Format: Hardback, 725 pages, height x width: 235x155 mm, 5 Illustrations, black and white; VII, 680 p. 5 illus., 1 Hardback
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Pub. Date: 20-Sep-2024
ISBN-13: 9783031641886
This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment.
The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium.
By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.
Degree Theory.- Fixed Point Theory.- Critical Point Theory.- Spectra of
Differential Operators.- Elliptic Boundary Value Problems.- Evolution
Equations.- Calculus of Variations.- Mathematical Economics and Game Theory.-
References.- Index.
Format: Paperback / softback, 332 pages, height x width: 240x168 mm, 9 Illustrations, color; 5 Illustrations, black and white; X, 210 p. 13 illus., 9 illus. in color., 1 Paperback / softback
Series: Frontiers in Mathematics
Pub. Date: 19-Sep-2024
ISBN-13: 9783031640902
The goal of this book is to investigate the behavior of weak solutions to the elliptic interface problem in a neighborhood of boundary singularities: angular and conic points or edges. This problem is considered both for linear and quasi-linear equations, which are among the less studied varieties. As a second edition of Transmission Problems for Elliptic Second-Order Equations for Non-Smooth Domains (Birkhäuser, 2010), this volume includes two entirely new chapters: one about the oblique derivative problems for the perturbed p(x)-Laplacian equation in a bounded n-dimensional cone, and another about the existence of bounded weak solutions.
Researchers and advanced graduate students will appreciate this compact compilation of new material in the field.
1. Preliminaries.-
2. Eigenvalue Problem and Integro-Differential Inequalities.-
3. Best Possible Estimates of Solutions to the Interface Problem for Linear Elliptic Divergence Second Order Equations in a Conical Domain.-
4. Interface Problem for the Laplace Operator with N Different Media.-
5. Interface Problem for Weak Quasi-Linear Elliptic Equations in a Conical Domain.-
6. Interface Problem for Strong Quasi-Linear Elliptic Equations in a Conical Domain.-
7. Best Possible Estimates of Solutions to the Interface Problem for a Quasi-LinearElliptic Divergence Second Order Equation in a Domain with a Boundary Edge.-
8. Interface Oblique Derivative Problem for Perturbed p(x)-Laplacian Equation in a Bounded n Dimensional Cone.- 9. Existence of Bounded Weak Solutions.
Format: Hardback, 221 pages, height x width: 235x155 mm, 7 Illustrations, black and white; XX, 210 p. 5 illus., 1 Hardback
Series: KIAS Springer Series in Mathematics 3
Pub. Date: 05-Nov-2024
ISBN-13: 9789819751723
This open access book focuses on the Ginibre ensembles that are non-Hermitian random matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within random matrix theory, featuring, for example, the first book on the subject written by Mehta in 1967. Their status has been consolidated and extended over the following years, as more applications have come to light, and the theory has developed to greater depths. This book sets about detailing much of this progress. Themes covered include eigenvalue PDFs and correlation functions, fluctuation formulas, sum rules and asymptotic behaviors, normal matrix models, and applications to quantum many-body problems and quantum chaos. There is a distinction between the Ginibre ensemble with complex entries (GinUE) and those with real or quaternion entries (GinOE and GinSE, respectively).
First, the eigenvalues of GinUE form a determinantal point process, while those of GinOE and GinSE have the more complicated structure of a Pfaffian point process. Eigenvalues on the real line in the case of GinOE also provide another distinction. On the other hand, the increased complexity provides new opportunities for research. This is demonstrated in our presentation, which details several applications and contains not previously published theoretical advances. The areas of application are diverse, with examples being diffusion processes and persistence in statistical physics and equilibria counting for a system of random nonlinear differential equations in the study of the stability of complex systems.
Introduction.- Eigenvalue PDFs and Correlations.- Fluctuation
Formulas.- Coulomb Gas Model, Sum Rules and Asymptotic Behaviours.- Normal
Matrix Models.- Further Theory and Applications.- Eigenvalue Statistics for
GinOE and Elliptic GinOE.- Analogues of GinUE Statistical Properties for
GinOE.- Further Extensions to GinOE.- Statistical Properties of GinSE and
Elliptic GinSE.- Further Extensions to GinSE.
