Format: Hardback, 526 pages, height x width: 279x210 mm, VIII, 526 p.
With online files/update.,
Pub. Date: 21-Jul-2022
ISBN-13: 9783031053542
This volume explores A.P. Morsefs (1911-1984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morsefs works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morsefs publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editorfs commentary serves to outline Morsefs goals, give informal explanations of Morsefs formal language, and compare Morsefs often unique approaches to more traditional approaches. Minor corrections to Morsefs previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editorfs introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morsefs methods.
A.P. Morsefs Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morsefs unique perspective and in the history of mathematics will also find this book to be of interest.
Preface.- Editor's Introduction.- Language and Inference.- Logic.- Set Theory.- Elementary Analysis.- Metrics.- Measure.- Linear Measure and Total Variation.- Integration.- Product Measures.- Web Derivatives.- Classical Differentiation.- The Construction of Definition.- The Consistency of the Axiom of Size.- Suggested Reading.- Publications of A.P. Morse.- Errata to A Theory of Sets, Second Edition.- Integration with Respect to Addor Functions.- The Henstock-Kurzweil Integral.
Format: Hardback, 560 pages, height x width: 235x155 mm, 133 Illustrations, color;
34 Illustrations, black and white; X, 560 p. 167 illus., 133 illus. in color
Series: SEMA SIMAI Springer Series 31
Pub. Date: 28-Aug-2022
ISBN-13: 9783030953188
The purpose of this book is to present the current state of the art of the Virtual Element Method (VEM) by collecting contributions from many of the most active researchers in this field and covering a broad range of topics: from the mathematical foundation to real life computational applications.
The book is naturally divided into three parts. The first part of the book presents recent advances in theoretical and computational aspects of VEMs, discussing the generality of the meshes suitable to the VEM, the implementation of the VEM for linear and nonlinear PDEs, and the construction of discrete hessian complexes. The second part of the volume discusses Virtual Element discretization of paradigmatic linear and non-linear partial differential problems from computational mechanics, fluid dynamics, and wave propagation phenomena. Finally, the third part contains challenging applications such as the modeling of materials with fractures, magneto-hydrodynamics phenomena and contact solid mechanics.
The book is intended for graduate students and researchers in mathematics and engineering fields, interested in learning novel numerical techniques for the solution of partial differential equations. It may as well serve as useful reference material for numerical analysts practitioners of the field.
1 Tommaso Sorgente et al., VEM and the Mesh.- 2 Dibyendu Adak et al., On the implementation of Virtual Element Method for Nonlinear problems over polygonal meshes.- 3 Long Chen and Xuehai Huang, Discrete Hessian Complexes in Three Dimensions.- 4 Edoardo Artioli et al., Some Virtual Element Methods for Infinitesimal Elasticity Problems.- 5 Lourenco Beirao da Veiga and Giuseppe Vacca, An introduction to second order divergence-free VEM for fluidodynamics.- 6 Gabriel N. Gatica et al, A virtual marriage a la mode: some recent results on the coupling of VEM and BEM.- 7 Daniele Boffi et al., Virtual element approximation of eigenvalue problems.- 8 David Mora and Alberth Silgado, Virtual element methods for a stream-function formulation of the Oseen equations.- 9 Lorenzo Mascotto et al., The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation.- 10 Paola F. Antonietti et al., The conforming virtual element method for polyharmonic and elastodynamics problems: a review.- 11 Edoardo Artioli et al., The virtual element method in nonlinear and fracture solid mechanics.- 12 Sebastian Naranjo Alvarez et al., The virtual element method for the coupled system of magneto-hydrodynamics.- 13 Peter Wriggers et al., Virtual Element Methods for Engineering Applications.
Format: Hardback, 690 pages, height x width: 235x155 mm, 3 Tables, color; 4 Illustrations, color;
5 Illustrations, black and white; X, 690 p. 9 illus., 4 illus. in color.
Series: Trends in Mathematics
Pub. Date: 19-Jul-2022
ISBN-13: 9783031021039
Inequalities play a central role in mathematics with various applications in other disciplines. The main goal of this contributed volume is to present several important matrix, operator, and norm inequalities in a systematic and self-contained fashion. Some powerful methods are used to provide significant mathematical inequalities in functional analysis, operator theory and numerous fields in recent decades. Some chapters are devoted to giving a series of new characterizations of operator monotone functions and some others explore inequalities connected to log-majorization, relative operator entropy, and the Ando-Hiai inequality. Several chapters are focused on Birkhoff-James orthogonality and approximate orthogonality in Banach spaces and operator algebras such as C*-algebras from historical perspectives to current development. A comprehensive account of the boundedness, compactness, and restrictions of Toeplitz operators can be found in the book. Furthermore, an overview of the Bishop-Phelps-Bollobas theorem is provided. The state-of-the-art of Hardy-Littlewood inequalities in sequence spaces is given. The chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.
