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Author: Jun Kigami
Publisher: Cambridge University Press
ISBN: 0521793211
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Author: Jun Kigami
Publisher: Cambridge University Press
ISBN: 0521793211
Category : Mathematics
Languages : en
Pages : 238
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Book Description
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
Author: Christoph Bandt
Publisher: Birkhäuser
ISBN: 3034883803
Category : Mathematics
Languages : en
Pages : 286
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Book Description
A collection of contributions by outstanding mathematicians, highlighting the principal directions of research on the combination of fractal geometry and stochastic methods. Clear expositions introduce the most recent results and problems on these subjects and give an overview of their historical development.
Author: David Carfi
Publisher: American Mathematical Soc.
ISBN: 0821891472
Category : Mathematics
Languages : en
Pages : 410
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Book Description
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
Author: Martin T. Barlow
Publisher: Springer
ISBN: 3540692282
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This volume contains lectures given at the Saint-Flour Summer School of Probability Theory during the period 10th - 26th July, 1995. These lectures are at a postgraduate research level. They are works of reference in their domain.
Author: Catherine Bandle
Publisher: Springer Science & Business Media
ISBN: 3764373849
Category : Mathematics
Languages : en
Pages : 466
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Book Description
Haim Brezis has made significant contributions in the fields of partial differential equations and functional analysis, and this volume collects contributions by his former students and collaborators in honor of his 60th anniversary at a conference in Gaeta. It presents new developments in the theory of partial differential equations with emphasis on elliptic and parabolic problems.
Author: Cinlar
Publisher: Springer Science & Business Media
ISBN: 1461203392
Category : Mathematics
Languages : en
Pages : 278
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Book Description
The 1992 Seminar on Stochastic Processes was held at the Univer sity of Washington from March 26 to March 28, 1992. This was the twelfth in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, University of Florida, University of Virginia, University of California, San Diego, University of British Columbia and University of California, Los An geles. Following the successful format of previous years, there were five invited lectures, delivered by R. Adler, R. Banuelos, J. Pitman, S. J. Taylor and R. Williams, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants cre ated a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1992 Seminar was made possible through the support of the National Science Foundation, the National Security Agency, the Institute of Mathematical Statistics and the University of Washing ton. We extend our thanks to them and to the publisher Birkhauser Boston for their support and encouragement. Richard F. Bass Krzysztof Burdzy Seattle, 1992 SUPERPROCESS LOCAL AND INTERSECTION LOCAL TIMES AND THEIR CORRESPONDING PARTICLE PICTURES Robert J.
Author: Peter D. Lax
Publisher: American Mathematical Soc.
ISBN: 0821806572
Category : Mathematics
Languages : en
Pages : 407
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Book Description
Lax and Nirenberg are two of the most distinguished mathematicians of our times. Their work on partial differential equations (PDEs) over the last half-century has dramatically advanced the subject and has profoundly influenced the course of mathematics. A huge part of the development in PDEs during this period has either been through their work, motivated by it or achieved by their postdocs and students. A large number of mathematicians honored these two exceptional scientists in a week-long conference in Venice (June 1996) on the occasion of their 70th birthdays. This volume contains the proceedings of the conference, which focused on the modern theory of nonlinear PDEs and their applications. Among the topics treated are turbulence, kinetic models of a rarefied gas, vortex filaments, dispersive waves, singular limits and blow-up solutions, conservation laws, Hamiltonian systems and others. The conference served as a forum for the dissemination of new scientific ideas and discoveries and enhanced scientific communication by bringing together such a large number of scientists working in related fields. THe event allowed the international mathematics community to honor two of its outstanding members.
Author: Leif O. Arkeryd
Publisher: Springer Science & Business Media
ISBN: 9401155445
Category : Mathematics
Languages : en
Pages : 374
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Book Description
1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im portant field of research in their own right. The current methods of NSA now greatly extend Robinson's original work with infinitesimals. However, while the range of applications is broad, certain fundamental themes re cur. The nonstandard framework allows many informal ideas (that could loosely be described as idealisation) to be made precise and tractable. For example, the real line can (in this framework) be treated simultaneously as both a continuum and a discrete set of points; and a similar dual ap proach can be used to link the notions infinite and finite, rough and smooth. This has provided some powerful tools for the research mathematician - for example Loeb measure spaces in stochastic analysis and its applications, and nonstandard hulls in Banach spaces. The achievements of NSA can be summarised under the headings (i) explanation - giving fresh insight or new approaches to established theories; (ii) discovery - leading to new results in many fields; (iii) invention - providing new, rich structures that are useful in modelling and representation, as well as being of interest in their own right. The aim of the present volume is to make the power and range of appli cability of NSA more widely known and available to research mathemati cians.
Author: Christoph Bandt
Publisher: Birkhäuser
ISBN: 3319186604
Category : Mathematics
Languages : en
Pages : 339
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Book Description
This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.
Author: Michele Matzeu
Publisher: Springer Science & Business Media
ISBN: 146124126X
Category : Mathematics
Languages : en
Pages : 609
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Book Description
The main purpose of the present volume is to give a survey of some of the most significant achievements obtained by topological methods in nonlin ear analysis during the last three decades. It is intended, at least partly, as a continuation of Topological Nonlinear Analysis: Degree, Singularity and Varia tions, published in 1995. The survey articles presented are concerned with three main streams of research, that is topological degree, singularity theory and variational methods, They reflect the personal taste of the authors, all of them well known and distinguished specialists. A common feature of these articles is to start with a historical introduction and conclude with recent results, giving a dynamic picture of the state of the art on these topics. Let us mention the fact that most of the materials in this book were pre sented by the authors at the "Second Topological Analysis Workshop on Degree, Singularity and Variations: Developments of the Last 25 Years," held in June 1995 at Villa Tuscolana, Frascati, near Rome. Michele Matzeu Alfonso Vignoli Editors Topological Nonlinear Analysis II Degree, Singularity and Variations Classical Solutions for a Perturbed N-Body System Gianfausto Dell 'A ntonio O. Introduction In this review I shall consider the perturbed N-body system, i.e., a system composed of N point bodies of masses ml, ... mN, described in cartesian co ordinates by the system of equations (0.1) where f) V'k,m == -£l--' m = 1, 2, 3.
