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Non-commutative Ring Theory

VON NULL AUF MATHE

Rechnen mit Buchstaben: Terme und Bruchterme

Calculus for the Curious

This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications.&nbsp;Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
&nbsp;

This textbook presents an introduction to continuum mechanics covering fundamental mathematical tools, general laws and major models. The material is based on lectures held at Gubkin's Russian State University of Oil and Gas. It also includes material related to a joint research seminar with the Institute of Problems in Mechanics of the Russian Academy of Science. The knowledge provided is necessary to understand the structure of existing models, to read and understand the literature and to apply existing methods consciously. Results from computer simulations of virtual models of oil-gas-production are presented to illustrate applications.&nbsp;Graduate students as well as researchers in applied mathematics will benefit from this self-contained text which is enriched by many examples and exercises.
&nbsp;

With Applications to Oil and Gas Development

Introduction to Continuum Mechanics

London Mathematical Society Lecture Note Series

The present volume features contributions from the 2022 BIRS-CMO workshop 'Moduli, Motives and Bundles - New Trends in Algebraic Geometry' held at the Casa Matemática Oaxaca (CMO), in partnership with the Banff International Research Station for Mathematical Innovation and Discovery (BIRS). The first part presents overview articles on enumerative geometry, moduli stacks of coherent sheaves, and torsors in complex geometry, inspired by related mini course lecture series of the workshop. The second part features invited contributions by experts on a diverse range of recent developments in algebraic geometry, and its interactions with number theory and mathematical physics, offering fresh insights into this active area. Students and young researchers will appreciate this text's accessible approach, as well as its focus on future research directions and open problems.

New Trends in Algebraic Geometry

Moduli, Motives and Bundles

Science Networks. Historical Studies

This unique reference work systematically presents and studies mathematical terms, sourcing literature from antiquity until the 20th century.
The book provides detailed and reliable information on the origins and developments of more than 1,000 mathematical terms from all branches of mathematics. The dictionary is based on extensive research of the primary literature, cites from original sources, provides historical illustrations, discusses synonyms and competing terms, and quotes critical or approving comments on newly created terms. Each entry is self-contained and includes a bibliography. All major mathematical fields are represented, ranging from geometry and arithmetic to, for example, calculus, topology, and category theory.
This set comprises both volumes I and II, covering the letters from A through Z.

Volumes I and II

A Historical Dictionary of Mathematical Terms

Signal processing is ubiquitous in many fields of science and engineering. This textbook is tailored specifically for graduate students and presents linear algebra, which is requisite knowledge in these fields, in a form explicitly targeted to signal processing and related disciplines. Written by an experienced author with over 35 years of expertise in signal processing research and teaching, this book provides the necessary foundation in a focused and accessible manner, offering a practical approach to linear algebra without sacrificing rigor. Emphasis is placed on a deeper conceptualization of material specific to signal processing so students may more readily adapt this knowledge to actual problems in the field. Since other emerging areas, such as machine learning, are closely related to signal processing, the book also provides the necessary background in this discipline. The book includes many examples and problems relevant to signal processing, offering explanations and insights that are difficult to find elsewhere.Fundamentals of Linear Algebra for Signal Processing&nbsp;will allow students to master the essential knowledge of linear algebra for signal processing. It is also an essential guide for researchers and practitioners in biomedical, electrical, chemical engineering, and related disciplines.<ul><li>All necessary algebraic concepts commonly used in the signal processing context are covered;</li><li>A rich set of carefully-constructed signal processing examples is provided throughout the text;</li><li>Designed as a primary text in linear algebra for engineering and science graduate students.</li></ul>

Signal processing is ubiquitous in many fields of science and engineering. This textbook is tailored specifically for graduate students and presents linear algebra, which is requisite knowledge in these fields, in a form explicitly targeted to signal processing and related disciplines. Written by an experienced author with over 35 years of expertise in signal processing research and teaching, this book provides the necessary foundation in a focused and accessible manner, offering a practical approach to linear algebra without sacrificing rigor. Emphasis is placed on a deeper conceptualization of material specific to signal processing so students may more readily adapt this knowledge to actual problems in the field. Since other emerging areas, such as machine learning, are closely related to signal processing, the book also provides the necessary background in this discipline. The book includes many examples and problems relevant to signal processing, offering explanations and insights that are difficult to find elsewhere.Fundamentals of Linear Algebra for Signal Processing&nbsp;will allow students to master the essential knowledge of linear algebra for signal processing. It is also an essential guide for researchers and practitioners in biomedical, electrical, chemical engineering, and related disciplines.

