Format: Hardback, 205 pages, height x width: 235x155 mm, 8 Illustrations, color; 1 Illustrations, black and white; X, 230 p., 1 Hardback
Series: Industrial and Applied Mathematics
Pub. Date: 19-Sep-2024
ISBN-13: 9789819732371
The book collects chapters on operator theory as well as related approximation results and analytic inequalities. It discusses the properties of various types of operators, methods for approximating such operators, proximity point problems, applications of approximation methods in other fields such as engineering, and some analytic inequalities. It seeks to capture both the pure and applied aspects of the topics discussed. Several of the concepts covered in the book are fundamental to many aspects of applied science and engineering. The intriguing and novel aspect of the book is that it focuses on foundational aspects of the topics as well as reasonable application ideas and inputs useful information for practical applications in a variety of other scientific and engineering fields.
Approximation by a Double Sequence of Operators involving Multivariable
q-LagrangeHermite Polynomials.- Some Properties of the Parametric
BaskakovCchurerSz?sz Operators.- Approximation Process of the Fuzzy
MeyerKonig and Zeller Operators.- On Approximation of Signals in the
Generalized Zygmund Class using (E, s)(N, qn) Mean.- Trigonometric
Approximation of Signals belonging to lip ((t), r) Class by (C, 1) (N,pm,
qm)(E, ) Means of Conjugate Fourier Series.- Tur?n-type Inequalities for the
(p, k)-generalization of the MittagLeffler Function.- Multiplicative
Generalized HardyRogers-type F-proximal Non-self Mappings and Best Proximity
Point Approximation.- Best Proximity Point Problems in G-metric Spaces and
its Applications.- On a New Subclass of Bi-univalent Analytic Functions
Characterized by (p, q)-Lucas Polynomial Coefficients via Slgean
Differential Operator.- Sufficient Conditions for Generalized Integral
Operators involving the Rabotnov Function.
Format: Hardback, 455 pages, height x width: 235x155 mm, 56 Illustrations, black and white; Approx. 420 p., 1 Hardback
Series: Algorithms and Computation in Mathematics 32
Pub. Date: 03-Oct-2024
ISBN-13: 9783031621260
This book presents version 1.0 of the new Computer Algebra System OSCAR.
Written in Julia, OSCAR builds on and vastly extends four cornerstone systems:
ANTIC for number theory, GAP for group and representation theory, polymake for polyhedral and tropical geometry, and Singular for commutative algebra and algebraic geometry.
It offers powerful computational tools that transcend the boundaries of the individual disciplines involved.
It is freely available, open source software.
The book is an invitation to use OSCAR. With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets. These are valuable for interested researchers from graduate students through established experts.
Commutative Algebra and Algebraic Geometry.- Number Theory.- Group
theory.- Polyhedral Geometry.- Toric Geometry.
Format: Hardback, 160 pages, height x width: 235x155 mm, X, 160 p., 1 Hardback
Series: University Texts in the Mathematical Sciences
Pub. Date: 17-Oct-2024
ISBN-13: 9789819746422
Primarily designed for graduate students of mathematics, this textbook delves into Na?ve set theory, offering valuable insights for senior undergraduate students and researchers specializing in set theory. Commencing with a comprehensive exploration of functions and relations, the book extends its coverage to various applications of Na?ve set theory across multiple mathematical branches, including real analysis, linear and abstract algebra, general topology, and introductory aspects of complex analysis and measure theory. The text meticulously introduces cardinal and ordinal numbers, along with transfinite induction, following the natural progression discovered by Cantor during his examination of trigonometric series. While this book provides a solid foundation, students intrigued by set theory for its intrinsic value should recognize that the subject extends far beyond the scope of this text.
Introduction.- Functions and Relations.- Ordinal and Cardinal Numbers.-
Applications in Other Branches of Mathematics.- Banach-Tarski Paradox.
Pages: 672
ISBN: 978-981-12-9079-4 (hardcover)
ISBN: 978-981-12-9162-3 (softcover)
This is a textbook that covers several selected topics in the theory of elliptic partial differential equations which can be used in an advanced undergraduate or graduate course.
