The Diverse World Of Pdes

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The Diverse World of PDEs

I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
The Diverse World of PDEs Book PDF

Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 250 pages
File Size : 40,6 Mb
Release : 2023-08-21
Category : Mathematics
ISBN : 9781470471477

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The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at the Independent University of Moscow and Moscow State University, Moscow, Russia. The papers are devoted to various interrelations of nonlinear PDEs with geometry and integrable systems. The topics discussed are: gravitational and electromagnetic fields in General Relativity, nonlocal geometry of PDEs, Legendre foliated cocycles on contact manifolds, presymplectic gauge PDEs and Lagrangian BV formalism, jet geometry and high-order phase transitions, bi-Hamiltonian structures of KdV type, bundles of Weyl structures, Lax representations via twisted extensions of Lie algebras, energy functionals and normal forms of knots, and differential invariants of inviscid flows. The companion volume (Contemporary Mathematics, Volume 789) is devoted to Algebraic and Cohomological Aspects of PDEs.

The Diverse World of PDEs

I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
The Diverse World of PDEs Book PDF

Author : I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky
Publisher : American Mathematical Society
Page : 236 pages
File Size : 55,6 Mb
Release : 2023-08-23
Category : Mathematics
ISBN : 9781470473556

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The Diverse World of PDEs by I. S. Krasil′shchik,A. B. Sossinsky,A. M. Verbovetsky Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

The Diverse World of PDEs

I. S. Krasil′shchik
The Diverse World of PDEs Book PDF

Author : I. S. Krasil′shchik
Publisher : Unknown
Page : 0 pages
File Size : 54,8 Mb
Release : 2023
Category : Electronic books
ISBN : 1470474093

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The Diverse World of PDEs by I. S. Krasil′shchik Pdf

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frolicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

Algebraic and Topological Aspects of Representation Theory

Mee Seong Im,Bach Nguyen,Arik Wilbert
Algebraic and Topological Aspects of Representation Theory Book PDF

Author : Mee Seong Im,Bach Nguyen,Arik Wilbert
Publisher : American Mathematical Society
Page : 240 pages
File Size : 46,9 Mb
Release : 2024-01-22
Category : Mathematics
ISBN : 9781470470340

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Algebraic and Topological Aspects of Representation Theory by Mee Seong Im,Bach Nguyen,Arik Wilbert Pdf

This volume contains the proceedings of the virtual AMS Special Session on Geometric and Algebraic Aspects of Quantum Groups and Related Topics, held from November 20–21, 2021. Noncommutative algebras and noncommutative algebraic geometry have been an active field of research for the past several decades, with many important applications in mathematical physics, representation theory, number theory, combinatorics, geometry, low-dimensional topology, and category theory. Papers in this volume contain original research, written by speakers and their collaborators. Many papers also discuss new concepts with detailed examples and current trends with novel and important results, all of which are invaluable contributions to the mathematics community.

Mathematical Analyses of Decisions, Voting and Games

Michael A. Jones,David McCune,Jennifer M. Wilson
Mathematical Analyses of Decisions Voting and Games Book PDF

Author : Michael A. Jones,David McCune,Jennifer M. Wilson
Publisher : American Mathematical Society
Page : 210 pages
File Size : 42,5 Mb
Release : 2024-03-25
Category : Mathematics
ISBN : 9781470469788

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Mathematical Analyses of Decisions, Voting and Games by Michael A. Jones,David McCune,Jennifer M. Wilson Pdf

This volume contains the proceedings of the virtual AMS Special Session on Mathematics of Decisions, Elections and Games, held on April 8, 2022. Decision theory, voting theory, and game theory are three related areas of mathematics that involve making optimal decisions in different contexts. While these three areas are distinct, much of the recent research in these fields borrows techniques from other branches of mathematics such as algebra, combinatorics, convex geometry, logic, representation theory, etc. The papers in this volume demonstrate how the mathematics of decisions, elections, and games can be used to analyze problems from the social sciences.

Recent Developments in Fractal Geometry and Dynamical Systems

Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Recent Developments in Fractal Geometry and Dynamical Systems Book PDF

Author : Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma
Publisher : American Mathematical Society
Page : 270 pages
File Size : 45,8 Mb
Release : 2024-04-18
Category : Mathematics
ISBN : 9781470472160

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Recent Developments in Fractal Geometry and Dynamical Systems by Sangita Jha,Mrinal Kanti Roychowdhury,Saurabh Verma Pdf

This volume contains the proceedings of the virtual AMS Special Session on Fractal Geometry and Dynamical Systems, held from May 14–15, 2022. The content covers a wide range of topics. It includes nonautonomous dynamics of complex polynomials, theory and applications of polymorphisms, topological and geometric problems related to dynamical systems, and also covers fractal dimensions, including the Hausdorff dimension of fractal interpolation functions. Furthermore, the book contains a discussion of self-similar measures as well as the theory of IFS measures associated with Bratteli diagrams. This book is suitable for graduate students interested in fractal theory, researchers interested in fractal geometry and dynamical systems, and anyone interested in the application of fractals in science and engineering. This book also offers a valuable resource for researchers working on applications of fractals in different fields.

Recent Advances in Diffeologies and Their Applications

Jean-Pierre Magnot
Recent Advances in Diffeologies and Their Applications Book PDF

Author : Jean-Pierre Magnot
Publisher : American Mathematical Society
Page : 272 pages
File Size : 45,8 Mb
Release : 2024-02-02
Category : Mathematics
ISBN : 9781470472542

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Recent Advances in Diffeologies and Their Applications by Jean-Pierre Magnot Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful.

