Tame Geometry With Application In Smooth Analysis

Author : Yosef Yomdin,Georges Comte
Publisher : Springer
Page : 190 pages
File Size : 46,9 Mb
Release : 2004-02-10
Category : Mathematics
ISBN : 9783540409601

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Tame Geometry with Application in Smooth Analysis by Yosef Yomdin,Georges Comte Pdf

The Morse-Sard theorem is a rather subtle result and the interplay between the high-order analytic structure of the mappings involved and their geometry rarely becomes apparent. The main reason is that the classical Morse-Sard theorem is basically qualitative. This volume gives a proof and also an "explanation" of the quantitative Morse-Sard theorem and related results, beginning with the study of polynomial (or tame) mappings. The quantitative questions, answered by a combination of the methods of real semialgebraic and tame geometry and integral geometry, turn out to be nontrivial and highly productive. The important advantage of this approach is that it allows the separation of the role of high differentiability and that of algebraic geometry in a smooth setting: all the geometrically relevant phenomena appear already for polynomial mappings. The geometric properties obtained are "stable with respect to approximation", and can be imposed on smooth functions via polynomial approximation.

Author : Yosef Yomdin,Georges Comte
Publisher : Unknown
Page : 200 pages
File Size : 50,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662214482

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Tame Geometry with Application in Smooth Analysis by Yosef Yomdin,Georges Comte Pdf

Author : Anonim
Publisher : Unknown
Page : 0 pages
File Size : 45,8 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:723062403

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Tame Geometry with Application in Smooth Analysis by Anonim Pdf

Author : Jianjun Paul Tian
Publisher : Springer Science & Business Media
Page : 136 pages
File Size : 46,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9783540742838

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Evolution Algebras and Their Applications by Jianjun Paul Tian Pdf

Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

Author : Vladimir I. Gurariy,Wolfgang Lusky
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 52,8 Mb
Release : 2005-11-03
Category : Mathematics
ISBN : 3540288007

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Geometry of Müntz Spaces and Related Questions by Vladimir I. Gurariy,Wolfgang Lusky Pdf

Starting point and motivation for this volume is the Müntz theorem. In the first part of the book the Banach spaces notions are introduced and are later on applied for Müntz spaces. They include the opening and inclination of subspaces, bases and boundedapproximation properties and versions of universality.

Author : Thomas Schuster
Publisher : Springer
Page : 202 pages
File Size : 43,9 Mb
Release : 2007-04-26
Category : Mathematics
ISBN : 9783540712275

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The Method of Approximate Inverse: Theory and Applications by Thomas Schuster Pdf

This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.

Author : Jin Ma,Jiongmin Yong
Publisher : Springer
Page : 278 pages
File Size : 46,5 Mb
Release : 2007-04-24
Category : Mathematics
ISBN : 9783540488316

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Forward-Backward Stochastic Differential Equations and their Applications by Jin Ma,Jiongmin Yong Pdf

This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.

Author : Charles Chidume
Publisher : Springer
Page : 326 pages
File Size : 49,5 Mb
Release : 2008-12-21
Category : Mathematics
ISBN : 9781848821903

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Geometric Properties of Banach Spaces and Nonlinear Iterations by Charles Chidume Pdf

The contents of this monograph fall within the general area of nonlinear functional analysis and applications. We focus on an important topic within this area: geometric properties of Banach spaces and nonlinear iterations, a topic of intensive research e?orts, especially within the past 30 years, or so. In this theory, some geometric properties of Banach spaces play a crucial role. In the ?rst part of the monograph, we expose these geometric properties most of which are well known. As is well known, among all in?nite dim- sional Banach spaces, Hilbert spaces have the nicest geometric properties. The availability of the inner product, the fact that the proximity map or nearest point map of a real Hilbert space H onto a closed convex subset K of H is Lipschitzian with constant 1, and the following two identities 2 2 2 ||x+y|| =||x|| +2 x,y +||y|| , (?) 2 2 2 2 ||?x+(1??)y|| = ?||x|| +(1??)||y|| ??(1??)||x?y|| , (??) which hold for all x,y? H, are some of the geometric properties that char- terize inner product spaces and also make certain problems posed in Hilbert spaces more manageable than those in general Banach spaces. However, as has been rightly observed by M. Hazewinkel, “... many, and probably most, mathematical objects and models do not naturally live in Hilbert spaces”. Consequently,toextendsomeoftheHilbertspacetechniquestomoregeneral Banach spaces, analogues of the identities (?) and (??) have to be developed.

