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51 produkter
51 produkter
Del 225 - London Mathematical Society Lecture Note Series
A Mathematical Introduction to String Theory
Variational Problems, Geometric and Probabilistic Methods
Häftad, Engelska, 1997
753 kr
Skickas inom 7-10 vardagar
Classical string theory is concerned with the propagation of classical 1-dimensional curves 'strings', and the theory has connections to the calculus of variations, minimal surfaces and harmonic maps. The quantization of string theory gives rise to problems in different areas, according to the method used. The representation theory of Lie, Kac-Moody and Virasoro algebras have been used for such quantization. In this lecture note the authors give an introduction to certain global analytic and probabilistic aspects of string theory. It is their intention to bring together, and make explicit the necessary mathematical tools. Researchers with an interest in string theory, in either mathematics or theoretical physics, will find this a stimulating volume.
1 278 kr
Skickas inom 11-20 vardagar
This volume and ""Stochastic Processes, Physics and Geometry: New Interplays II"" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, 'Infinite Dimensional (Stochastic) Analysis and Quantum Physics', was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry.The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and non commutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers.
641 kr
Skickas inom 10-15 vardagar
This textbook is intended for students who wish to obtain an introduction to the theory of partial di?erential equations (PDEs, for short), in particular, those of elliptic type. Thus, it does not o?er a comprehensive overview of the whole ?eld of PDEs, but tries to lead the reader to the most important methods and central results in the case of elliptic PDEs. The guiding qu- tion is how one can ?nd a solution of such a PDE. Such a solution will, of course, depend on given constraints and, in turn, if the constraints are of the appropriate type, be uniquely determined by them. We shall pursue a number of strategies for ?nding a solution of a PDE; they can be informally characterized as follows: (0) Write down an explicit formula for the solution in terms of the given data (constraints). This may seem like the best and most natural approach, but this is possible only in rather particular and special cases. Also, such a formula may be rather complicated, so that it is not very helpful for detecting qualitative properties of a solution. Therefore, mathematical analysis has developed other, more powerful, approaches. (1) Solve a sequence of auxiliary problems that approximate the given one, and show that their solutions converge to a solution of that original pr- lem. Di?erential equations are posed in spaces of functions, and those spaces are of in?nite dimension.
747 kr
Skickas inom 10-15 vardagar
Mathematical models can be used to meet many of the challenges and opportunities offered by modern biology. The description of biological phenomena requires a range of mathematical theories. This is the case particularly for the emerging field of systems biology. Mathematical Methods in Biology and Neurobiology introduces and develops these mathematical structures and methods in a systematic manner. It studies:• discrete structures and graph theory • stochastic processes• dynamical systems and partial differential equations • optimization and the calculus of variations.The biological applications range from molecular to evolutionary and ecological levels, for example:• cellular reaction kinetics and gene regulation• biological pattern formation and chemotaxis• the biophysics and dynamics of neurons • the coding of information in neuronal systems• phylogenetic tree reconstruction• branching processes and population genetics• optimal resource allocation• sexual recombination • the interaction of species.Written by one of the most experienced and successful authors of advanced mathematical textbooks, this book stands apart for the wide range of mathematical tools that are featured. It will be useful for graduate students and researchers in mathematics and physics that want a comprehensive overview and a working knowledge of the mathematical tools that can be applied in biology. It will also be useful for biologists with some mathematical background that want to learn more about the mathematical methods available to deal with biological structures and data.
958 kr
Skickas inom 10-15 vardagar
This book offers an ideal graduate-level introduction to the theory of partial differential equations. The first part of the book describes the basic mathematical problems and structures associated with elliptic, parabolic, and hyperbolic partial differential equations, and explores the connections between these fundamental types. Aspects of Brownian motion or pattern formation processes are also presented. The second part focuses on existence schemes and develops estimates for solutions of elliptic equations, such as Sobolev space theory, weak and strong solutions, Schauder estimates, and Moser iteration. In particular, the reader will learn the basic techniques underlying current research in elliptic partial differential equations. This revised and expanded third edition is enhanced with many additional examples that will help motivate the reader. New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more. Also, the new edition contains additional material on systems of elliptic partial differential equations, and it explains in more detail how the Harnack inequality can be used for the regularity of solutions.
694 kr
Skickas inom 10-15 vardagar
New features include a reorganized and extended chapter on hyperbolic equations, as well as a new chapter on the relations between different types of partial differential equations, including first-order hyperbolic systems, Langevin and Fokker-Planck equations, viscosity solutions for elliptic PDEs, and much more.