Fundamentals of Linear Algebra for Signal Processing

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double-inflection saddles,&nbsp;-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;inflection-source (sink) flows,-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;parabola-saddles (saddle-center),-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;third-order parabola-saddles,&nbsp;-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;third-order saddles and centers.&nbsp;·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Develops a theory of crossing and product cubic systems with a self-linear and crossing-quadratic product vector field;·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Presents singular equilibrium series with inflection-source (sink) flows and networks of simple equilibriums;·&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Shows equilibrium appearing bifurcations of (2,2)-double-inflection saddles and inflection-source (sink) flows.

This book, the 14th of 15 related monographs on Cubic Dynamical Systems, discusses crossing and product cubic systems with a self-linear and crossing-quadratic product vector field. Dr. Luo discusses singular equilibrium series with inflection-source (sink) flows that are switched with parabola-source (sink) infinite-equilibriums. He further describes networks of simple equilibriums with connected hyperbolic flows are obtained, which are switched with inflection-source (sink) and parabola-saddle infinite-equilibriums, and nonlinear dynamics and singularity for such crossing and product cubic systems. In such cubic systems, the appearing bifurcations are:-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;double-inflection saddles,&nbsp;-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;inflection-source (sink) flows,-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;parabola-saddles (saddle-center),-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;third-order parabola-saddles,&nbsp;-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;third-order saddles and centers.

Self-linear and Crossing-quadratic Product Vector Field

Two-dimensional Crossing and Product Cubic Systems, Vol. I

Annals of Mathematics Studies

A comprehensive new theory of adelic line bundles on quasi-projective varieties over finitely generated fieldsThis book introduces a comprehensive theory of adelic line bundles on quasi-projective varieties over finitely generated fields, developed in both geometric and arithmetic contexts. In the geometric setting, adelic line bundles are defined as limits of line bundles on projective compactifications under the boundary topology. In the arithmetic setting, they are defined as limits of Hermitian line bundles on projective arithmetic compactifications, also under the boundary topology. After establishing these foundational definitions, the book uses the theory to explore key concepts such as intersection theory, effective sections, volumes, and positivity of adelic line bundles. It also applies these results to study height functions of algebraic points and prove an equidistribution theorem on quasi-projective varieties. This theory has broad applications in the study of numerical, dynamical, and Diophantine properties of moduli spaces, quasi-projective varieties, and varieties over finitely generated fields.

Adelic Line Bundles on Quasi-projective Varieties

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

Textbooks in Mathematics

This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Eleventh Edition and the only official one. It is designed to supplement the text and the author's original approach to instruction.

This is the only available student solutions manual prepared by the author of Contemporary Abstract Algebra, Eleventh Edition and the only official one. It is designed to supplement the text and the author’s original approach to instruction.

Student Solutions Manual for Gallian's Contemporary Abstract Algebra

De Gruyter Series in Nonlinear Analysis and Applications

Electrodynamics, Hydrodynamics, Field Theory, and Quantum Mechanics

Space-Time Algebra of Sedeons

Algorithms and Computation in Mathematics

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,&nbsp; polymake for polyhedral and tropical geometry, and&nbsp; 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.&nbsp;The book is an invitation to use OSCAR.&nbsp; With discussions of theoretical and algorithmic aspects included, it offers a multitude of explicit code snippets.&nbsp; These are valuable for interested researchers from graduate students through established experts.

Algorithms and Examples

The Computer Algebra System OSCAR

Non-commutative Ring Theory

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