Springer Asia Pacific Mathematics Series – serie

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12 produkter

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Generalized Heisenberg Groups and the Schrödinger–Weil Representation
AvJae-Hyun Yang
Inbunden, Engelska, 2026
1 725 kr
Skickas inom 11-20 vardagar
This book presents a detailed study of the generalized Heisenberg group, a 2‑step nilpotent Lie group that plays an important role in the theory of smooth compactifications of the Siegel modular variety, number theory, and mathematical physics. The text explicates its connections with theta functions, the Weil representation, and the Schrödinger–Weil representation, emphasizing their structural and conceptual relationships.Heisenberg groups, theta functions, and the Schrödinger–Weil representation occupy central positions in modern mathematics and mathematical physics. By providing explicit descriptions and clear explanations, this book aims to serve as a valuable resource for researchers working in these areas. The material is intended for both mathematicians and physicists interested in the interplay between representation theory, automorphic forms, and physical models.
Del 3 - Springer Asia Pacific Mathematics Series
Functional Analysis and Applications
AvShiqing Zhang
Inbunden, Engelska, 2026
658 kr
Skickas inom 10-15 vardagar
The core of this book is variational methods and their applications in geometry, physics, mechanics engineering control and economics. The author set out to solve the classical and famous problems including Isoperimetric Problem, Brachistochrone Curve Problem, N-Body Problems, Geodesic Curve Problem, Minimal Surface Problem, Dirichlet Principle, Minimax Problems, Rabinowitz Minimal Period Conjecture, etc. The book contains many interesting historic backgrounds and important examples, explains profound theories in simple language, which can help readers to follow in order and advance step by step. The proofs for very difficult theorems are also clearly expressed, and all chapters and appendixes are very well-written. The book has 8 organized appendixes that are important and appropriate supplements to the main texts. Appendices 1 to 7 are related with some famous classical theorems while Appendix 8 is related with the famous Rabinowitz's minimum period conjecture.The level of this book is between the textbook for graduate students and monograph. The prerequisites on Calculus, Classical Mechanics, Ordinary Differential Equations and Real and Functional Analysis are required. It is very useful for graduate students in mathematics, physics, mechanics and related engineering majors who want to improve their knowledge in Nonlinear Sciences.
Modeling in Life Sciences and Ecology
Machine Learning and Dynamical Systems
AvJingli Ren,Yiwen Tao
Inbunden, Engelska, 2026
1 851 kr
Skickas inom 10-15 vardagar
This book begins by exploring the fundamental concepts of dynamical systems and machine learning modeling, elucidating the workflow of these two modeling approaches. While primarily tailored as an introductory textbook for both undergraduate and graduate students, its broader aim is to captivate the interest of seasoned ecologists and life scientists, beckoning them to explore the realm of modeling. The introduction and development of each section adhere to a practical problem-driven approach, aiming to address real-world issues. The focus is on addressing how to establish and evolve appropriate models based on practical problems or data.Throughout the book, the authors deliver rich content and diverse models. A detailed overview of the workflow for both machine learning and dynamical system modeling is provided, covering topics such as stability and bifurcation theory, fundamentals of machine learning algorithms, data processing, and visualization methods. Regarding dynamical systems, the authors encompass various types of models, including delay, diffusion, continuous, and discrete models. For machine learning, both black-box and interpretable models are covered in this book, including neural network model, ensemble learning model, SHAP, LIME, and more.Ecologists, life scientists, and applied mathematicians might find this book helpful. It can be also used as a textbook for both undergraduate and graduate students.This book is related to SDG 15: Life on Land
Del 1 - Springer Asia Pacific Mathematics Series
Pattern Recognition and Machine Learning for Self-Study I
Supervised Learning
AvKenichiro Ishii,Naonori Uedam. fl.
Inbunden, Engelska, 2026
785 kr
Skickas inom 5-8 vardagar
