Format: Hardback, 571 pages, height x width: 235x155 mm, 30 Illustrations, black and white; XXIV, 571 p. 30 illus
Series: PNLDE Subseries in Control 104
Pub. Date: 10-Feb-2024
ISBN-13: 9783031493706
This monograph presents the most recent developments in the study of Hamilton-Jacobi equations and control problems with discontinuities, mainly from the viewpoint of partial differential equations. Two main cases are investigated in detail: the case of codimension 1 discontinuities and the stratified case in which the discontinuities can be of any codimensions. In both, connections with deterministic control problems are carefully studied, and numerous examples and applications are illustrated throughout the text.
After an initial section that provides a “toolbox” containing key results which will be used throughout the text, Parts II and III completely describe several recently introduced approaches to treat problems involving either codimension 1 discontinuities or networks. The remaining sections are concerned with stratified problems either in the whole space R^N or in bounded or unbounded domains with state-constraints. In particular, the use of stratified solutions to treat problems with boundary conditions, where both the boundary may be non-smooth and the data may present discontinuities, is developed. Many applications to concrete problems are explored throughout the text ? such as Kolmogorov-Petrovsky-Piskunov (KPP) type problems, large deviations, level-sets approach, large time behavior, and homogenization ? and several key open problems are presented.
This monograph will be of interest to graduate students and researchers working in deterministic control problems and Hamilton-Jacobi equations, network problems, or scalar conservation laws.
General Introduction.- Basic Continuous Framework and Classical Assumptions Revisited.- Part I: A Toolbox for Discontinuous Hamilton-Jacobi Equations and Control Problems.- PDE Tools.- Control Tools.- Mixed Tools.- Other Tools.- Part II: Deterministic Control Problems and Hamilton-Jacobi Equations for Codimension One Discontinuities.- Introduction: Ishii Solutions for the Hyperplane Case.- The Control Problem and the "Natural" Value Function.- A Less Natural Value-Function, Regular and Singular Dynamics.- Uniqueness and Non-Uniqueness Features.- Adding a Specific Problem on the Interface.- Remarks on the Uniqueness Proofs, Problems without Controllability.- Further Discussions and Open Problems.- Part III: Hamilton-Jacobi Equations with Codimension One Discontinuities: The "Network" Point of View.- Introduction.- Flux-Limited Solutions for Control Problems and Quasi-Convex Hamiltonians.- Junction Viscosity Solutions.- From One Notion of Solution to the Others.- Applications and Emblematic Examples.- Further Discussions and Open Problems.- Part IV: General Discontinuities: Stratified Problems.- Stratified Solutions.- Connections with Control Problems and Ishii Solutions.- Stability Results.- Applications.- Further Discussions and Open Problems.- Part V: State-Constraint Problems.- Introduction to State-Constraint Problems.- Stratified Solutions for State-Constraint Problems.- Classical Boundary Conditions and Stratified Formulation.- Stability for Singular Boundary Value Problems.- Further Discussions and Open Problems.- Part VI: Investigating Other Applications.- KPP-Type Problems with Discontinuities.- And What about Jumps? And What about Networks.- Further Discussions and Open Problems.- Part VII: Appendices.- Notations and Terminology.- Assumptions, Hypotheses, Notions of Solutions.
Format: Hardback, 416 pages, height x width: 235x155 mm, 69 Illustrations, color;
38 Illustrations, black and white; XII, 416 p. 107 illus., 69 illus. in color.
Pub. Date: 12-Feb-2024
ISBN-13: 9789819980628
This book provides first-year graduate engineering students and practicing engineers with a solid introduction to random signals and estimation. It includes a statistical background that is often omitted in other textbooks but is essential for a clear understanding of estimators and their properties. The book emphasizes applicability rather than mathematical theory. It includes many examples and exercises to demonstrate and learn the theory that makes extensive use of MATLAB and its toolboxes. Although there are several excellent books on random signals and Kalman filtering, this book fulfills the need for a book that is suitable for a single-semester course that covers both random signals and Kalman filters and is used for a two-semester course for students that need remedial background. For students interested in more advanced studies in the area, the book provides a bridge between typical undergraduate engineering education and more advanced graduate-level courses.
Review of Probability Theory.- Random Variables.- Random Signals (autocorrelation, power spectral density).- Response of Linear Systems to Random Inputs (continuous, discrete).- Estimation and Estimator Properties (small sample and large sample properties of estimators, CRLB).- Least Square Estimation Likelihood (likelihood function, detection).- Maximum Likelihood Estimation.- Minimum Mean-Square Error Estimation (Kalman Filter, information filter, filter stability).- Generalizing the Basic Kalman Filter (colored noise, correlated noise, reduced-order estimator, Schmidt Kalman filter sequential computation).- Prediction and Smoothing.- Nonlinear Filtering (Extended Kalman filter, unscented Kalman filter, ensemble Kalman filter, particle filter).- The Expectation Maximization Algorithm.- Markov Models.
Format: Hardback, 422 pages, height x width: 235x155 mm, 2 Illustrations, black and white; VIII, 422 p. 2 illus.
Series: Problem Books in Mathematics
Pub. Date: 07-Feb-2024
ISBN-13: 9783031487835
Presenting a rich collection of exercises on partial differential equations, this textbook equips readers with 96 examples, 222 exercises, and 289 problems complete with detailed solutions or hints. It explores a broad spectrum of partial differential equations, fundamental to mathematically oriented scientific fields, from physics and engineering to differential geometry and variational calculus.