1 064 kr
Skickas inom 10-15 vardagar
After over a century of research, we still do not understand the principle by which a stimulus, such as an odour or a sound, is represented by distributed neural ensembles within the brain; by which an individual is developed by the control of gene networks. While past studies have made detailed analysis of response profiles of single cells and the properties of a single gene in isolation, such techniques and approaches cannot easily address holistic issues of how large ensembles of neurons and genes can integrate information both spatially and temporally. There is little doubt that much of the info processing power of the brain or a gene network resides in the activities of co-operating and competing networks of neurons and genes and that if we unlock the principles whereby info is encoded and processed within these networks as a whole, rather than within single neurones or genes in isolation, we may be able to understand how the brain or gene network works. Our book will contribute to the development of such a study.
1 064 kr
Skickas inom 10-15 vardagar
After over a century of research, we still do not understand the principle by which a stimulus, such as an odour or a sound, is represented by distributed neural ensembles within the brain; by which an individual is developed by the control of gene networks. While past studies have made detailed analysis of response profiles of single cells and the properties of a single gene in isolation, such techniques and approaches cannot easily address holistic issues of how large ensembles of neurons and genes can integrate information both spatially and temporally. There is little doubt that much of the info processing power of the brain or a gene network resides in the activities of co-operating and competing networks of neurons and genes and that if we unlock the principles whereby info is encoded and processed within these networks as a whole, rather than within single neurones or genes in isolation, we may be able to understand how the brain or gene network works. Our book will contribute to the development of such a study.
1 064 kr
Skickas inom 10-15 vardagar
This book not only provides a positive answer to the question, it provides the formal models and available data to model chemical knowledge as a complex dynamical system based on the mutual interaction of the social, semiotic and material systems of chemistry.
Del 2 - Mathematics of Data
Mathematical Principles of Topological and Geometric Data Analysis
Inbunden, Engelska, 2023
758 kr
Skickas
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with somekind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
631 kr
Skickas inom 5-8 vardagar
Del 2 - Mathematics of Data
Mathematical Principles of Topological and Geometric Data Analysis
Häftad, Engelska, 2024
588 kr
Skickas inom 10-15 vardagar
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information.In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with somekind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately.Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use.
1 592 kr
Skickas inom 10-15 vardagar
This book presents William Clifford’s English translation of Bernhard Riemann’s seminal text, accompanied by detailed mathematical, historical, and philosophical commentary. It explores Riemann’s revolutionary ideas on space, placing them within the broader framework developed by later thinkers such as Helmholtz, Ricci, Weyl, and Einstein. A historical introduction situates Riemann’s work in its 19th-century context, while subsequent chapters trace the evolution of the concept of space across philosophy, physics, and mathematics, and examine its enduring influence up to modern research.The second edition includes expanded mathematical commentary, a new section on metric geometry and machine learning, a systematic bibliography, and numerous updates throughout.Appealing to mathematicians, historians, and readers with an interest in physics or philosophy, this book provides a comprehensive perspective on Riemann’s groundbreaking contributions and their lasting impact.
Del 3 - Mathematics of Data
Data Visualization with Category Theory and Geometry
With a Critical Analysis and Refinement of UMAP
Inbunden, Engelska, 2025
533 kr
Skickas inom 5-8 vardagar
This open access book provides a robust exposition of the mathematical foundations of data representation, focusing on two essential pillars of dimensionality reduction methods, namely geometry in general and Riemannian geometry in particular, and category theory.Presenting a list of examples consisting of both geometric objects and empirical datasets, this book provides insights into the different effects of dimensionality reduction techniques on data representation and visualization, with the aim of guiding the reader in understanding the expected results specific to each method in such scenarios.As a showcase, the dimensionality reduction method of “Uniform Manifold Approximation and Projection” (UMAP) has been used in this book, as it is built on theoretical foundations from all the areas we want to highlight here. Thus, this book also aims to systematically present the details of constructing a metric representation of a locally distorted metric space, which is essentially the problem that UMAP is trying to address, from a more general perspective. Explaining how UMAP fits into this broader framework, while critically evaluating the underlying ideas, this book finally introduces an alternative algorithm to UMAP. This algorithm, called IsUMap, retains many of the positive features of UMAP, while improving on some of its drawbacks.
Nonlinear Methods in Riemannian and Kählerian Geometry
Delivered at the German Mathematical Society Seminar in Düsseldorf in June, 1986
Häftad, Engelska, 2013
535 kr
Skickas inom 10-15 vardagar
In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Düsseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature Ieads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second ordernonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more pro~inent röle in geometry. Let us Iist some of the most important ones: - harmonic maps between Riemannian and Kählerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kähler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can Iead to very signifi cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones.
852 kr
Skickas inom 10-15 vardagar
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used:· simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure· by itself as a first introduction to abstract mathematics· together with existing textbooks, to put their results into a more general perspective· to gain a new and hopefully deeper perspective after having studied such textbooksMathematical Concepts has a broader scope and is less detailed than standard mathematical textbooks so that the reader can readily grasp the essential concepts and ideas for individual needs. It will be suitable for advanced mathematicians, postgraduate students and for scientists from other fields with some background in formal reasoning.