This book explains the basic principles of pattern recognition (PR) and machine learning (ML) in an easy-to-understand manner for beginners who are trying to learn these principles on their own. Readers with a basic knowledge of linear algebra and probability theory will find it easy to follow.Many excellent books in this field have been published in the past. However, these books are not necessarily intended for self-study by beginners.This book limits the topics to the minimum essential themes that beginners should learn, and explains them in detail. This book focuses on supervised learning, first introducing classical but important methods that have contributed to the development of the field. It then explains various methods that have since attracted attention. In explaining these methods, the book also provides a historical account of how new technologies were created as a result of combining classical ideas. The book emphasizes that Bayes decision rule is a fundamental concept in PR and ML.The following points make this book suitable for self-study by beginners.(1) The book is self-contained, so that the reader does not need to refer to other books or literature. (2) To deepen the reader's understanding, exercises are provided at the end of each chapter with detailed solutions available online.(3) To promote the reader's intuitive understanding, the book presents as many concrete examples as possible.(4) ‘Coffee Break’ columns introduce knowledge and know-how from the author's experience. Unsupervised learning will be discussed in a sequel.
Del 8 - Springer Asia Pacific Mathematics Series
Liouville’s Theory in Linear and Nonlinear Partial Differential Equations
AvTakashi Suzuki
Inbunden, Engelska, 2025
1 842 kr
Skickas inom 5-8 vardagar
A variety of theorems named the Liouville property play fundamental roles in modern theory of mathematical analysis. Understanding each of them individually is not so difficult nowadays. What are they pointing toward in their totality, however? This monograph asserts that self-organization may be an answer, searching recent studies on linear and nonlinear partial differential equations. Critical breakthroughs have emerged in accordance with the widely spread classical ideas of J. Liouville in various forms, that is, the spectral, elliptic, surface, and transport theories, in turn. A fusion of them is seen in recently developing research fields—mathematical oncology, non-equilibrium statistical mechanics, dynamical theory, and shape optimization—which taken together may be called the potential for self-organization.
Del 5 - Springer Asia Pacific Mathematics Series
Spectral Analysis of Infinite-Dimensional Hamiltonian Operators
AvAlatancang Chen,Deyu Wum. fl.
Inbunden, Engelska, 2026
1 634 kr
Skickas inom 10-15 vardagar
This book provides a systematic summary and condensation of research on infinite-dimensional Hamiltonian operator spectrum theory over the past thirty years, and offers simple and concise proofs for some new achievements. The book first introduces Hamiltonian systems, both finite-dimensional and infinite-dimensional, laying the foundation for the subsequent introduction of infinite-dimensional Hamiltonian operator spectrum theory. Chapter 2 presents the infinite-dimensional Hamiltonian operator and systematically elaborates on its spectral properties. Chapters 3 and 4 focus on the completeness of the characteristic function system and the symplectic self-adjointness of infinite-dimensional Hamiltonian operators, respectively, achieving improvements and deepening of the relevant content. Chapters 5 and 6 introduce the numerical range and the theory of indefinite metric spaces related to infinite-dimensional Hamiltonian operators, reflecting the broader application prospects of such operators and the novelty of the book's scope.This book will be useful for senior undergraduate students, graduate students, and teachers specializing in mathematics. To read this book, readers are expected to have knowledge of mathematical analysis and advanced algebra, including matrix theory and some basic knowledge of operator theory.
Del 7 - Springer Asia Pacific Mathematics Series
Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains
Computation Using Orthonormal Basis Vectors
AvSehun Chun
Inbunden, Engelska, 2025
1 634 kr
Skickas inom 10-15 vardagar
