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Ivan I. Kyrchei: Quaternion Generalized
Inverses

Quaternion Generalized Inverses

Foundations, Theory, Problems, and Solutions

Calculus for the Curious

This textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo.
This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving &nbsp;problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.

This textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo.This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving &nbsp;problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.

Analytical Methods in Physics

A Textbook

Linear Algebra and Optimization for Machine Learning

CMS/CAIMS Books in Mathematics

This book is about semisimple Banach algebras with a focus on those that are commutative. After laying out the necessary background material from functional analysis, geometry of Banach spaces and measure theory, we introduce many specific Banach algebras from operator theory, harmonic analysis, and function theory and study their basic properties. Some of the questions dealt with in the book are: Whether the introduced Banach algebras are BSE-algebras, whether they have BSE norms, whether they have the separating ball property or some variant of it, and whether they are Arens regular. The book contains quite a few new results, as well as new proofs of a good many known results.The book is intended for those who are preparing to work in Banach algebras or who have been doing research in related areas.

Banach Function Algebras, Arens Regularity, and BSE Norms

Mathematics Study Resources

This textbook presents the topics typically covered in a standard course on discrete structures. It is aimed at students of computer science and mathematics (teaching degree and Bachelor's/Master's) and is designed to accompany lectures, for self-study, and for exam preparation. 
 
Through explanatory introductions to definitions, numerous examples, counterexamples, diagrams, cross-references, and outlooks, the authors manage to present the wide range of topics concisely and comprehensibly. 
 
Numerous exercises facilitate the deepening of the material. Due to its compact presentation of all important discrete and algebraic structures and its extensive index, the book also serves as a reference for mathematicians, computer scientists, and natural scientists. 
 
Contents: From propositional and predicate logic to sets and combinatorics, numbers, relations and mappings, graphs, to the rich spectrum of algebraic structures, and a brief introduction to category theory. Additional chapters include rings and modules as well as matroids. 
 
This book is a translation of the second German edition. The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content, so the book may read stylistically differently from a conventional translation. 
 
&nbsp;

The Authors 
Prof. Dr. Dr. h.c. Ulrich Knauer is a retired professor of mathematics at Carl von Ossietzky University of Oldenburg (Germany).

Dr. habil. Kolja Knauer is an associate professor in discrete mathematics and computer science at Aix-Marseille University (France) and at the University of Barcelona (Spain).

&nbsp;

A Concise Introduction

Discrete and Algebraic Structures

Mathematics in Mind

This book addresses the well-known capability and flexibility of classical and constructive semigroups (inherited from algebraic structures), to model, solve problems in extremely diverse situations, and develop interesting new algebraic ideas with many applications and connections to other areas of mathematics (logic, biomathematics, analysis, geometry, etc.), natural sciences, engineering and life sciences, interconnections between semigroups, cognitive sciences, social sciences, arts and humanities. The book promotes the idea that algebra came at the core of interdisciplinarity, belongs to all life disciplines, and serves in a variety of mathematics applications. It focuses on recent developments in classical and constructive semigroups, and other basic algebraic structures as well as on some of their potential applications in other fields. Further, it helps shed light on ways in which classical and constructive semigroups have been developing and applying in various domains, and extended with other sciences. The content is based on contributions of an international team of renowned scientists with expertise in different disciplines of mathematics, classical and constructive semigroups, other algebraic structures and their applications in logic, cognitive sciences, linguistics, biology, machine learning, and collective phenomena.

Classical and Constructive Semigroups and Applications

Algebra Without Borders

Springer Monographs in Mathematics

This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. The authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem, etc., and then discuss isolated hypersurface and plane curve singularities, including the finite determinacy, classification of simple singularities, topological and analytic invariants, and resolution. In the local deformation theory emphasis is placed on the issues of the versality, obstructions, and equisingular deformations. The book includes a thorough treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum based on deformations of the parametrization.

Introduction to Singularities and Deformations

Monografie Matematyczne

This book presents the monodromy group, underlining the unifying role it plays in a variety of theories and mathematical areas. In singularity theory and algebraic geometry, the monodromy group is embodied in the Picard-Lefschetz formula and the Picard-Fuchs equations. It has applications in the weakened 16th Hilbert problem and in mixed Hodge structures. In the theory of systems of linear differential equations, one has the Riemann-Hilbert problem, the Stokes phenomena and the hypergeometric functions with their multidimensional generalizations. In the theory of homomorphic foliations, there appear the Ecalle-Voronin-Martinet-Ramis moduli. Moreover, there is a deep connection of monodromy theory with Galois theory of differential equations and algebraic functions.&nbsp;The material is addressed to a wide audience, ranging from specialists in the theory of ordinary differential equations to algebraic geometers. Readers will quickly get introduced to modern and vital mathematical theories, such as singularity theory, analytic theory of ordinary differential equations, holomorphic foliations, Galois theory, and parts of algebraic geometry, without searching in vast literature.This second edition has been enlarged by several sections, presenting new results appeared since the first edition.

The Monodromy Group

VON NULL AUF MATHE

Rechnen mit Buchstaben: Terme und Bruchterme

Differential algebra explores properties of solutions of systems of (ordinary or partial, linear or non-linear) differential equations from an algebraic point of view. It includes as special cases algebraic systems as well as differential systems with algebraic constraints. This algebraic theory of Joseph F Ritt and Ellis R Kolchin is further enriched by its interactions with algebraic geometry, Diophantine geometry, differential geometry, model theory, control theory, automatic theorem proving, combinatorics, and difference equations. Differential algebra now plays an important role in computational methods such as symbolic integration and symmetry analysis of differential equations. These proceedings consist of tutorial and survey papers presented at the Second International Workshop on Differential Algebra and Related Topics at Rutgers University, Newark in April 2007. As a sequel to the proceedings of the First International Workshop, this volume covers more related subjects, and provides a modern and introductory treatment to many facets of differential algebra, including surveys of known results, open problems, and new, emerging, directions of research. It is therefore an excellent companion and reference text for graduate students and researchers.

Differential Algebra and Related Topics II

Number Systems: A Path into Rigorous Mathematics aims to introduce number systems to an undergraduate audience in a way that emphasises the importance of rigour, and with a focus on providing detailed but accessible explanations of theorems and their proofs.

Quaternion Generalized Inverses

Bibliografische Angaben

Schlagworte

Bibliografische Angaben

Schlagworte

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