Part I Matrix and Operator Inequalities.- Log-majorization Type Inequalities.- Ando-Hiai Inequality: Extensions and Applications, - Relative Operator Entropy.- Matrix Inequalities and Characterizations of Operator Monotone Functions.- Perspectives, Means and their Inequalities.- Cauchy-Schwarz Operator and Norm Inequalities for Inner Product Type Transformers in Norm Ideals of Compact Operators, with Applications.- Norm Estimations for the Moore-Penrose Inverse of the Weak Perturbation of Hilbert C -module Operators.- Part II Orthogonality and Inequalities.- Birkhoff-James Orthogonality: Characterizations, Preservers, and Orthogonality Graphs.- Approximate Birkhoff-James Orthogonality in Normed Linear Spaces and Related Topics.- Orthogonally Additive Operators on Vector Lattices.- Part III Inequalities Related to Types of Operators.- Normal Operators and their Generalizations.- On Wold Type Decomposition for Closed Range Operators.- (Asymmetric) Dual Truncated Toeplitz Operators.- Boundedness of Toeplitz Operators in Bergman-type Spaces.- Part IV Inequalities in Various Banach Spaces.- Disjointness Preservers and Banach-Stone Theorems.- The Bishop-Phelps-Bollobas Theorem: An Overview.- A New Proof of the Power Weighted Birman-Hardy-Rellich Inequalities.- An Excursion to Multiplications and Convolutions on Modulation Spaces.- The Hardy-Littlewood Inequalities in Sequence Spaces.- Symmetries of C -algebras and Jordan Morphisms.- Part V Inequalities in Commutative and Noncommutative Probability Spaces.- Mixed Norm Martingale Hardy Spaces and Applications in Fourier Analysis.- The First Eigenvalue for Nonlocal Operators.- Comparing Banach Spaces for Systems of Free Random Variables Followed by the Semicircular Law.
Format: Paperback / softback, 604 pages, height x width: 235x155 mm, 5 Illustrations,
black and white; XXIV, 604 p. 5 illus
Series: Trends in Logic 58
Pub. Date: 26-Jul-2022
ISBN-13: 9783030949280
This open access book is the first ever collection of Karl Popper's writings on deductive logic.
Karl R. Popper (1902-1994) was one of the most influential philosophers of the 20th century. His philosophy of science ("falsificationism") and his social and political philosophy ("open society") have been widely discussed way beyond academic philosophy. What is not so well known is that Popper also produced a considerable work on the foundations of deductive logic, most of it published at the end of the 1940s as articles at scattered places. This little-known work deserves to be known better, as it is highly significant for modern proof-theoretic semantics.
This collection assembles Popper's published writings on deductive logic in a single volume, together with all reviews of these papers. It also contains a large amount of unpublished material from the Popper Archives, including Popper's correspondence related to deductive logic and manuscripts that were (almost) finished, but did not reach the publication stage. All of these items are critically edited with additional comments by the editors. A general introduction puts Popper's work into the context of current discussions on the foundations of logic. This book should be of interest to logicians, philosophers, and anybody concerned with Popper's work.
Format: Hardback, 451 pages, height x width: 235x155 mm, weight: 865 g,
69 Illustrations, black and white; XX, 451 p. 69 illus.
Series: Algorithms and Computation in Mathematics 26
Pub. Date: 29-May-2022
ISBN-13: 9783662652763
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects.
Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics.
The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Format: Hardback, 222 pages, height x width: 235x155 mm,
61 Illustrations, black and white; XV, 222 p. 61 illus.,
Series: Texts and Readings in Mathematics 55
Pub. Date: 06-Aug-2022
ISBN-13: 9789811913358
Description
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pickfs theorem on areas of lattice polygons and Graham?Pollakfs work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Table of Contents
Chapter
1. Basic Graph Theory.
Chapter
2. Basic Counting.
Chapter
3. The Principle of Inclusion and Exclusion.
Chapter
4. Graphs and Matrices.-
Chapter
5. Trees.
Chapter
6. Mobius Inversion and Graph Colouring.
Chapter
7. Enumeration under Group Action.
Chapter
8. Matching Theory.
Chapter
9. Block Designs.
Chapter
10. Planar Graphs.
Chapter
11. Edges and Cycles.-
Chapter
12. Expanders and Ramanujan Graphs.
Chapter
13. Hints.