This book presents a comprehensive and geometrical approach to solving partial differential equations (PDEs) on complex curved domains using orthonormal moving frames. Rooted in Élie Cartan’s classical theory but adapted for computational practicality, the framework aligns local basis vectors with the intrinsic geometry and anisotropy of the domain, enabling accurate and efficient discretization without requiring explicit metric tensors or Christoffel symbols. Topics include the construction of moving frames on general manifolds, covariant derivatives via connection 1-forms, and frame-based formulations of gradient, divergence, curl, and Laplacian operators. Extensive MATLAB and C++ implementations (via Nektar++) are provided for benchmark problems in diffusion-reaction systems, shallow water equations, and Maxwell’s equations on complex surfaces such as the sphere, pseudosphere, and atrial tissue. Emphasizing clarity and accessibility, the book blends theory, visualization, and numerical practice, making it an essential resource for graduate students and researchers in scientific computing, applied mathematics, and engineering disciplines dealing with PDEs on non-Euclidean domains.
Del 10 - Springer Asia Pacific Mathematics Series
First Lectures in Algebra
Why do Normal Subgroups and Ideals Matter?
AvShuichi Yukita
Inbunden, Engelska, 2026
658 kr
Skickas inom 10-15 vardagar
This book is designed as an undergraduate textbook for students in science and engineering, rather than for mathematics majors, yet it maintains full mathematical rigor. It covers groups, rings, modules over rings, finite fields, polynomial rings over finite fields, and error-correcting codes. Even in mathematics departments, undergraduates often wonder why concepts like normal subgroups and ideals matter, and standard textbooks may not provide satisfying answers. This book addresses such questions with both intuition and precision. For example: (1) A normal subgroup is the kernel of a group homomorphism and gives rise to a factor group; a non-normal subgroup does neither. (2) An ideal is a special additive subgroup that serves as the kernel of a ring homomorphism and yields a factor ring; a non-ideal additive subgroup does not. The reader will appreciate the elegant parallelism between these ideas. Key features include:A prerequisite chapter that subtly introduces module theory through an elementary presentation of the Euclidean algorithm, accessible even to high school students.Recurring use of orbits and clusters, with intuitive illustrations, to clarify the operational meaning of normal subgroups and ideals via homomorphisms.Emphasis on proof design patterns, inspired by fields like architecture and software engineering.Extensive use of diagrams to support conceptual understanding. Readers are encouraged to draw, compute, design reasoning flows, and then write proofs.Complete answers to quizzes and exercises are provided, allowing readers to check their understanding after thoughtful attempts.
Del 9 - Springer Asia Pacific Mathematics Series
Numerical Solutions to Partial Differential Equations with Finite Difference Methods
AvZhi-Zhong Sun,Qifeng Zhangm. fl.
Inbunden, Engelska, 2026
712 kr
Skickas inom 10-15 vardagar
This book presents finite difference methods for three types of classical linear PDEs, three types of nonlinear PDEs and fractional PDEs. Specific topics cover two-point boundary value problems, elliptic equations, parabolic equations, hyperbolic equations, high-dimensional evolution equations, Schr\''{o}dinger equations, the Burgers' equation, the Korteweg-de Vries equation, and fractional diffusion-wave equations.The book strives to achieve:(a) Featured content. Thorough and dedicated presentations are provided for the finite difference methods. (b) Scattered difficulty. Starting from a simple two-point boundary value problem for an ODE, authors introduce core concepts and analytical techniques of the finite difference methods, then apply them to handle with various partial differential equations.(c) Emphasis on practicability. For each algorithm, provided numerical examples enable students to learn how to apply it and verify theoretical results with numerical outcomes.The book is suitable for advanced undergraduate and beginning graduate students in applied mathematics and engineering.
Del 14 - Springer Asia Pacific Mathematics Series
Topological Dynamics from a Measure-Theoretic Viewpoint
AvKeonhee Lee,Carlos Moralesm. fl.
Inbunden, Engelska, 2026
1 410 kr
Skickas inom 5-8 vardagar