Developments in Statistical Modelling
Format: Hardback, 270 pages, height x width: 235x155 mm, 78 Illustrations, color; 16 Illustrations, black and white; X, 270 p. 94 illus., 78 illus. in color., 1 Hardback
Series: Contributions to Statistics
Pub. Date: 12-Jul-2024
ISBN-13: 9783031657221
This volume on the latest developments in statistical modelling is a collection of refereed papers presented at the 38th International Workshop on Statistical Modelling, IWSM 2024, held from 14 to 19 July 2024 in Durham, UK. The contributions cover a wide range of topics in statistical modelling, including generalized linear models, mixture models, regularization techniques, hidden Markov models, smoothing methods, censoring and imputation techniques, Gaussian processes, spatial statistics, shape modelling, goodness-of-fit problems, and network analysis. Various highly topical applications are presented as well, especially from biostatistics. The approaches are equally frequentist and Bayesian, a categorization the statistical modelling community has synergetically overcome. The book also features the workshops keynote contribution on statistical modelling for big and little data, highlighting that both small and large data sets come with their own challenges.
The International Workshop on Statistical Modelling (IWSM) is the annual workshop of the Statistical Modelling Society, with the purpose of promoting important developments, extensions, and applications in statistical modelling, and bringing together statisticians working on related problems from various disciplines. This volume reflects this spirit and contributes to initiating and sustaining discussions about problems in statistical modelling and triggers new developments and ideas in the field.
REML for two dimensional P splines.- Learning Bayesian networks from ordinal data The Bayesian way.- Latent Dirichlet allocation and hidden Markov models to identify public perception of sustainability in social media data.- Bayesian approaches to model overdispersion in Spatio temporal binomial data.- Elicitation of priors for intervention effects in educational trial data.- Elicitation of priors for intervention effects in educational trial data.- Optimism correction of the AUC with complex survey data.- Statistical models for patient centered outcomes in clinical studies.- Bayesian hidden Markov models for early warning.- A Bayesian Markov-switching for smooth modelling of extreme value distributions.
Paperback
Format: Paperback / softback, 168 pages, height x width: 235x155 mm, VIII, 168 p. With online files/update., 1 Paperback / softback
Pub. Date: 17-Jul-2024
ISBN-13: 9783031651601
This colorful and concise little book is uniquely tailored for those who write mathematical texts at any level and are eager to improve their English writing skills. The easy-to-read guide focuses on helping the writer avoid common English mistakes in mathematical writing. With just a few minutes of engaging, light reading each day, the reader will learn to create clearer, more readable, math texts.
The book covers 23 crucial topics, ranging from correct article and preposition usage to proper usage of dashes, conjunctions, and prepositions. It also addresses the construction of direct sentences, effective introductory phrases for formulas, and more. As a bonus to the reader, Practice makes perfect exercises relating to each topic are freely accessible on this books Springer website.
Appendix A gives a quick tutorial on grammatical terms and constructs. Appendix B looks at ChatGPT and the positive aspects of its powerful capabilities. Additionally, Paul Halmoss article on How to write mathematics is included in Appendix C. It deals with the mathematical aspects of writing.
Introduction.- Overview.-
1. Little words I. Prepositions.-
2. Little words II. Pronouns.-
3. Little words III. Conjunctions.-
4. Little Words IV. So, such, that.-
5. Little words V. Like, such as.-
6. Little words VI. Either, or, both.-
7. Little marks I. Punctuation.-
8. Little marks II. Hyphens.-
9. Little marks III. Dashes.-
10. Little transitions. Short version.-
11. Little transitions. Longer version.-
12. Little Intros.-
13. Little run. Run-on sentences.-
14. Little trip. To go or going.-
15. Little dangling.-
16. Little numbers. Les and fewer, both and two.-
17. Little pause. Comma before if.-
18. Little ambiguity.-
19. Little active vs. passive.-
20. Little speed. Faster and fastests.-
21. Little distinctions.-
22. Little modification.-
23. Little only.- A. Little grammar.- B. Little ChatGPT.- C. How to write mathematics by P.R. Halmos.- Bibliography.
Format: Hardback, 153 pages, height x width: 235x155 mm, 15 Illustrations, black and white; Approx. 160 p., 1 Hardback
Series: RSME Springer Series 13
Pub. Date: 04-Oct-2024
ISBN-13: 9783031620249
The book contains a selection of research and expository papers in pure and applied mathematics presented by various authors as plenary or invited speakers at the biennial congress of the Spanish Royal Mathematical Society held in Ciudad Real (Spain) in January 2022. The main results focus on the Yang problem and its solution proposed by Globevnik; a phylogenetic reconstruction based on algebra; the Calderon problem for local and nonlocal Schrödinger equations; some open problems in orthogonal polynomial theory; Quillens rational homotopy theory; Ulrich bundles and applications; and free objects in theory of Banach spaces. Researchers in these fields are potential audiences.