The book considers many important issues such as existence, regularity, qualitative properties, and all the classical topics useful in the wide world of partial differential equations. It also includes applications with interesting examples.
The structure of the book is flexible enough to allow different chapters to be taught independently.
The book is friendly, welcoming, and written for a newcomer to the subject.
It is essentially self-contained, making it easy to read, and all the concepts are fully explained from scratch, combining intuition and rigor, and therefore it can also be read independently by students, with limited or no supervision.
What is the Laplacian?
The Laplace Operator and Harmonic Functions
Upper Semicontinuity and Subharmonicity
Equations in Nondivergence Form: C2.ƒ¿-Regularity Theory
Equations in Nondivergence Form: W2.p-Regularity Theory
The Dirichlet Problem in the Light of Capacity Theory
Some Interesting Problems Arising from the Poisson Equation
The Moving Plane Method
Local Existence Theory in the Real Analytic Setting
Appendix A: An Interesting Example
Appendix B: An Application to Physical Geodesy
Readership: Undergraduate and graduate students in applied mathematics courses, lecturers and researchers.
Pages: 180
Series on Knots and Everything: Volume 76
ISBN: 978-981-12-9272-9 (hardcover)
A classic knot is an embedded simple loop in 3-dimensional space. It can be described as a 4-valent planar graph or network in the horizontal plane, with the vertices or crossings corresponding to double points of a projection. At this stage we have the shadow of the knot defined by the projection. We can reconstruct the knot by lifting the crossings into two points in space, one above the other. This information is preserved at the vertices by cutting the arc which appears to go under the over crossing arc. We can then act on this diagram of the knot using the famous Reidemeister moves to mimic the motion of the knot in space. The result is classic combinatorial knot theory. In recent years, many different types of knot theories have been considered where the information stored at the crossings determines how the Reidemeister moves are used, if at all.
In this book, we look at all these new theories systematically in a way which any third-year undergraduate mathematics student would understand. This book can form the basis of an undergraduate course or as an entry point for a postgraduate studying topology.
Introduction
Basic Concepts
Generalised Knot Theories
Chord Diagrams
Virtual Crossings and Virtual Knots
Max Newman's Proof Technique
Generalised Braids
Alexander and Markov Theorems
Unfinished Business from Chapter 7
The Sorting Method: Invariants
Appendices:
The Homflypt Polynomial
Categories
Codes for Curves
Examples of Planar Doodles
Index
Bibliography
Textbook or for self-study for advanced university undergraduate and postgraduate courses on topology. Researchers who wish to extend their knowledge on knot theory.
Pages: 1000
ISBN: 978-981-12-8842-5 (hardcover)
This book provides a comprehensive introduction to Fock space theory and its applications to mathematical quantum field theory. The first half of the book, Part I, is devoted to detailed descriptions of analysis on abstract Fock spaces (full Fock space, boson Fock space, fermion Fock space and boson-fermion Fock space). It includes the mathematics of second quantization, representation theory of canonical commutation and anti-commutation relations, Bogoliubov transformations, infinite-dimensional Dirac operators and supersymmetric quantum field in an abstract form. The second half of the book, Part II, covers applications of the mathematical theories in Part I to quantum field theory. Four kinds of free quantum fields are constructed and detailed analyses are made. A simple interacting quantum field model, called the van Hove-Miyatake model, is fully analyzed in an abstract form. Moreover, a list of interacting quantum field models is presented and an introductory description to each model is given. In this second edition, a new chapter (Chapter 15) is added to describe a mathematical theory of spontaneous symmetry breaking which is an important subject in modern quantum physics.
This book is a good introductory text for graduate students in mathematics or physics who are interested in the mathematical aspects of quantum field theory. It is also well-suited for self-study, providing readers a firm foundation of knowledge and mathematical techniques for more advanced books and current research articles in the field of mathematical analysis on quantum fields. Numerous problems are added to aid readers in developing a deeper understanding of the field.