This book introduces a new measurable perspective on dynamical systems by connecting concepts from topological dynamics with their measure-theoretic counterparts. A central theme is the translation of topological notions into measurable ones. For example, minimality in topological dynamics suggests a measurable analogue in ergodicity, where every invariant measurable set has either zero or full measure, offering an intuitive parallel between the two settings. Likewise, the notion of expansiveness is reinterpreted through expansive measures, in which almost all orbits separate beyond a fixed radius. These measurable analogues extend naturally to homeomorphisms and flows on compact metric spaces, which are explored in depth in Chapters 3 and 7.Building on this framework, the book develops measurable versions of several structural results from topological dynamics. Walters’ stability theorem-grounded in shadowing, expansiveness, and topological stability-is revisited in Chapters 4 and 8 from a measurable perspective, while Smale’s spectral decomposition theorem is reformulated in measurable terms in Chapters 5 and 9. By bridging topological and measurable viewpoints, the book offers a cohesive approach that provides new insights and directions for the study of dynamical systems.
Model Order Reduction via Orthogonal Polynomial Approximation
AvYao-Lin Jiang
Inbunden, Engelska, 2026
1 989 kr
Kommande
This monograph presents a comprehensive exploration of model order reduction techniques rooted in orthogonal polynomials, addressing diverse dynamical systems such as linear, coupled, bilinear, time-delay, and nonlinear systems. By integrating general and specific polynomials—such as Laguerre and Chebyshev—as well as discrete orthogonal polynomials, the monograph introduces unified frameworks and innovative approaches, including structure-preserving reduction and hybrid methods. Organized thematically, the monograph combines theory with practical algorithms, emphasizing efficiency and accuracy. It features dedicated chapters on continuous-time and discrete-time systems, step-by-step derivations, and computational case studies. Readers will gain cutting-edge tools to simplify complex systems, accelerate simulations, and enhance design processes in engineering and applied mathematics.
Del 2 - Springer Asia Pacific Mathematics Series
Geometric Aspects of General Topology
AvKatsuro Sakai
Inbunden, Engelska, 2026
2 177 kr
Skickas inom 10-15 vardagar
This book is designed for graduate students to acquire knowledge of simplicial complexes, Dimension Theory, ANR Theory (Theory of Retracts), and related topics. These theories are connected with various ﬁelds in Geometric Topology, Algebraic Topology as well as General Topology. Except for the second half of the last chapter, this book is entirely self-contained. To make the ideas of proofs easier to understand, many proofs are illustrated with ﬁgures or diagrams. While exercises are not explicitly included, some results are provided with only sketches of proofs. Completing the proofs in detail is a good exercise for the reader. Researchers will also ﬁnd this book very helpful, as it contains many important results not presented in usual textbooks, such as dim X × I = dim X + 1 for a metrizable space X; the difference between small and large inductive dimensions; a hereditarily inﬁnite-dimensional space; the ANR property of locally contractible countable-dimensional metrizable spaces; an inﬁnite-dimensional space with ﬁnite cohomological dimension; a dimension-raising cell-like map; and a non-AR metric linear space. The last three subjects are linked to each other, demonstrating how deeply related the two theories are. Simplicial complexes are very useful in various ﬁelds of Topology and are indispensable for studying theories of dimension and ANR. Many textbooks deal with simplicial complexes, but none discuss in detail what is non-locally ﬁnite. For example, J.H.C. Whitehead's theorem on small subdivisions is very important, but its proof cannot be found in any other book. The homotopy type of simplicial complexes is discussed in textbooks on Algebraic Topology using CW complexes, but geometrical arguments using simplicial complexes are relatively easy. Many contents have been added to this edition to make it more comprehensive.

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Springer Asia Pacific Mathematics Series – serie

Generalized Heisenberg Groups and the Schrödinger–Weil Representation

Functional Analysis and Applications

Modeling in Life Sciences and Ecology

Pattern Recognition and Machine Learning for Self-Study I

Liouville’s Theory in Linear and Nonlinear Partial Differential Equations

Spectral Analysis of Infinite-Dimensional Hamiltonian Operators

Moving Frames for the Numerical Solution of Partial Differential Equations in Complex Domains

First Lectures in Algebra

Numerical Solutions to Partial Differential Equations with Finite Difference Methods

Topological Dynamics from a Measure-Theoretic Viewpoint

Model Order Reduction via Orthogonal Polynomial Approximation

Geometric Aspects of General Topology

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