Author : Ben Andrews,Christopher Hopper
Publisher : Springer Science & Business Media
Page : 306 pages
File Size : 49,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9783642162855

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The Ricci Flow in Riemannian Geometry by Ben Andrews,Christopher Hopper Pdf

This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem.

Author : Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul Vojta
Publisher : Springer
Page : 251 pages
File Size : 41,8 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9783642159459

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Arithmetic Geometry by Jean-Louis Colliot-Thélène,Peter Swinnerton-Dyer,Paul Vojta Pdf

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

Author : Min Qian,Jian-Sheng Xie,Shu Zhu
Publisher : Springer
Page : 292 pages
File Size : 41,8 Mb
Release : 2009-07-07
Category : Mathematics
ISBN : 9783642019548

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Smooth Ergodic Theory for Endomorphisms by Min Qian,Jian-Sheng Xie,Shu Zhu Pdf

Ideal for researchers and graduate students, this volume sets out a general smooth ergodic theory for deterministic dynamical systems generated by non-invertible endomorphisms. Its focus is on the relations between entropy, Lyapunov exponents and dimensions.

Author : Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano
Publisher : Springer Science & Business Media
Page : 228 pages
File Size : 44,6 Mb
Release : 2008-04-18
Category : Technology & Engineering
ISBN : 9783540782766

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Mathematical Models of Granular Matter by Gianfranco Capriz,Pasquale Giovine,Paolo Maria Mariano Pdf

Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Author : Anonim
Publisher : Springer Science & Business Media
Page : 263 pages
File Size : 49,7 Mb
Release : 2021
Category : Electronic
ISBN : 9783540693918

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Information Geometry by Anonim Pdf

Author : Avner Friedman
Publisher : Springer
Page : 246 pages
File Size : 42,9 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9783540324157

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Tutorials in Mathematical Biosciences III by Avner Friedman Pdf

This volume introduces some basic mathematical models for cell cycle, proliferation, cancer, and cancer therapy. Chapter 1 gives an overview of the modeling of the cell division cycle. Chapter 2 describes how tumor secretes growth factors to form new blood vessels in its vicinity, which provide it with nutrients it needs in order to grow. Chapter 3 explores the process that enables the tumor to invade the neighboring tissue. Chapter 4 models the interaction between a tumor and the immune system. Chapter 5 is concerned with chemotherapy; it uses concepts from control theory to minimize obstacles arising from drug resistance and from cell cycle dynamics. Finally, Chapter 6 reviews mathematical results for various cancer models.

Author : Roger Mansuy,Marc Yor
Publisher : Springer
Page : 158 pages
File Size : 54,9 Mb
Release : 2006-07-25
Category : Mathematics
ISBN : 9783540324164

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Random Times and Enlargements of Filtrations in a Brownian Setting by Roger Mansuy,Marc Yor Pdf

In November 2004, M. Yor and R. Mansuy jointly gave six lectures at Columbia University, New York. These notes follow the contents of that course, covering expansion of filtration formulae; BDG inequalities up to any random time; martingales that vanish on the zero set of Brownian motion; the Azéma-Emery martingales and chaos representation; the filtration of truncated Brownian motion; attempts to characterize the Brownian filtration. The book accordingly sets out to acquaint its readers with the theory and main examples of enlargements of filtrations, of either the initial or the progressive kind. It is accessible to researchers and graduate students working in stochastic calculus and excursion theory, and more broadly to mathematicians acquainted with the basics of Brownian motion.