Organized thoughtfully into seven chapters, the journey begins with fundamental problems in the realm of PDEs. Readers progress through first and second-order equations, wave and heat equations, and finally, the Laplace equation. The text adopts a highly readable and mathematically solid format, ensuring concepts are introduced with clarity and organization.
Designed to cater to upper undergraduate and graduate students, this book offers a comprehensive understanding of partial differential equations. Researchers and practitioners seeking to strengthen their problem-solving skills will also find this exercise collection both challenging and beneficial.
Preface.- General Introduction.- First Order Partial Differential
Equations.- Classifications of Second Order Partial Differential
Equations.- Classifications and Canonical Forms for Linear Second Order
Partial Differential Equations.- The Laplace Equation.- The Heat
Equation.- The Wave Equation.- Solutions, Hints and Answers to the
Exercises.- Solutions, Hints and Answers to the Problems.- Index.
Format: Hardback, height x width: 235x155 mm, 600 Illustrations, black and white; Approx. 610 p. 600 illus.,
ISBN-13: 9783031489051
This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.
The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature.
The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.
Format: Hardback, height x width: 235x155 mm, 300 Illustrations, black and white; Approx. 460 p. 300 illus
Pub. Date: 13-Feb-2024
ISBN-13: 9783031489099
This is a comprehensive two-volumes text on plane and space geometry, transformations and conics, using a synthetic approach. The first volume focuses on Euclidean Geometry of the plane, and the second volume on Circle measurement, Transformations, Space geometry, Conics.
The book is based on lecture notes from more than 30 courses which have been taught over the last 25 years. Using a synthetic approach, it discusses topics in Euclidean geometry ranging from the elementary (axioms and their first consequences), to the complex (the famous theorems of Pappus, Ptolemy, Euler, Steiner, Fermat, Morley, etc.). Through its coverage of a wealth of general and specialized subjects, it provides a comprehensive account of the theory, with chapters devoted to basic properties of simple planar and spatial shapes, transformations of the plane and space, and conic sections. As a result of repeated exposure of the material to students, it answers many frequently asked questions. Particular attention has been given to the didactic method; the text is accompanied by a plethora of figures (more than 2000) and exercises (more than 1400), most of them with solutions or expanded hints. Each chapter also includes numerous references to alternative approaches and specialized literature.
The book is mainly addressed to students in mathematics, physics, engineering, school teachers in these areas, as well as, amateurs and lovers of geometry. Offering a sound and self-sufficient basis for the study of any possible problem in Euclidean geometry, the book can be used to support lectures to the most advanced level, or for self-study.
Format: Hardback, 408 pages, height x width: 235x155 mm, X, 408 p., 1 Hardback
Series: Springer Tracts in Modern Physics 291
Pub. Date: 10-Feb-2024
ISBN-13: 9783031490347
This book describes the direct and inverse problems of the multidimensional Schrodinger operator with a periodic potential, a topic that is especially important in perturbation theory, constructive determination of spectral invariants and finding the periodic potential from the given Bloch eigenvalues. It provides a detailed derivation of the asymptotic formulas for Bloch eigenvalues and Bloch functions in arbitrary dimensions while constructing and estimating the measure of the iso-energetic surfaces in the high-energy regime. Moreover, it presents a unique method proving the validity of the BetheSommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed, it determines the spectral invariants of the multidimensional operator from the given Bloch eigenvalues. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential, making it possible to determine the potential constructively using Bloch eigenvalues as input data. Lastly, the book presents an algorithm for the unique determination of the potential. This updated and significantly expanded third edition features an extension of this framework to all dimensions, offering a now complete theory of self-adjoint Schrodinger operators within periodic potentials. Drawing from recent advancements in mathematical analysis, this edition delves even deeper into the intricacies of the subject. It explores the connections between the multidimensional Schrodinger operator, periodic potentials, and other fundamental areas of mathematical physics. The book's comprehensive approach equips both students and researchers with the tools to tackle complex problems and contribute to the ongoing exploration of quantum phenomena.
Preliminary Facts.- From One-dimensional to
Multidimensional.- Asymptotic Formulas for the Bloch Eigenvalues and Bloch
Functions.- Constructive Determination of the Spectral Invariants.- Periodic
Potential from the Spectral Invariants.- Conclusions and Some Generalization.
Format: Hardback, 273 pages, height x width: 235x155 mm, 9 Illustrations, black and white; XI, 273 p. 9 illus.
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics 77
Pub. Date: 03-Feb-2024
ISBN-13: 9783031484421
In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group theory. This monograph provides an account of this theory, along with other modern techniques in geometric group theory.
Structured around the theme of group actions on contractible polyhedra, this book explores two prominent methods for constructing such actions: utilizing the group of deck transformations of the universal cover of a nonpositively curved polyhedron and leveraging the theory of simple complexes of groups. The book presents various approaches to obtaining cubical examples through CAT(0) cube complexes, including the polyhedral product construction, hyperbolization procedures, and the Sageev construction. Moreover, it offers a unified presentation of important non-cubical examples, such as Coxeter groups, Artin groups, and groups that act on buildings.
Designed as a resource for graduate students and researchers specializing in geometric group theory, this book should also be of high interest to mathematicians in related areas, such as 3-manifolds.
Part I: Introduction.- 1 Introduction.- Part II: Nonpositively curved
cube complexes.- 2 Polyhedral preliminaries.- 3 Right-angled spaces and
groups.- Part III: Coxeter groups, Artin groups, buildings.- 4 Coxeter
groups, Artin groups, buildings.- Part IV: More on NPC cube complexes.- 5
General theory of cube complexes.- 6 Hyperbolization.- 7 Morse theory and
BestvinaBrady groups.- Appendix A: Complexes of groups.