Student Mathematical Library, Volume: 38
2007; 252 pp; softcover
ISBN-10: 0-8218-4333-8
ISBN-13: 978-0-8218-4333-8
Expected publication date is October 14, 2007.
Filtering and prediction is about observing moving objects when the observations are corrupted by random errors. The main focus is then on filtering out the errors and extracting from the observations the most precise information about the object, which itself may or may not be moving in a somewhat random fashion. Next comes the prediction step where, using information about the past behavior of the object, one tries to predict its future path.
The first three chapters of the book deal with discrete probability spaces, random variables, conditioning, Markov chains, and filtering of discrete Markov chains. The next three chapters deal with the more sophisticated notions of conditioning in nondiscrete situations, filtering of continuous-space Markov chains, and of Wiener process. Filtering and prediction of stationary sequences is discussed in the last two chapters.
The authors believe that they have succeeded in presenting necessary ideas in an elementary manner without sacrificing the rigor too much. Such rigorous treatment is lacking at this level in the literature. In the past few years the material in the book was offered as a one-semester undergraduate/beginning graduate course at the University of Minnesota. Some of the many problems suggested in the text were used in homework assignments.
Readership
Undergraduate and graduate students interested in filtering and prediction for random processes.
Table of Contents
Preliminaries
Markov chains
Filtering of discrete Markov chains
Conditional expectations
Filtering of continuous-space Markov chains
Wiener process and continuous time filtering
Stationary sequences
Prediction of stationary sequences
Bibliography
Index
American Mathematical Society Translations--Series 2, Volume: 221
2007; approx. 213 pp; hardcover
ISBN-10: 0-8218-4371-0
ISBN-13: 978-0-8218-4371-0
Expected publication date is December 2, 2007.
The Institute for Theoretical and Experimental Physics (ITEP) is internationally recognized for achievements in various branches of theoretical physics. For many years, the seminars at ITEP have been among the main centers of scientific life in Moscow. This volume is a collection of articles by participants of the seminar on mathematical physics that has been held at ITEP since 1983. This is the second such collection; the first was published in the same series, AMS Translations, Series 2, vol. 191.
The papers in the volume are devoted to several mathematical topics that strongly influenced modern theoretical physics. Among these topics are cohomology and representations of infinite Lie algebras and superalgebras, Hitchin and Knizhnik-Zamolodchikov-Bernard systems, and the theory of $D$-modules.
The book is intended for graduate students and research mathematicians working in algebraic geometry, representation theory, and mathematical physics.
Readership
Graduate students and research mathematicians interested in mathematical physics.
Table of Contents
B. Enriquez and V. Rubtsov -- Hecke-Tyurin parametrization of the Hitchin and KZB systems
B. Feigin, A. N. Kirillov, and S. Loktev -- Combinatorics and geometry of higher level Weyl modules
V. V. Fock -- Cosh-Gordon equation and quasi-Fuchsian groups
A. Gerasimov, S. Kharchev, D. Lebedev, and S. Oblezin -- On a class of representations of quantum groups and its applications
A. L. Gorodentsev, A. S. Khoroshkin, and A. N. Rudakov -- On syzygies of highest weight orbits
A. L. Gorodentsev and S. A. Kuleshov -- On finest and modular t-stabilities
D. Kaledin -- Hochschild homology and Gabber's theorem
S. Khoroshkin and S. Pakuliak -- Method of projections of Drinfeld currents
A. Levin and A. Zotov -- On rational and elliptic forms and Painleve VI equation
Y. A. Neretin -- Determinantal point processes and fermionic Fock space
Y. A. Neretin -- On adelic model of boson Fock space
M. Verbitsky -- Hypercomplex manifolds with trivial canonical bundle and their holonomy
Contemporary Mathematics, Volume: 438
2007; 192 pp; softcover
ISBN-10: 0-8218-4246-3
ISBN-13: 978-0-8218-4246-1
Expected publication date is October 4, 2007.
Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science.
Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.
Readership
Graduate students and research mathematicians interested in the application of topological methods of robotics.
Table of Contents
R. Ghrist -- Winding numbers for networks with weak angular data
E. Rodriguez -- The snake charmer's algorithm
B. Tovar, L. Freda, and S. M. LaValle -- Using a robot to learn geometric information from permutations of landmarks
J.-Cl. Hausmann -- Geometric descriptions of polygon and chain spaces
Y. Gur and N. Sochen -- Diffusion over tensor fields via Lie group pde flows: Lagrangian action approach
M. Farber, M. Grant, and S. Yuzvinsky -- Topological complexity of collision free motion planning algorithms in the presence of multiple moving obstacles
M. Farber and M. Grant -- Symmetric motion planning
L. Lechuga and A. Murillo -- Topological complexity of formal spaces
S. Yuzvinsky -- Topological complexity of generic hyperplane complements
A. D. Ames -- Homotopy meaningful hybrid model structures
D. Farley -- Presentations for the cohomology rings of tree braid groups
Y. Gabriely and E. Rimon -- Competitive disconnection detection in on-line mobile robot navigation
Contemporary Mathematics, Volume: 439
2007; 133 pp; softcover
ISBN-10: 0-8218-3740-0
ISBN-13: 978-0-8218-3740-5
Expected publication date is October 5, 2007.
