Macques Francheteau and Guy Métivier
Existence de Chocs Faibles pour des Systèmes Quasi-Linéaires Hyperboliques Multidimensionnels
Description
In this work, the authors consider weak shocks for systems of conservation laws in any space dimension. The main result is the construction on a space-time domain, independent of the parameter $\varepsilon$, of families of weak solutions $u^\varepsilon$, discontinuous along a smooth hypersurface $\Sigma^\varepsilon$, with jumps of order $\varepsilon$. For a fixed $\varepsilon$, the problem can be recast as a nonlinear mixed hyperbolic problem with a free noncharacteristic boundary. It has been solved by A. Majda. When $\varepsilon$ tends to zero, the front tends to be characteristic. This induces a loss of stability and regularity. As a consequence, the classical nonlinear methods based on Picard's iterations and differentiation of the equations do not apply. In this work, to prove the suitable a priori estimates and to construct the solutions, the authors use more sophisticated methods, such as the paradifferential calculus and Nash-Moser-type iteration schemes. An important application of the results concern Euler's equations of gas dynamics. They apply to the full system and to the isentropic system. The authors construct and compare weak shock solutions of these two systems.
Contents
Introduction
Résultats principaux
Les étapes des preuves
Estimations préliminaires
Opérateurs de traces et de relèvement de traces
Compatibilités, constructions de solutions approchées
Paralinéarisation
Estimations d'énergie conormales
Estimations a priori pour le problème non-linéaire
Le théorème de prolongement à $\varepsilon$ fixé
Prolongement de la régularité
Application au système d'Euler. Comparaison des solutions
Bibliographie
Details:
Publisher: Société Mathématique de France
Series: Astérisque,Number: 268
Publication Year: 2000
ISBN: 2-85629-092-2
Paging: 198 pp.
Binding: Softcover
P. Manoilov, /G. Manoilov, /B. Delijska, Sofia, Bulgaria
Elsevier's Dictionary of Computer Graphics
In English, German, French and Russian
Description
Elsevier's Dictionary of Computer Graphics contains 10,540 terms with more than 2,600 cross-references that are commonly used in the theory and practice of computer
graphics. Included are terms from all areas related to a) the theory of computer graphics - descriptive geometry, projective geometry, topology, fractal geometry, color
science; and b) the practice of computer graphics - computer-aided design (CAD) systems, technical drawing, computer art, computer animation, business graphics,
scientific visualization, virtual reality, graphical programming, image processing, graphical computer devices.
As well as the commonly used terms in the above-mentioned areas, the dictionary also includes terms that are currently coming into use, especially in the areas of
computer-aided design systems, computer art, computer animation, virtual reality and graphical programming.
Elsevier's Dictionary of Computer Graphics will be a valuable tool for engineers, scientists, artists, students and for everyone who takes an interest in computer graphics.
Year 2000
Hardbound
ISBN: 0-444-50027-8
800 pages
10,540 terms
Haake, F., University of Essen, Germany
Quantum Signatures of Chaos, 2. Aufl.
2000. XX, 460 pp. 67 figs.
3-540-67723-2
This textbook provides an excellent introduction to a new and rapidly developing field of research. The
topics treated include a detailed exploration of the quantum aspects of nonlinear dynamics, quantum criteria
to distinguish regular and irregular motion, antiunitary symmetries (generalized time reversal) and a
thorough account of the quantum mechanics of dissipative systems. Each chapter is accompanied by a
selection of problems which will help the student to test and deepen his/her understanding and to acquire
an active command of the methods.
The second edition is significantly expanded. Of the considerable theoretical progress lately achieved, the
book focusses on the deeper statistical exploitation of level dynamics, improved control of semiclassical
periodic-orbit expansions, and superanalytic techniques for dealing with various types of random matrices.
Keywords: Quantum Physics, Synergetics, Chaos, Complex Systems .
Contents: From the contents: Introduction.- Time Reversal and Unitary Symmetries.- Level Repulsion.-
Random-Matrix Theory.- Level Clustering.- Level Dynamics.- Quantum Localization.- Semiclassical Roles for
Classical Orbits.- Dissipative Systems.- Superanalysis for Random-Matrix Theory.
Series: Springer Series in Synergetics.VOL. 54
Ying, M., Tsinghua University, Beijing, China
Topology in Process Calculus
Approximate Correctness and Infinite Evolution of Concurrent Programs
2001. Approx. 240 pp.
0-387-95092-3
Communication and concurrency are essential in understanding complex dynamic systems, and there have
been many theories to deal with them such as Petri nets, CSP and ACP. Among them, CCS (process
calculus is one of the most important and mathematically developed models of communication and
concurrency. Various behavior equivalences between agents, such as (strong and weak) bisimilarity,
observation congruence, trace equivalence, testing equivalence and failure equivalence, are central notions
in process calculus. In the real applications of process calculus, specification and implementation are
described as two agents, correctness of programs is treated as a certain behavior equivalence between
specification and implementation, and then the proof of correctness of programs is a task to establish some
behavior equivalence between them. The goal of this book is to provide some suitable and useful concepts
and tools for the understanding and analysis of approximate correctness of programs in concurrent
systems. Throughout this book the focus is on the framework of process calculus, and the main idea is to
construct some natural and reasonable topological structures which can reveal suitably a mechanism of
approximate computation in process calculus and to work out various relationships among processes which
are compatible with these topological structures.
Contents: 1.Introduction.- 2.Process Calculus.- 3.Bisimulation and Trace Limits of Agents.- 4.Limit Behavior
of Agents.- 5.Near Bisimulations Defined by Closures.- 6.Bisimulation Indexes Induced by Metrics.-
7.Conclusion.- References.
Goodman,A.
Algebra from A to Z
This book deals with algebra at the high-school and the college-freshman level. The first few chapters are devoted to understanding numbers and thus cover elementary counting - material for grades 1 to 5 - but the subject is treated in an adult fashion. The book starts at the very beginning of counting and covers everything in elementary algebra, including a few topics that most books omit. For example the text includes a thorough treatment of the summation symbol and discusses the Peano axioms.
Contents: Volume 1 Symbols - Why, When and How; Elementary Arithmetic - The Integers; Rational Numbers and Fractions; Irrational Numbers; Symbolic Manipulations, Exponents, Roots and Radicals; Volume 2: Functions and Linear Equations; Quadratic Equations; Graphing Equations; Inequalities; Parabolas, Ellipses, and Hyperbolas; Volume 3: More About Functions; A Little Set Theory; Sequences, Series, and Mathematical Induction; Combinations and Permutations; The Binomial Theorem and Related Topics; More About Polynomials; Volume 4: Probability; Graphs of Functions; Exponential and Logarithmic Functions; Systems of Equations; Matrices and Determinants; Volume 5: A Little Trigonometry; An Introduction to Vector Algebra; The Scalar and Vector Product of Two Vectors; Complex Numbers; The Peano Axioms.