الصفحة 4
الصفحة 4
Lectures on Symplectic Geometry
Provides a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.
Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.
Jamming, Yielding, and Irreversible Deformation in Condensed Matter
This collection ot ten tutorial reviews by leading researchers in the field introduces and renews recent advances on irreversible deformation phenomena in solid state and soft condensed matter physics. The focus in applications is on amorphous materials, crystalline solids under stress and more generally, elastic manifolds driven by external processes. This book addresses in particular nonspecialists and graduate students wishing to enter the field.
Comprehensive mathematics for computer scientists 1 : Sets and numbers, graphs and algebra, logic and machines, linear geometry
This two-volume textbook Comprehensive Mathematics for Computer Scientists is a self-contained comprehensive presentation of mathematics including sets, numbers, graphs, algebra, logic, grammars, machines, linear geometry, calculus, ODEs, and special themes such as neural networks, Fourier theory, wavelets, numerical issues, statistics, categories, and manifolds. The concept framework is streamlined but defining and proving virtually everything.
Complex, Contact and Symmetric Manifolds : In Honor of L. Vanhecke
This volume contains introductory and contextual material, describe recent developments and research trends in spectral geometry, the theory of geodesics and curvature, contact and symplectic geometry, complex geometry, algebraic topology, homogeneous and symmetric spaces, and various applications of partial differential equations and differential systems to geometry. One of the key strengths of these articles is their appeal to non-specialists, as well as researchers and differential geometers.
Complex Nonlinearity : Chaos, Phase Transitions, Topology Change and Path Integrals
The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism.
Complex Geometry : An Introduction
Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, both for mathematicians and theoretical physicists. The book contains detailed accounts of the basic concepts and the many exercises illustrate the theory. Appendices to various chapters allow an outlook to recent research directions.
Complex Analysis with Applications to Number Theory
The book discusses major topics in complex analysis with applications to number theory.It 's including the theory of several finitely and infinitely complex variables, hyperbolic geometry, two- and three-manifolds, and number theory. In addition to solved examples and problems, the book covers most topics of current interest, such as Cauchy theorems, Picard’s theorems, Riemann–Zeta function, Dirichlet theorem, Gamma function, and harmonic functions.
Complex Analysis : In the Spirit of Lipman Bers
In this book, the main focus is the theory of complex-valued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and three-manifolds, and number theory.
Compactifications of Symmetric and Locally Symmetric Spaces
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces.
Compact Lie Groups
This book covers the structure and representation theory of compact Lie groups. The necessary Lie algebra theory is also developed in the text with a streamlined approach focusing on linear Lie groups.
Communicative figurations : Transforming communications in times of deep mediatization
This open access volume is about how to research the influence of our changing media environment. Today, there is not one single medium that is the driving force of change. With the spreading of various technical communication media such as mobile phone and internet platforms, we are confronted with a media manifold of deep mediatization. But how can we investigate its transformative capability? This book answers this question by taking a non-media-centric perspective, researching the various figurations of collectivities and organizations humans are involved in. The first part of the book outlines a fundamental understanding of the changing media environment of deep mediatization and its transformative capacity. The second part focuses on collectivities and movements: communities in the city, critical social movements, maker, online gaming groups and networked groups of young people. The third part moves institutions and organizations into the foreground, discussing the transformation of journalism, religion, politics, and education, whilst the fourth and final part is dedicated to methodologies and perspectives.
Calculus and mechanics on two-point homogenous riemannian spaces
The present monograph gives a short and concise introduction to classical and quantum mechanics on two-point homogenous Riemannian spaces, with empahsis on spaces with constant curvature. Chapter 1-4 provide the basic notations from differential geometry for studying two-body dynamics in these spaces. Chapter 5 deals with the problem of finding explicitly invariant expressions for the two-body quantum Hamiltonian. Chapter 6 addresses one-body problems in a central potential. Chapter 7 studies the classical counterpart of the quantum system of chapter 5. Chapter 8 investigates some applications in the quantum realm, namely for the coulomb and oscillator potentials.
C*-algebras and Elliptic Theory II
This book consists of a collection of original, refereed research and expository articles on elliptic aspects of geometric analysis on manifolds, including singular, foliated and non-commutative spaces. There are contributions from leading specialists, and the book maintains a reasonable balance between research, expository and mixed papers.
C*-algebras and Elliptic Theory
This volume contains the proceedings of the conference on "C*-algebras and Elliptic Theory" held in Bedlewo, Poland, in February 2004. It consists of original research papers and expository articles focussing on index theory and topology of manifolds.The collection offers a cross-section of significant recent advances in several fields, the main subject being K-theory (of C*-algebras, equivariant K-theory). A number of papers is related to the index theory of pseudodifferential operators on singular manifolds (with boundaries, corners) or open manifolds. Further topics are Hopf cyclic cohomology, geometry of foliations, residue theory, Fredholm pairs and others.
Basic Notions of Algebra
Aims to present a general survey of algebra, of its basic notions and main branches.Those parts of the book devoted to the systematic treatment of notions and results of algebra make very limited demands on the reader: we presuppose only that the reader knows calculus, analytic geometry and linear algebra in the form taught in many high schools and colleges. The extent of the prerequisites required in our treatment of examples is harder to state; an acquaintance with projective space, topological spaces, differentiable and complex analytic manifolds and the basic theory of functions of a complex variable is desirable, but the reader should bear in mind that difficulties arising in the treatment of some specific example are likely to be purely local in nature, and not to affect the understanding of the rest of the book.
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Applied Stratigraphy
This book aims to incorporate major aspects and essential elements underpinning the modern applications and perspectives of stratigraphy. It focuses on traditional and innovative techniques and how these can be utilized in reconstructing the geological history of sedimentary basins and in solving manifold geological problems and phenomena. Each chapter summarizes contributions by leading researchers in the field. It is hoped that this book will provide the reader with key insights into all these aspects and applications.
Analysis II
As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may find it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many.
An Invitation to Statistics in Wasserstein Space
This book presents the key aspects of statistics in Wasserstein spaces, i.e. statistics in the space of probability measures when endowed with the geometry of optimal transportation.
