Introduction To Heat Potential Theory

Author : N. A. Watson
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 50,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821849989

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Introduction to Heat Potential Theory by N. A. Watson Pdf

This book is the first to be devoted entirely to the potential theory of the heat equation, and thus deals with time dependent potential theory. Its purpose is to give a logical, mathematically precise introduction to a subject where previously many proofs were not written in detail, due to their similarity with those of the potential theory of Laplace's equation. The approach to subtemperatures is a recent one, based on the Poisson integral representation of temperatures on a circular cylinder. Characterizations of subtemperatures in terms of heat balls and modified heat balls are proved, and thermal capacity is studied in detail. The generalized Dirichlet problem on arbitrary open sets is given a treatment that reflects its distinctive nature for an equation of parabolic type. Also included is some new material on caloric measure for arbitrary open sets. Each chapter concludes with bibliographical notes and open questions. The reader should have a good background in the calculus of functions of several variables, in the limiting processes and inequalities of analysis, in measure theory, and in general topology for Chapter 9.

Author : Matthias Brockmann
Publisher : Apprimus Wissenschaftsverlag
Page : 159 pages
File Size : 46,7 Mb
Release : 2016-01-20
Category : Technology & Engineering
ISBN : 9783863594015

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On the Use of Potential Theory for Thermal Modeling in Metal Cutting by Matthias Brockmann Pdf

Evolving temperature distributions during metal cutting are of major significance. Present analytical models are not capable to predict temperature fields to a sufficient degree. This lack of model validity is caused by the limited mathematical approaches. The present thesis deals with the development of methodologies for thermal modeling based on a class of complex functions termed potential functions. This approach has never been used before for metal cutting applications.

Author : Gregory Berkolaiko,Peter Kuchment
Publisher : American Mathematical Soc.
Page : 291 pages
File Size : 50,5 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821892114

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Introduction to Quantum Graphs by Gregory Berkolaiko,Peter Kuchment Pdf

A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Author : Charlotte Hardouin,Jacques Sauloy,Michael F. Singer
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 41,7 Mb
Release : 2016-04-27
Category : Difference and functional equations -- Difference equations -- Linear equations
ISBN : 9781470426552

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Galois Theories of Linear Difference Equations: An Introduction by Charlotte Hardouin,Jacques Sauloy,Michael F. Singer Pdf

This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

Author : Grégory Berhuy,Frédérique Oggier
Publisher : American Mathematical Soc.
Page : 288 pages
File Size : 44,7 Mb
Release : 2013-07-05
Category : Mathematics
ISBN : 9780821849378

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An Introduction to Central Simple Algebras and Their Applications to Wireless Communication by Grégory Berhuy,Frédérique Oggier Pdf

Central simple algebras arise naturally in many areas of mathematics. They are closely connected with ring theory, but are also important in representation theory, algebraic geometry and number theory. Recently, surprising applications of the theory of central simple algebras have arisen in the context of coding for wireless communication. The exposition in the book takes advantage of this serendipity, presenting an introduction to the theory of central simple algebras intertwined with its applications to coding theory. Many results or constructions from the standard theory are presented in classical form, but with a focus on explicit techniques and examples, often from coding theory. Topics covered include quaternion algebras, splitting fields, the Skolem-Noether Theorem, the Brauer group, crossed products, cyclic algebras and algebras with a unitary involution. Code constructions give the opportunity for many examples and explicit computations. This book provides an introduction to the theory of central algebras accessible to graduate students, while also presenting topics in coding theory for wireless communication for a mathematical audience. It is also suitable for coding theorists interested in learning how division algebras may be useful for coding in wireless communication.

Author : Sylvan Burgstahler
Publisher : Unknown
Page : 196 pages
File Size : 51,7 Mb
Release : 1963
Category : Heat
ISBN : MINN:31951T004029489

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Contributions to the Study of Heat Conduction in Composite Systems and to Heat Potential Theory by Sylvan Burgstahler Pdf

Author : Philippe Biane,Luc Bouten,Fabio Cipriani,Norio Konno,Quanhua Xu
Publisher : Springer
Page : 464 pages
File Size : 49,6 Mb
Release : 2008-10-16
Category : Mathematics
ISBN : 9783540693659

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Quantum Potential Theory by Philippe Biane,Luc Bouten,Fabio Cipriani,Norio Konno,Quanhua Xu Pdf

This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.

Author : Nassif Ghoussoub,Amir Moradifam
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 54,7 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9780821891520

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Functional Inequalities: New Perspectives and New Applications by Nassif Ghoussoub,Amir Moradifam Pdf

"The book describes how functional inequalities are often manifestations of natural mathematical structures and physical phenomena, and how a few general principles validate large classes of analytic/geometric inequalities, old and new. This point of view leads to "systematic" approaches for proving the most basic inequalities, but also for improving them, and for devising new ones--sometimes at will and often on demand. These general principles also offer novel ways for estimating best constants and for deciding whether these are attained in appropriate function spaces. As such, improvements of Hardy and Hardy-Rellich type inequalities involving radially symmetric weights are variational manifestations of Sturm's theory on the oscillatory behavior of certain ordinary differential equations. On the other hand, most geometric inequalities, including those of Sobolev and Log-Sobolev type, are simply expressions of the convexity of certain free energy functionals along the geodesics on the Wasserstein manifold of probability measures equipped with the optimal mass transport metric. Caffarelli-Kohn-Nirenberg and Hardy-Rellich-Sobolev type inequalities are then obtained by interpolating the above two classes of inequalities via the classical ones of Hölder. The subtle Moser-Onofri-Aubin inequalities on the two-dimensional sphere are connected to Liouville type theorems for planar mean field equations."--Publisher's website.

Author : Horatio Scott Carslaw
Publisher : Unknown
Page : 298 pages
File Size : 52,9 Mb
Release : 1945
Category : History
ISBN : STANFORD:36105030172444

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Introduction to the Mathematical Theory of the Conduction of Heat in Solids by Horatio Scott Carslaw Pdf

Introduction to the Mathematical Theory of the Conduction of Heat in Solids by Horatio Scott Carslaw, first published in 1945, is a rare manuscript, the original residing in one of the great libraries of the world. This book is a reproduction of that original, which has been scanned and cleaned by state-of-the-art publishing tools for better readability and enhanced appreciation. Restoration Editors' mission is to bring long out of print manuscripts back to life. Some smudges, annotations or unclear text may still exist, due to permanent damage to the original work. We believe the literary significance of the text justifies offering this reproduction, allowing a new generation to appreciate it.

Author : Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov
Publisher : American Mathematical Soc.
Page : 194 pages
File Size : 40,9 Mb
Release : 2014-11-19
Category : Mathematics
ISBN : 9781470416973

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Foundations of Free Noncommutative Function Theory by Dmitry S. Kaliuzhnyi-Verbovetskyi,Victor Vinnikov Pdf

In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 43,8 Mb
Release : 2017-05-17
Category : Electronic
ISBN : 9781470434434

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Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot Pdf

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Author : Gershon Kresin,V. G. Maz_i_a_
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 42,5 Mb
Release : 2012-08-15
Category : Mathematics
ISBN : 9780821889817

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Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems by Gershon Kresin,V. G. Maz_i_a_ Pdf

The main goal of this book is to present results pertaining to various versions of the maximum principle for elliptic and parabolic systems of arbitrary order. In particular, the authors present necessary and sufficient conditions for validity of the classical maximum modulus principles for systems of second order and obtain sharp constants in inequalities of Miranda-Agmon type and in many other inequalities of a similar nature. Somewhat related to this topic are explicit formulas for the norms and the essential norms of boundary integral operators. The proofs are based on a unified approach using, on one hand, representations of the norms of matrix-valued integral operators whose target spaces are linear and finite dimensional, and, on the other hand, on solving certain finite dimensional optimization problems. This book reflects results obtained by the authors, and can be useful to research mathematicians and graduate students interested in partial differential equations.

Author : Alberto Elduque,Mikhail Kochetov
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 50,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821898468

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Gradings on Simple Lie Algebras by Alberto Elduque,Mikhail Kochetov Pdf

This monograph is a self-contained exposition of the classification of gradings by arbitrary groups on classical simple Lie algebras over algebraically closed fields of characteristic not equal to 2 as well as on some non-classical simple Lie algebras in positive characteristic. Other important algebras also enter the stage: matrix algebras, the octonions, and the Albert algebra. Most of the presented results are recent and have not yet appeared in book form.

Author : David Lannes
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 47,7 Mb
Release : 2013-05-08
Category : Mathematics
ISBN : 9780821894705

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The Water Waves Problem by David Lannes Pdf

This monograph provides a comprehensive and self-contained study on the theory of water waves equations, a research area that has been very active in recent years. The vast literature devoted to the study of water waves offers numerous asymptotic models.

Author : J. L. Doob
Publisher : Springer Science & Business Media
Page : 865 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461252085

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Classical Potential Theory and Its Probabilistic Counterpart by J. L. Doob Pdf

Potential theory and certain aspects of probability theory are intimately related, perhaps most obviously in that the transition function determining a Markov process can be used to define the Green function of a potential theory. Thus it is possible to define and develop many potential theoretic concepts probabilistically, a procedure potential theorists observe withjaun diced eyes in view of the fact that now as in the past their subject provides the motivation for much of Markov process theory. However that may be it is clear that certain concepts in potential theory correspond closely to concepts in probability theory, specifically to concepts in martingale theory. For example, superharmonic functions correspond to supermartingales. More specifically: the Fatou type boundary limit theorems in potential theory correspond to supermartingale convergence theorems; the limit properties of monotone sequences of superharmonic functions correspond surprisingly closely to limit properties of monotone sequences of super martingales; certain positive superharmonic functions [supermartingales] are called "potentials," have associated measures in their respective theories and are subject to domination principles (inequalities) involving the supports of those measures; in each theory there is a reduction operation whose properties are the same in the two theories and these reductions induce sweeping (balayage) of the measures associated with potentials, and so on.