Analysis on Fock Spaces:
Theory of Linear Operators
Tensor Product Hilbert Spaces
Tensor Product of Linear Operators
Full Fock Spaces and Second Quantization Operators
Boson Fock Spaces
Fermion Fock Spaces
Boson-Fermion Fock Spaces and Infinite-Dimensional Dirac Type Operators
Mathematical Theory of Quantum Fields:
General Theory of Quantum Fields
Non-relativistic QFT
Relativistic Free Quantum Scalar Fields
Quantum Theory of Electromagnetic Fields
Free Quantum Dirac Field
Van Hover-Miyatake Model
Models in QFT
Mathematical Formulation of Spontaneous Symmetry Breaking
Appendices:
Weak Convergence of Vectors and Strong Convergence of Bounded Linear Operators in Hilbert Spaces
Operators on a Direct Sum Hilbert Space
Absolutely Continuous Spectrum and Singular Continuous Spectrum of a Self-adjoint Operator
Elements of the Theory of Distributions
Integrations of Functions with Values in a Hilbert Space
Representations of Linear Lie Groups and Lie Algebras
Advanced undergraduate and graduate students (the book may be used as a textbook for a one-year course in mathematics or mathematical physics for first year graduate students), researchers in the fields of functional analysis and mathematical quantum field theory.
Series on Knots and Everything: Volume 77
Pages: 456
ISBN: 978-981-12-9275-0 (hardcover)
This book studies dihedral groups, dicyclic groups, other finite subgroups of the 3-dimensional sphere, and the 2-fold extensions of the symmetric group on 4 letters from the point of view of decorated string diagrams of permutations. These are our metaphorical quipu. As you might expect, the book is replete with illustrations. In (almost) all cases, explicit diagrams for the elements of the group are given. The exception is the binary icosahedral group in which only the generators and relations are exhibited.
Introduction
Background and Motivating Examples
Matrix Descriptions
The 3-Dimensional Sphere is a Group
Extensions of the Permutation Group ƒ°4
The Binary Tetrahedral Group
The Binary Icosahedral Group
Computing Group 2-Cocycles
Advanced undergraduates, beginning graduate students in mathematics, mathematical hobbyists, visual learners, young physicists.
Selected Chapters of Number Theory: Special Numbers: Volume 4
Pages: 290
Catalan numbers, named after the French-Belgian mathematician Eugene Charles Catalan (1814?1894), arise in a variety of combinatorial problems. They have many interesting properties, a rich history, and numerous arithmetic, number-theoretical, analytical and combinatorial connections, as well as a variety of classical and modern applications. Considering the long list of open problems and questions related to the classical case, its relatives (Bell numbers, Motzkin numbers, Narayana numbers, etc.) and its generalizations, this book provides a broad perspective on the theory of this class of special numbers that will be useful and of interest to both professionals and a general audience.
The book begins with the history of the problem, before defining the considered numerical sets. The recurrence equation, closed formula, and generating function are then presented, followed by the simplest properties and number-theoretical properties. Later chapters discuss the relationships between Catalan numbers and other special numbers, as well as their applications and open problems.
Preliminaries
Pascal's Triangle and Other Arithmetic Triangles
Catalan Numbers
Relatives of Catalan Numbers
Catalan Numbers and Their Relatives on the Square Lattice
Zoo of Numbers
Mini Dictionary
Exercises
The target audience for this book is university teachers and students at the undergraduate and postgraduate levels interested in combinatorics, number theory, general algebra, cryptography and related fields, as well as a general audience of amateur mathematicians.
Pages: 272
ISBN: 978-981-12-8659-9 (hardcover)
It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.
Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.
Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.
New Presentation of Bieberbach Theorems
Methods of Classification
Flat Manifolds with the First Betti Number Zero
Symmetris of Flat Manifolds
Spin Structures and Dirac Operator
Flat Manifolds with Complex Structures
Crystallographic Groups as Isometries of Hyperbolic Space
Fenomen of Hantzsche-Wendt Groups
Open Problems
Researchers in geometry and topology, algebra and theory students, Institutes of Crystallography, University Chemistry departments.