This volume contains research and expository articles based on talks presented at the 2nd Symposium on Analysis and PDEs, held at Purdue University. The Symposium focused on topics related to the theory and applications of nonlinear partial differential equations that are at the forefront of current international research. Papers in this volume provide a comprehensive account of many of the recent developments in the field.
The topics featured in this volume include: kinetic formulations of nonlinear PDEs; recent unique continuation results and their applications; concentrations and constrained Hamilton-Jacobi equations; nonlinear Schrodinger equations; quasiminimal sets for Hausdorff measures; Schrodinger flows into Kahler manifolds; and parabolic obstacle problems with applications to finance.
The clear and concise presentation in many articles makes this volume suitable for both researchers and graduate students.
Readership
Graduate students and research mathematicians interested in partial differential equations.
Table of Contents
L. C. Evans -- Lectures on kinetic formulations of nonlinear PDE
C. E. Kenig -- Some recent applications of unique continuation
G. Barles and B. Perthame -- Concentrations and constrained Hamilton-Jacobi equations arising in adaptive dynamics
J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao -- The energy-critical nonlinear Schrodinger equation in $\mathbb{R}^3$
G. David -- Quasiminimal sets for Hausdorff measures
C. E. Kenig, G. Ponce, and L. Vega -- The initial value problem for the general quasi-linear Schrodinger equation
A. Petrosyan and H. Shahgholian -- Parabolic obstacle problems applied to finance. A free-boundary-regularity approach
History of Mathematics, Volume: 33
2007; 438 pp; hardcover
ISBN-10: 0-8218-3550-5
ISBN-13: 978-0-8218-3550-0
Expected publication date is November 10, 2007.
Gerhard Gentzen (1909-1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called "proof theory" but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today.
The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945.
Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for "German logic", and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smorynski on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Godel; and its development up to the present day. Smorynski explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program.
This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.
Co-published with the London Mathematical Society beginning with Volume 4. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Readership
Mathematicians, scientists, and all others interested in the history of mathematics, the history of mathematical logic, and history in general.
Table of Contents
Early youth and abitur
1928-1938--Weimar Republic and National Socialism in peace. From the beginning of studies to the extension of the unscheduled assistantship for another year with effect from 1 October 1938
1939-1942--From the beginning of the war to dismissal from the Wehrmacht and the wartime habilitation under Helmut Hasse
The fight over "German logic" from 1940 to 1945: A battle between amateurs
Recovery and docent position 1942 to 1944
Arrest, imprisonment, death and Nachlass
Conclusion
Tables of the life of Gerhard Gentzen
Appendix A: Gentzen and geometry, by C. Smorynski
Appendix B: Hilbert's programme, by C. Smorynski
Appendix C: Three lectures, by Gerhard Gentzen
Appendix D: From Hilbert's programme to Gentzen's programme, by Jan von Plato
Bibliography
Index
Graduate Studies in Mathematics, Volume: 86
2007; approx. 636 pp; hardcover
ISBN-10: 0-8218-3667-6
ISBN-13: 978-0-8218-3667-5
Expected publication date is November 16, 2007.
The book combines the features of a graduate-level textbook with those of a research monograph and survey of the recent results on analysis and geometry of differential equations in the real and complex domain. As a graduate textbook, it includes self-contained, sometimes considerably simplified demonstrations of several fundamental results, which previously appeared only in journal publications (desingularization of planar analytic vector fields, existence of analytic separatrices, positive and negative results on the Riemann-Hilbert problem, Ecalle-Voronin and Martinet-Ramis moduli, solution of the Poincare problem on the degree of an algebraic separatrix, etc.). As a research monograph, it explores in a systematic way the algebraic decidability of local classification problems, rigidity of holomorphic foliations, etc. Each section ends with a collection of problems, partly intended to help the reader to gain understanding and experience with the material, partly drafting demonstrations of the more recent results surveyed in the text.
The exposition of the book is mostly geometric, though the algebraic side of the constructions is also prominently featured. On several occasions the reader is introduced to adjacent areas, such as intersection theory for divisors on the projective plane or geometric theory of holomorphic vector bundles with meromorphic connections. The book provides the reader with the principal tools of the modern theory of analytic differential equations and intends to serve as a standard source for references in this area.
Readership
Graduate students and research mathematicians interested in analysis and geometry of differential equations in real and complex domain.
Table of Contents
Normal forms and desingularization
Singular points of planar analytic vector fields
Local and global theory of linear systems
Functional moduli of analytic classification of resonant germs and their applications
Global properties of complex polynomial foliations
Appendix. First aid
Bibliography
Index