Paperback ISBN: 9780128197813
Published Date: 1st June 2020
Page Count: 320
Series: Mathematics in Science and Engineering
Transmutation methods are a universal instrument for solving many problems in different subjects. Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar simple ones. Its strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science, and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools but also vehicles that deliver theoretical insights.
Presents the universal transmutation method as the most powerful for solving
many problems in mathematics, mathematical physics, probability and statistics,
applied computer science and numerical methods
Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details
Enables researchers, lecturers, and students to find material under the single "roof"
Researchers, students working in the area of partial differential equations. Advanced undergraduate students, postgraduate students, researchers interested in new methods in differential equations and mathematical physics
1. Basic definitions and propositions
2. Essentials on transmutations
3. Basics of fractional calculus and fractional order differential equations
4. Weighted generalized functions generated by indefinite quadratic form
5. Buschman-Erdelyi integral operators and transmutations
6. Integral transforms compositions method (ITCM) for transmutations
7. Differential equations with Bessel operator(without fractional powers operators)
8. Transmutations for 1D Schrodinger equation
9. B-potentials theory
10. Fractional powers of Bessel operators
11. Differential equations (based on fractional powers operators)
12. Fractional differential equations with singular coefficients
13. Applications of Buschman?Erdelyi integral operators
14. Applications of Euler-Poisson-Darboux differential equations
15. Applications of B?potentials theory and fractional differential equations
16. Different applications
Part of Cambridge Studies in Advanced Mathematics
AVAILABILITY: Not yet published - available from June 2020
FORMAT: Hardback ISBN: 9781108479622
Category theory provides structure for the mathematical world and is seen
everywhere in modern mathematics. With this book, the author bridges the
gap between pure category theory and its numerous applications in homotopy
theory, providing the necessary background information to make the subject
accessible to graduate students or researchers with a background in algebraic
topology and algebra. The reader is first introduced to category theory,
starting with basic definitions and concepts before progressing to more
advanced themes. Concrete examples and exercises illustrate the topics,
ranging from colimits to constructions such as the Day convolution product.
Part II covers important applications of category theory, giving a thorough
introduction to simplicial objects including an account of quasi-categories
and Segal sets. Diagram categories play a central role throughout the book,
giving rise to models of iterated loop spaces, and feature prominently
in functor homology and homology of small categories.
Includes diagrammatical proofs, examples and exercises to encourage an active way of learning
Provides enough background from category theory to make advanced topics such as K-theory, iterated loop spaces and functor homology accessible to readers Makes abstract concepts tangible, encouraging readers to learn what can be an intimidating subject
Introduction
Part I. Category theory:
1. Basic notions in category theory
2. Natural transformations and the Yoneda lemma
3. (Co)Limits
4. Kan extensions
5. Comma categories and the Grothendieck construction
6. Monads and comonads
7. Abelian categories
8. Symmetric monoidal categories
9. Enriched categories
Part II. From categories to homotopy theory:
10. Simplicial objects
11. The nerve and the classifying space of a small category
12. A brief introduction to operads
13. Classifying spaces of symmetric monoidal categories
14. Approaches to iterated loop spaces via diagram categories
15. Functor homology
16. Homology and cohomology of small categories
References
Index.
Part of Encyclopedia of Mathematics and its Applications
AVAILABILITY: Not yet published - available from May 2020
FORMAT: Hardback ISBN: 9781108495806
The goal of this monograph is to develop Hopf theory in a new setting which
features centrally a real hyperplane arrangement.
The new theory is parallel to the classical theory of connected Hopf algebras,
and relates to it when specialized to the braid arrangement. Joyal's theory
of combinatorial species, ideas from Tits' theory of buildings, and Rota's
work on incidence algebras inspire and find a common expression in this
theory. The authors introduce notions of monoid, comonoid, bimonoid, and
Lie monoid relative to a fixed hyperplane arrangement. They also construct
universal bimonoids by using generalizations of
the classical notions of shuffle and quasishuffle, and establish the Borel?Hopf,
Poincare?Birkhoff?Witt,and Cartier-Milnor-Moore theorems in this setting.
This monograph opens a vast new area of research. It will be of interest
to students and researchers working in the areas of hyperplane arrangements,
semigroup theory, Hopf algebras, algebraic Lie theory, operads, and category
theory.