Information Geometry and Population Genetics
The Mathematical Structure of the Wright-Fisher Model
Inbunden, Engelska, 2017
1 422 kr
Skickas inom 10-15 vardagar
The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner.
Del 64 - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Information Geometry
Inbunden, Engelska, 2017
1 697 kr
Skickas inom 10-15 vardagar
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.
1 064 kr
Skickas inom 10-15 vardagar
This established reference work continues to introduce its readers to some of the hottest topics in contemporary mathematical research. This sixth edition includes, among other new additions, a systematic treatment of eigenvalues of Riemannian manifolds.
970 kr
Skickas inom 5-8 vardagar
This book presents William Clifford’s English translation of Bernhard Riemann’s classic text together with detailed mathematical, historical and philosophical commentary.
Information Geometry and Population Genetics
The Mathematical Structure of the Wright-Fisher Model
Häftad, Engelska, 2018
1 205 kr
Skickas inom 5-8 vardagar
The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner.
Del 64 - Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Information Geometry
Häftad, Engelska, 2018
1 275 kr
Skickas inom 10-15 vardagar
The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory.
Del 1062 - Lecture Notes in Mathematics
Harmonic Maps Between Surfaces
(With a Special Chapter on Conformal Mappings)
Häftad, Engelska, 1984
271 kr
Skickas inom 10-15 vardagar
641 kr
Skickas inom 10-15 vardagar
Our aim is to introduce, explain, and discuss the fundamental problems, ideas, concepts, results, and methods of the theory of dynamical systems and to show how they can be used in speci?c examples. We do not intend to give a comprehensive overview of the present state of research in the theory of dynamical systems, nor a detailed historical account of its development. We try to explain the important results, often neglecting technical re?nements 1 and, usually, we do not provide proofs. One of the basic questions in studying dynamical systems, i.e. systems that evolve in time, is the construction of invariants that allow us to classify qualitative types of dynamical evolution, to distinguish between qualitatively di?erent dynamics, and to studytransitions between di?erent types. Itis also important to ?nd out when a certain dynamic behavior is stable under small perturbations, as well as to understand the various scenarios of instability. Finally, an essential aspect of a dynamic evolution is the transformation of some given initial state into some ?nal or asymptotic state as time proceeds. Thetemporalevolutionofadynamicalsystemmaybecontinuousordiscrete, butitturnsoutthatmanyoftheconceptstobeintroducedareusefulineither case.
799 kr
Skickas inom 10-15 vardagar
In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while.
799 kr
Skickas inom 10-15 vardagar
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps. For this new edition, the author has expanded and rewritten several sections to include additional material and to improve the presentation.
501 kr
Skickas inom 10-15 vardagar
Dieses Lehrbuch bietet eine Einführung in die moderne Theorie der partiellen Differentialgleichungen. Der Leser wird zu den wichtigen Methoden und den wesentlichen Aussagen in diesem Bereich hingeführt, wobei der Schwerpunkt auf den elliptischen partiellen Differentialgleichungen liegt. Ausgehend von der Laplace-Gleichung (harmonische Funktionen) entwickelt der Autor systematische Techniken, die auch auf größere Klassen von Differentialgleichungen, und hier insbesondere auch auf nichtlineare Differentialgleichungen, anwendbar sind. Zur Veranschaulichung wurden zahlreiche Übungsaufgaben aufgenommen. Das Buch richtet sich vor allem an Studenten der Mathematik im Hauptstudium, kann aber für interessierte Studenten auch gegebenenfalls schon ab dem dritten Semester verwendet werden.
747 kr
Skickas inom 10-15 vardagar
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
599 kr
Skickas inom 10-15 vardagar
Das vorliegende Lehrbuch bietet eine moderne Einführung in die Differenzialgeometrie - etwa im Umfang einer einsemestrigen Vorlesung. Zunächst behandelt es die Geometrie von Flächen im Raum. Viele Beispiele schulen Leser in geometrischer Anschauung, deren wichtigste Klasse die Minimalflächen bilden. Zu ihrem Studium entwickeln die Autoren analytische Methoden und lösen in diesem Zusammenhang das Plateausche Problem. Es besteht darin, eine Minimalfläche mit vorgegebener Berandung zu finden. Als Beispiel einer globalen Aussage der Differenzialgeometrie beweisen sie den Bernsteinschen Satz. Weitere Kapitel behandeln die innere Geometrie von Flächen einschließlich des Satzes von Gauss-Bonnet, und stellen die hyperbolische Geometrie ausführlich dar. Die Autoren verknüpfen geometrische Konstruktionen und analytische Methoden und folgen damit einem zentralen Trend der modernen mathematischen Forschung. Verschiedene geistesgeschichtliche Bemerkungen runden den Text ab. Die Neuauflage wurde überarbeitet und aktualisiert.Hinweise und Errata auf Webseite des Autors: https://myweb.rz.uni-augsburg.de/~eschenbu/
747 kr
Skickas inom 10-15 vardagar
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry.