Format: Paperback / softback, 204 pages, height x width: 240x168 mm, weight: 374 g, 26 Illustrations, color; 31 Illustrations, black and white; X, 204 p. 57 illus., 26 illus. in color.,
Pub. Date: 21-Jan-2024
This textbook is an introduction to the methods needed to solve partial differential equations (PDEs). Readers are introduced to PDEs that come from a variety of fields in engineering and the natural sciences. The chapters include the following topics: First Order PDEs, Second Order PDEs, Fourier Series, Separation of Variables, the Fourier Transform, and higher dimensional problems. Readers are guided through these chapters where techniques for solving first and second order PDEs are introduced. Each chapter ends with series of exercises to facilitate learning as well as illustrate the material presented in each chapter.
Introduction.- First Order PDEs.- Second Order Linear PDEs.- Fourier
Series.- Separation of Variables.- Fourier Transform.
Format: Paperback / softback, 616 pages, height x width: 235x155 mm, weight: 949 g, 30 Tables, color; 1 Illustrations, black and white; IX, 616 p. 1 illus.
Series: Operator Theory: Advances and Applications 289
Pub. Date: 03-Jan-2024
ISBN-13: 9783031138539
This volume is dedicated to the memory of Harold Widom (19322021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a HeisenbergIsing chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.
Part I Harold Widoms Life, Work, and Last Paper.- Biography of Harold
Widom.- Domain Walls in the Heisenberg-Ising Spin-1/2 Chain.- Harold Widoms
Contributions to the Spectral Theory and Asymptotics of Toeplitz Operators
and Matrices.- Visualizations of Two Functions Emerging in Connection with
Toeplitz Determinants.- Part II Personal Notes.- A Remarkable Advisor,
Mentor, and Friend.- My Encounters with Harold Widom.- Memories of Harold
Widom.- Personal Reflection on Harold Widom.- Part III Invited
Contributions.- Loops in SU (2) and Factorization, II.- Openness of Regular
Regimes of Complex Random Matrix Models.- Focusing Nonlocal Nonlinear
Schrodinger Equation with Asymmetric Boundary Conditions: Large-Time
Behavior.- Algebras of Commuting Differential Operators for Kernels of Airy
Type.- A Random Walk on the Rado Graph.- Widom Factors and SzegoWidom
Asymptotics, a Review.- Some Recent Progress on the Stationary Measure for
the Open KPZ Equation.- Probability of Two Large Gaps in the Bulk and at the
Edge of the Spectrum of Random Matrices.- Multiplicative Properties of
Infinite Block Toeplitz and Hankel Matrices.- Toeplitz and Related Operators
on Polyanalytic Fock Spaces.- Strong Szego Theorem on a Jordan Curve.-
Toeplitz Operators with Non-trivial Kernels and Non-dense Ranges on Weak
Hardy Spaces.- Renyi Entropies of the Free Fermi Gas in Multi-Dimensional
Space at High Temperature.- Spectral Asymptotics for Toeplitz Matrices Having
Certain Piecewise Continuous Symbols.- Global and Local Scaling Limits for
Linear Eigenvalue Statistics of Jacobi -Ensembles.- On the Limit of Some
Variable-Coefficient Toeplitz-Like Determinants.- On Diagonalizable Quantum
Weighted Hankel Matrices.- On the Product Formula for Toeplitz and Related
Operators.
Format: Paperback / softback, 750 pages, height x width: 235x155 mm, weight: 1151 g, 21 Illustrations, color; 106 Illustrations, black and white; XIII, 750 p. 127 illus., 21 illus. in color.
Series: Studies in Universal Logic
Pub. Date: 12-Jan-2024
ISBN-13: 9783030944544
This contributed volume collects papers related to the Logic in Question workshop, which has taken place annually at Sorbonne University in Paris since 2011. Each year, the workshop brings together historians, philosophers, mathematicians, linguists, and computer scientists to explore questions related to the nature of logic and how it has developed over the years. As a result, chapter authors provide a thorough, interdisciplinary exploration of topics that have been studied in the workshop. Organized into three sections, the first part of the book focuses on historical questions related to logic, the second explores philosophical questions, and the third section is dedicated to mathematical discussions. Specific topics include:
?logic and analogy
?Chinese logic
?nineteenth century British logic (in particular Boole and Lewis Carroll)
?logical diagrams
?the place and value of logic in Louis Couturat’s philosophical thinking
?contributions of logical analysis for mathematics education
?the exceptionality of logic
?the logical expressive power of natural languages
?the unification of mathematics via topos theory
Logic in Question will appeal to pure logicians, historians of logic, philosophers, linguists, and other researchers interested in the history of logic, making this volume a unique and valuable contribution to the field.
Inference in nineteenth century British logic .- The representation of
negative terms with Euler diagrams .- Logical hylemorphism in the 13th Latin
century .- What is the relation between Peirces logic and his philosophy of
logic? .- Booles symbolized laws of thought facing empiricism .- Lewis
Carrolls almost diagrammatic notation .- Boole's untruth tables: The formal
conditions of meaning before the emergence of propositional logic .- What is
ancient Chinese logic? .- Husserlian pure logic from the standpoint of
intentionality .- Definition and inference in Leniewskis logic .- The place
and value of logic in Louis Couturats philosophical thinking .- Freges
silence about Bolzano .- Symbolism and unintepretability in Boole .- Tabular
notations .- Identity, equality in logic, mathematics and politics .- Logic
and metaphysics .- Can logic be cartesian?.- Images and their ability to
negate .- What does best explaining" mean? Explanatory virtues and the role
of context in IBE .- What does a concept entail? .- The analytic and the
synthetic from homology to heterology .- About all and nothing. Meinongian
views of all and nothing as maximal and minimal objects of thought .- On
dichotomy and analogy: A question on the next unbloody revolution in logic
.- Logic and analogy .- A Carnapian logic of conceivability .- No, no and no
.- Philosophical logic = philosophy + logic? .- Grammar is not a mechanism
(Wittgenstein) or what could an anthropology of mathematics? .- Existential
Presupposition and Logical Square .- The unification of mathematics via topos
theory .- Quasi-topological structuring of extensions within logic of
typicals and atypicals (LTA) .- Contributions of logical analysis for
mathematics education .- A categorical aspect of the analogy between
quantifiers and modalities .- The relevance logic program: Failed or just
stalled? .- Is logic relevant to classifications? .- Logic and theory of
representation .- Back and forth in positive logic.
Format: Paperback / softback, 295 pages, height x width: 235x155 mm, weight: 480 g, 3 Tables, color;
3 Illustrations, color; 7 Illustrations, black and white; XIV, 295 p. 10 illus., 3 illus. in color.,
Series: Computer Science Foundations and Applied Logic
Pub. Date: 03-Jan-2024
ISBN-13: 9783031211140
This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas.The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.
Preface.- 1 Introduction.- 2 Answers to Readers Questions.-
3 Preliminary Concepts.- 4 Syntax.- 5 Semantics.- 6 Additional Notation.- 7
Beta-reduction and Substitution.- 8 Proof Systems.- 9 Theories.- 10
Sequences.- 11 Developments.- 12 Real Number Mathematics.- 13 Morphisms 14
Alonzo Variants.- 15 Software Support.- Appendix A: Metatheorems of μ.-
Appendix B: Soundness of μ.- Appendix C: Henkins Theorem for μ.-
Bibliography.- List of Figures.- List of Tables.- List of Theorems, Examples,
Remarks, and Modules.- Index
Format: Paperback / softback, 237 pages, height x width: 235x155 mm, weight: 391 g,
2 Illustrations, color; 5 Illustrations, black and white; XII, 237 p. 7 illus., 2 illus. in color.,
Series: Trends in Mathematics
Pub. Date: 17-Jan-2024
ISBN-13: 9783031190841
The chapters in this contributed volume explore new results and existing problems in algebra, analysis, and related topics. This broad coverage will help generate new ideas to solve various challenges that face researchers in pure mathematics. Specific topics covered include maximal rotational hypersurfaces, k-Horadam sequences, quantum dynamical semigroups, and more. Additionally, several applications of algebraic number theory and analysis are presented. Algebra, Analysis, and Associated Topics will appeal to researchers, graduate students, and engineers interested in learning more about the impact pure mathematics has on various fields.
Maximal Rotational Hypersurfaces Having Spacelike Axis, Spacelike
Profile Curve in Minkowski Geometry.- On the generalized k-Horadam like
sequences.- New Results on (p1, p2,pn, k) -Analogue of Lauricella function
with transforms and Fractional calculus operator.- Absolute Linear Method of
Summation for Orthogonal Series.- Derivations and Special Functions over
Fields.- On Equalities of Central Automorphisms Group With Various
Automorphism Groups.- Automorphism Group and Laplacian Spectrum of a Graph
over Brandt Semigroups.- Unified iteration scheme in CAT(0) spaces and fixed
point approximation of mean nonexpansive mappings.- Semigroups of Completely
Positive Maps.- On Sumset Problems And Their Various Types.- Vector-Valued
Affine Bi-Frames on Local Fields.- A New Perspective on I2-statistical limit
points and I2-statistical cluster points in probabilistic normed
spaces.- Evaluation of Integral transforms in terms of Humbert and Lauricella
functions and their applications.- Some Spaces in Neutrosophic e-Open
Sets.- Generalized Finite Continuous Ridgelet Transform.