The first book on the subject; readers will learn the theory first-hand from its original creators
Carefully designed chapters, with effective use of tables, diagrams, pictures, and exercises, making the book accessible to a wide audience
Touches many different areas of mathematics with minimum prerequisites,
so readers can choose entry points depending on their background and interest
Close
Introduction
Part I. Species and Operads:
1. Hyperplane arrangements
2. Species and bimonoids
3. Bimonads on species
4. Operads
Part II. Basic Theory of Bimonoids:
5. Primitive filtrations and decomposable filtrations
6. Universal constructions
7. Examples of bimonoids
8. Hadamard product
9. Exponential and logarithm
10. Characteristic operations
11. Modules over monoid algebras and bimonoids in species
12. Antipode
Part III. Structure Results for Bimonoids:
13. Loday-Ronco, Leray-Samelson, Borel ?Hopf
14. Hoffman?Newman?Radford
15. Freeness under Hadamard products
16. Lie monoids
17. Poincare-Birkhoff-Witt and Cartier-Milnor-Moore
Appendix A. Linear algebra
Appendix B. Higher monads
Appendix C. Internal hom
Appendix D. Semidirect products
References
Notation index
Author index
Subject index.
Hardback
Published November 8, 2019
Reference - 262 Pages
ISBN 9780367345471
Series: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
Spectral Methods Using Multivariate Polynomials on the Unit Ball is a research level text on a numerical method for the solution of partial differential equations. The authors introduce, illustrate with examples, and analyze 'spectral methods' that are based on multivariate polynomial approximations. The method presented is an alternative to finite element and difference methods for regions that are diffeomorphic to the unit disk, in two dimensions, and the unit ball, in three dimensions. The speed of convergence of spectral methods is usually much higher than that of finite element or finite difference methods.
Introduces the use of multivariate polynomials for the construction and analysis of spectral methods for linear and nonlinear boundary value problems
Suitable for researchers and students in numerical analysis of PDEs, along with anyone interested in applying this method to a particular physical problem
One of the few texts to address this area using multivariate orthogonal polynomials, rather than tensor products of univariate polynomials.
Chapter 1: Introduction
Chapter 2: Multivariate Polynomials
Chapter 3: Creating Transformations of Regions
Chapter 4: Galerkin's method for the Dirichlet and Neumann Problems
Chapter 5: Eigenvalue Problems
Chapter 6: Parabolic problems
Chapter 7: Nonlinear Equations
Chapter 8: Nonlinear Neumann Boundary Value Problem
Chapter 9: The biharmonic equation
Chapter 10: Integral Equations
Hardback
December 4, 2019 Forthcoming
Reference - 416 Pages - 40 B/W Illustrations
ISBN 9780367235031
Series: Discrete Mathematics and Its Applications
50 Years of Combinatorics, Graph Theory, and Computing advances research
in discrete mathematics by providing current research surveys, each written
by experts in their subjects.
The book also celebrates outstanding mathematics from 50 years at the Southeastern
International Conference on Combinatorics, Graph Theory & Computing
(SEICCGTC). The conference is noted for the dissemination and stimulation
of research, while fostering collaborations among mathematical scientists
at all stages of their careers.
The authors of the chapters highlight open questions. The sections of the
book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory;
Designs, Geometry, Packing and Covering. Readers will discover the breadth
and depth of the presentations at the SEICCGTC, as well as current research
in combinatorics, graph theory and computer science.
Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys
Surveys highlight open questions to inspire further research
Chapters are written by experts in their fields
Extensive bibliographies are provided at the end of each chapter
Personal Reflections of the SEICCGTC: Origins and Beyond
I: Combinatorics
Some of My Favorite Problems
Variations on the Sequenceable Theme
Survey of Stack Sortable Permutations
Dimensions for Posets and Chromatic Number for Graphs
Edros Magic
II: Graph Theory
Developments on Saturated Graphs
Magic Labeling Basics
Block Colorings of Graph Decompositions
Reconfiguration of Colourings and Dominating Sets in Graphs
Edge Intersection Graphs of Paths on a Grid
III: Combinatorial Matrix Theory
A Jaunt in Spectral Graph Theory
Inverse Eigenvalue Problem of a Graph
Rank Functions