" in particular that the homogeneous equation x3 + y3 + z3 = 0 defines a torus in the complex projective plane.
Coordination models and languages ; Vol.4038 ; 8th International Conference, COORDINATION 2006, Bologna, Italy, June 14-16, 2006, Proceedings
This book constitutes the refereed proceedings of the 8th International Conference on Coordination Models and Languages, COORDINATION 2006, held in Bologna, Italy, June 2006. The 17 revised full papers presented were carefully reviewed and selected from 50 submissions. Among the topics addressed are component connectors, negotiation in service-oriented computing, process algebraic specification, workflow patterns, reactive XML, ubiquitous coordination, type systems, ad-hoc network coordination, choreography, communication coordination, and distributed embedded systems.
Convergence and Applications of Newton-type Iterations
Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, modeling dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter.
Continuum Mechanics using Mathematica® : Fundamentals, Applications and Scientific Computing
This book's methodological approach familiarizes readers with the mathematical tools required to correctly define and solve problems in continuum mechanics. The book covers essential principles and fundamental applications, and provides a solid basis for a deeper study of more challenging and specialized problems related to elasticity, fluid mechanics, plasticity, materials with memory, piezoelectricity, ferroelectricity, magneto-fluid mechanics, and state changes.
Continuous System Simulation
Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.
Constructive Negations and Paraconsistency
This book presents the author’s recent investigations of the two main concepts of negation developed in the constructive logic: the negation as reduction to absurdity (L.E.J. Brouwer) and the strong negation (D. Nelson) are studied in the setting of paraconsistent logic. The paraconsistent logics are those, which admit inconsistent but non-trivial theories, i.e., the logics which allow making inferences in non-trivial fashion from an inconsistent set of hypotheses. The study is based on algebraic methods, demonstrates the remarkable regularity and the similarity of structures of both lattices of logics, and gives essential information on the paraconsistent nature of logics Lj and N4.The methods developed in this book can be applied for investigation of other classes of paraconsistent logics.
Constructing Correct Software
Central to Formal Methods is the so-called Correctness Theorem which relates a specification to its correct Implementations. This theorem is the goal of traditional program testing and, more recently, of program verification (in which the theorem must be proved). Proofs are difficult, though even with the use of powerful theorem provers. This volume explains and illustrates an alternative method, which allows the construction of (necessarily correct) algorithms from a specification using algebraic transformations and refinement techniques which prevent the introduction of errors. Based on teaching material used extensively at Loughborough University, John Cooke introduces the basics, using simple examples and lots of detailed working (which can often be re-used). Constructing Correct Software will provide invaluable reading for students and practitioners of Computer Science and Software Engineering to whom correctness of software is of prime importance.
Conics and Cubics : A Concrete Introduction to Algebraic Curves
Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas: homogenous coordinates and intersection multiplicities. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves.The book is a text for a one-semester course on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus.
Conformal Groups in Geometry and Spin Structures
This book provides a self-contained overview of this important area of mathematical physics, beginning with its origins in the works of Cartan and Chevalley and progressing to recent research in spinors and conformal geometry. Key topics and features: * Focuses initially on the basics of Clifford algebras * Studies the spaces of spinors for some even Clifford algebras * Examines conformal spin geometry, beginning with an elementary study of the conformal group of the Euclidean plane * Treats covering groups of the conformal group of a regular pseudo-Euclidean space, including a section on the complex conformal group * Introduces conformal flat geometry and conformal spinoriality groups, followed by a systematic development of riemannian or pseudo-riemannian manifolds having a conformal spin structure * Discusses links between classical spin structures and conformal spin structures in the context of conformal connections * Examines pseudo-unitary spin structures and pseudo-unitary conformal spin structures using the Clifford algebra associated with the classical pseudo-unitary space
Conflicts Between Generalization, Rigor, and Intuition : Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany
Conflicts Between Generalization, Rigor, and Intuition undertakes a historical analysis of the development of two mathematical concepts -negative numbers and infinitely small quantities, mainly in France and Germany, but also in Britain, and the different paths taken there.This book not only discusses the history of the two concepts, but it also introduces a wealth of new knowledge and insights regarding their interrelation as necessary foundations for the emergence of the 19th century concept of analysis. The historical investigation unravels several processes underlying and motivating conceptual change: generalization (in particular, algebraization as an agent for generalizing) and a continued effort of intuitive accessibility which often conflicted with likewise desired rigor. The study focuses on the 18th and the 19th centuries.The book provides a productive unity to a large number of historical sources.
Computing in Algebraic Geometry : A Quick Start using SINGULAR
Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. … This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones.
Computing and Combinatorics ; 13th Annual International Conference, COCOON 2007, Banff, Canada, July 16-19, 2007, Proceedings
The Book covers most aspects of theoretical computer scienceand combinatorics related to computing.It exploring research, development, and novel applications of computing and combinatorics.
Computer Performance Engineering ; 5th European Performance Engineering Workshop, EPEW 2008, Palma de Mallorca, Spain, September 24-25, 2008. Proceedings
This book constitutes the proceedings of the Fifth European Performance Engineering Workshop, EPEW 2008, held in Palma de Mallorca, Spain, in September 24-25, 2008.
Computer Mathematics ; 8th Asian Symposium, ASCM 2007, Singapore, December 15-17, 2007. Revised and Invited Papers
This book constitutes thoroughly refereed post-conference proceedings of the 8th Asian Symposium on Computer Mathematics, ASCM 2007, held in Singapore in December 2007.
Computer Algebra Recipes for Mathematical Physics
Over two hundred novel and innovative computer algebra worksheets or ""recipes"" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn.