A survey on applications of a new approach to Quillen rational homotopy
theory.- The Yang problem for complete bounded complex submanifolds a
survey.- Orthogonal polynomials and operator theory.- Open problems and
applications.- A Sample of problems where ULRICH BUNDLES show up.
Format: Paperback / softback, 276 pages, height x width: 235x155 mm, 18 Illustrations, color; 36 Illustrations, black and white; Approx. 340 p., 1 Paperback / softback
Series: Mathematics Study Resources 12
Pub. Date: 18-Oct-2024
ISBN-13: 9783662691144
This textbook presents a direct path from real analysis of one variable to function theory. Classical topics of one-dimensional real analysis, such as differential and integral calculus, are largely presented from a complex perspective. The goal is a self-contained exposition extending to the Runge theorems and the dynamics of entire functions. Short sections appended to each chapter on concepts of function theory provide glimpses into higher-dimensional analysis and an impression of its universal significance for mathematics. The book is structured so that parts can also serve as a basis for a seminar.
Thus, this fascinating area of mathematics becomes accessible to students whose programs do not focus on mathematics and for whom a classical introduction to function theory would be too time-consuming. This book enables them to take a step into complex analysis, through which they can recognize a multitude of connections that remain hidden in real analysis.
The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.
Rules of the Game: Sets, mappings, numbers.- Basics: Limits, elementary functions, and metric spaces.- Up and Down: Differentiation and integration; Magic Circles: Circular functions and local function theory.- Wonder Worlds: Global function theory.- Normal or Not: Conformal mappings and complex dynamics.- Extras: Runge theory and applications.
Format: Hardback, 196 pages, height x width: 235x155 mm, 24 Illustrations, color; 43 Illustrations, black and white; X, 220 p. 90 illus., 10 illus. in color., 1 Hardback
Series: Behaviormetrics: Quantitative Approaches to Human Behavior 19
Pub. Date: 20-Sep-2024
ISBN-13: 9789819748716
This is the first book that focusses the attention on applying asymmetric multidimensional scaling (MDS) and describes how to apply it in a practical manner. The book provides the know-how for prominent methods of asymmetric MDS: analysis of asymmetric relationships and the efficient use of programs of asymmetric MDS based on a distance model. These features will facilitate the work of researchers and enlighten students in disciplines such as statistics, psychology, sociology, education, marketing science, medicine, education, and other fields. Support is provided for practitioners in these areas who are, for instance, developing new products or services, investigating dominance relationships among brands or products, researching the use of antibiotics against resistance bacteria, and developing items for tests. This informative book demonstrates the analyses of data from diverse areas to show how asymmetric relationships are prevalent in real-world relationships and helps readers grasp the meanings and implications of those relationships. The results of the analyses illustrate the importance of analyzing asymmetric relationships that cannot be perceived by analysis using traditional methods, which ignore asymmetry in the data.
Introduction.- Representing asymmetric relationships by symmetric multidimensional scaling.- Representing asymmetric relationships by asymmetric multidimensional scaling.- Applications of asymmetric multidimensional scaling.- Remarks: Rescaling, degeneration, local minimum, and initial configuration.
Format: Paperback / softback, 150 pages, height x width: 235x155 mm, 27 Illustrations, black and white; XVII, 150 p. 27 illus., 1 Paperback / softback
Series: Mathematics Study Resources 9
Pub. Date: 23-Jul-2024
ISBN-13: 9783662691014
Starting with the Shannon-Wiener approach to mathematical information theory, allowing a mathematical "measurement" of an amount of information, the book begins by defining the terms message and information and axiomatically assigning an amount of information to a probability. The second part explores countable probability spaces, leading to the definition of Shannon entropy based on the average amount of information; three classical applications of Shannon entropy in statistical physics, mathematical statistics, and communication engineering are presented, along with an initial glimpse into the field of quantum information. The third part is dedicated to general probability spaces, focusing on the information-theoretical analysis of dynamic systems.
The book builds on bachelor-level knowledge and is primarily intended for mathematicians and computer scientists, placing a strong emphasis on rigorous proofs.
Introduction - Symbols - List of figures - Part I Fundamentals. Message and information.- Information and chance.- Part II Countable systems. The entropy.- The maximum entropy principle.- Conditional probabilities.- Quantum information.- Part III General systems.- The entropy of partitions.- Stationary information sources.- Density functions and entropy.- Conditional expectations.- Literature.- Index.