Establishes a self-contained theoretical framework for graph theory from a topological point of view.
Explains the embedding of graphs on non-zero genus surfaces.
Discusses graphic matroids and knot polynomials.
This book introduces polyhedra as a tool for graph theory and discusses their properties and applications in solving the Gauss crossing problem. The discussion is extended to embeddings on manifolds, particularly to surfaces of genus zero and non-zero via the joint tree model, along with solution algorithms. Given its rigorous approach, this book would be of interest to researchers in graph theory and discrete mathematics.
24.0 x 17.0 cm
Approx. x, 290 pages
75 Fig. 5 Tables
Language: English
Type of Publication: Monograph
Series:Fractional Calculus in Applied Sciences and Engineering
First attempt to use fractional calculus to model and control of crownd dynamics.
Modeling, simulation and control methods explored at micro-, meso- and macrio- scales.
Individuals with disabilities are considered in the framework.
The book illustrates the application of fractional calculus in crowd dynamics via modeling pedestrians group. Decision decision making process, conversation law of mass/momentum, micro-macro model are employed to describe system dynamics and cooperative movements, reaction-advection-diffusion model are studied to control the group. With practical issue considered, the book is of interests to mathematicians, civil engineers, and physicists.
24.0 x 17.0 cm
Approx. xx, 200 pages
30 Fig.
Language: English
Type of Publication: Monograph
To Be Published: 30 December 2016
Hardcover
190 pages
Finite group theory is a topic remarkable for the simplicity of its statements and the difficulty of their proofs. It is used in an essential way in several branches of mathematics?for instance, in number theory.
This book is a short introduction to the subject, written both for beginners and for mathematicians at large. There are ten chapters: Preliminaries, Sylow theory, Solvable groups and nilpotent groups, Group extensions, Hall subgroups, Frobenius groups, Transfer, Characters, Finite subgroups of GLn, and Small groups.
Each chapter is followed by a series of exercises.
Jean-Pierre Serre attended the Ecole Normale Superieure (1945?48) and the Sorbonne (Ph.D., 1951), both now part of the Universities of Paris. Between 1948 and 1954 he was at the National Center for Scientific Research in Paris, and after two years at the University of Nancy he returned to Paris for a professorship at the College de France. He retired in 1994. Between 1983 and 1986 he served as vice president of the International Mathematical Union. Serre’s mathematical contributions, leading to a Fields Medal in 1954, were largely in the field of algebraic topology, but his later work ranged widely?within algebraic geometry, group theory, and especially number theory. By seeing unifying ideas, he helped to unite disparate branches of mathematics. One of the more recent phenomena to which he was a principal contributor was the application of algebraic geometry to number theory?applications now falling into a separate subclass called arithmetic geometry. Serre has published many books: Groupes algebriques et corps de classes (1959); Corps Locaux (1962); Cohomologie Galoisienne (1964); Lie Algebras and Lie Groups (1965); Algebre locale, multiplicites (1965); Algebres de Lie semi-simples complexes (1966); Representations lineaires des groupes finis (1967); Abelian l-adic Representations and Elliptic Curves (1968); Cours d’arithmetique (1970); Arbres, amalgames, SL2 (1977); Lectures on the Mordell-Weil Theorem (1989); Topics in Galois Theory (1992); Lectures on Nx(p) (2012). His Collected Works (1949?1984) were published in 1986, followed in 2000 by Collected Works (1985?1998). In 1995 Serre received a Leroy P. Steele Prize for A Course in Arithmetic, and in 2003 he was awarded the first Abel Prize by the Norwegian Academy of Science and Letters.
Paperback | March 2017 | $75.00 | ￡55.95 | ISBN: 9780691174839
Hardcover | March 2017 | $165.00 | ￡122.95 | ISBN: 9780691174822
216 pp. | 6 x 9
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Holder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations.
The construction itself an intricate algorithm with hidden symmetries mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma" used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture.
Philip Isett is assistant professor of mathematics at the University of Texas, Austin.
Series:
Annals of Mathematics Studies
Paperback | May 2017 | $75.00 | ￡55.95 | ISBN: 9780691175430
Hardcover | May 2017 | $165.00 | ￡122.95 | ISBN: 9780691175423
880 pp. | 6 x 9 | 12 line illus.
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems.
This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Matthias Aschenbrenner is professor of mathematics at the University of California, Los Angeles. Lou van den Dries is professor of mathematics at the University of Illinois, Urbana-Champaign. Joris van der Hoeven is director of research at the French National Center for Scientific Research (CNRS).
Series:
Annals of Mathematics Studies
Paperback | June 2017 | $75.00 | ￡55.95 | ISBN: 9780691160559
Hardcover | June 2017 | $165.00 | ￡122.95 | ISBN: 9780691160542
776 pp. | 6 x 9 | 35 line illus.
This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.
Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws?PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs?mixed type, free boundaries, and corner singularities?that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
Gui-Qiang G. Chen is the Statutory Professor in the Analysis of Partial Differential Equations at the Mathematical Institute of the University of Oxford, where he is also professorial fellow at Keble College. Mikhail Feldman is professor of mathematics at the University of Wisconsin?Madison.
Series:
Annals of Mathematics Studies
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