Series:De Gruyter Studies in Mathematics 55
Elliptic partial differential equations is one of the main and most active areas in mathematics. In our book we study linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments. For this reason the book is addressed to master students, PhD students and anyone who wants to begin research in this mathematical field.
Details
24 x 17 cmApprox. x, 200 pages
Language: English
Type of Publication: Monograph
Nonlinear Elliptic Partial Differential Equations in Divergence Form; Dirichlet Problems for Elliptic Equations; Distributional Solution; Entropy Solutions; Leray-Lions Problem; Sobolev Space
Series:De Gruyter Studies in Mathematics 56
The book gives a systematical presentation of stochastic approximation methods for models of American type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area.
This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Details
24 x 17 cmApprox. x, 490 pages
Language: English
Type of Publication: Monograph
American Option; Optimal Stopping; Convergence of Rewards; Markov Chain; Approximation Algorithm
Published: June 2013
Publisher: International Press
Paperback
138 pages
International Press of Boston is pleased to announce publication of the
first issue (July 2013) of its all-new Notices of the International Congress
of Chinese Mathematicians (or ICCM Notices, for short), the official periodical
of the ICCM organization.
The ICCM Notices brings news, research, and presentation of various perspectives, relevant to Chinese mathematics development and education. It will be published semi-annually.
The ICCM Notices will be of interest to all people?whether of Chinese background or not?who are interested in following Chinese mathematics.
Note: This first issue of the ICCM Notices, Volume 1, No. 1, July 2013, may be purchased individually. Subscription sales of the ICCM Notices will commence with the 2014 subscription year.
ISBN-13 9781571462725
2013 Jun
paperback
8.375h x 10.875h
Advanced Lectures in Mathematics Volume 27
Published: July 2013
Publisher: International Press
Paperback
240 pages
2013 Jul
ISBN: 9781571462732
The papers comprising this volume explore various fields of number theory, including: the congruent property of solutions of quadratic Diophantine equations, K-groups over the ring of integers of number fields, L-functions of global function fields, automorphic forms, p-adic representations, and more. Applications of number theory, as in design and coding theory, are also explored. The research found in this volume can be seen as a reflection of the influence of Professor Keqin Feng upon the development of number theory studies in China, and this volume is therefore dedicated to him.
Number Theory and Related Areas is a valuable reference for experts in these fields, as well as an excellent introduction for graduate students.
Textbook
To Be Published: 1 September 2013
Hardcover
792 pages
iISBN 9781571462640
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence.
In this ambitious new work, authors David Bleecker and Bernhelm Boos-Bavnbek give two proofs of the Atiyah-Singer Index Theorem in impressive detail: one based on K-theory and the other on the heat kernel approach. As a preparation for this, the authors explain all the background information on such diverse topics as Fredholm operators, pseudo-differential operators, analysis on manifolds, principal bundles and curvature, and K-theory?carefully and with concern for the reader. Many applications of the theorem are given, as well as an account of some of the most important recent developments in the subject, with emphasis on gauge theoretic physical models and low-dimensional topology.
The 18 chapters and two appendices of the book introduce different topics and aspects, often beginning gfrom scratchh without presuming full knowledge of all the preceding chapters. Learning paths, through a restricted selection of topics and sections, are suggested and facilitated. The chapters are written for students of mathematics and physics: some for the upper-undergraduate level, some for the graduate level, and some as an inspiration and support for researchers.
Index Theory with Applications to Mathematics and Physics is a textbook, a reference book, a survey, and much more. Written in a lively fashion, it contains a wealth of basic examples and exercises. The authors have included many discussion sections that are both entertaining and informative, which illuminate the thinking behind the more general theory. A detailed bibliography and index facilitate the orientation.