Recent Advances in Noncommutative Algebra and Geometry

K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang
Recent Advances in Noncommutative Algebra and Geometry Book PDF

Author : K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang
Publisher : American Mathematical Society
Page : 288 pages
File Size : 48,6 Mb
Release : 2024-05-30
Category : Mathematics
ISBN : 9781470472399

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Recent Advances in Noncommutative Algebra and Geometry by K. A. Brown,T. J. Hodges,M. Vancliff,J. J. Zhang Pdf

This volume contains the proceedings of the conference Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, held from June 20–24, 2022, at the University of Washington, Seattle, in honor of S. Paul Smith's 65th birthday. The articles reflect the wide interests of Smith and provide researchers and graduate students with an indispensable overview of topics of current interest. Specific fields covered include: noncommutative algebraic geometry, representation theory, Hopf algebras and quantum groups, the elliptic algebras of Feigin and Odesskii, Calabi-Yau algebras, Artin-Schelter regular algebras, deformation theory, and Lie theory. In addition to original research contributions the volume includes an introductory essay reviewing Smith's research contributions in these fields, and several survey articles.

Advances in Functional Analysis and Operator Theory

Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Advances in Functional Analysis and Operator Theory Book PDF

Author : Marat V. Markin,Igor V. Nikolaev,Carsten Trunk
Publisher : American Mathematical Society
Page : 250 pages
File Size : 43,8 Mb
Release : 2024-04-09
Category : Mathematics
ISBN : 9781470473051

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Advances in Functional Analysis and Operator Theory by Marat V. Markin,Igor V. Nikolaev,Carsten Trunk Pdf

This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18–22, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison–Singer transforms.

Optimal Control of Partial Differential Equations

Fredi Tröltzsch
Optimal Control of Partial Differential Equations Book PDF

Author : Fredi Tröltzsch
Publisher : American Mathematical Society
Page : 417 pages
File Size : 54,5 Mb
Release : 2024-03-21
Category : Mathematics
ISBN : 9781470476441

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Optimal Control of Partial Differential Equations by Fredi Tröltzsch Pdf

Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.

Compactifications, Configurations, and Cohomology

Peter Crooks,Alexandru I. Suciu
Compactifications Configurations and Cohomology Book PDF

Author : Peter Crooks,Alexandru I. Suciu
Publisher : American Mathematical Society
Page : 168 pages
File Size : 42,8 Mb
Release : 2023-09-25
Category : Mathematics
ISBN : 9781470469924

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Compactifications, Configurations, and Cohomology by Peter Crooks,Alexandru I. Suciu Pdf

This volume contains the proceedings of the Conference on Compactifications, Configurations, and Cohomology, held from October 22–24, 2021, at Northeastern University, Boston, MA. Some of the most active and fruitful mathematical research occurs at the interface of algebraic geometry, representation theory, and topology. Noteworthy examples include the study of compactifications in three specific settings—algebraic group actions, configuration spaces, and hyperplane arrangements. These three types of compactifications enjoy common structural features, including relations to root systems, combinatorial descriptions of cohomology rings, the appearance of iterated blow-ups, the geometry of normal crossing divisors, and connections to mirror symmetry in physics. On the other hand, these compactifications are often studied independently of one another. The articles focus on new and existing connections between the aforementioned three types of compactifications, thereby setting the stage for further research. It draws on the discipline-specific expertise of all contributors, and at the same time gives a unified, self-contained reference for compactifications and related constructions in different contexts.

Imaging, Vision and Learning Based on Optimization and PDEs

Xue-Cheng Tai,Egil Bae,Marius Lysaker
Imaging Vision and Learning Based on Optimization and PDEs Book PDF

Author : Xue-Cheng Tai,Egil Bae,Marius Lysaker
Publisher : Springer
Page : 255 pages
File Size : 40,8 Mb
Release : 2018-11-19
Category : Computers
ISBN : 9783319912745

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Imaging, Vision and Learning Based on Optimization and PDEs by Xue-Cheng Tai,Egil Bae,Marius Lysaker Pdf

This volume presents the peer-reviewed proceedings of the international conference Imaging, Vision and Learning Based on Optimization and PDEs (IVLOPDE), held in Bergen, Norway, in August/September 2016. The contributions cover state-of-the-art research on mathematical techniques for image processing, computer vision and machine learning based on optimization and partial differential equations (PDEs). It has become an established paradigm to formulate problems within image processing and computer vision as PDEs, variational problems or finite dimensional optimization problems. This compact yet expressive framework makes it possible to incorporate a range of desired properties of the solutions and to design algorithms based on well-founded mathematical theory. A growing body of research has also approached more general problems within data analysis and machine learning from the same perspective, and demonstrated the advantages over earlier, more established algorithms. This volume will appeal to all mathematicians and computer scientists interested in novel techniques and analytical results for optimization, variational models and PDEs, together with experimental results on applications ranging from early image formation to high-level image and data analysis.

Partial Differential Equations in Classical Mathematical Physics

Isaak Rubinstein,Lev Rubinstein
Partial Differential Equations in Classical Mathematical Physics Book PDF

Author : Isaak Rubinstein,Lev Rubinstein
Publisher : Cambridge University Press
Page : 704 pages
File Size : 47,7 Mb
Release : 1998-04-28
Category : Mathematics
ISBN : 0521558468

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Partial Differential Equations in Classical Mathematical Physics by Isaak Rubinstein,Lev Rubinstein Pdf

The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.

An Introduction to Nonlinear Partial Differential Equations

J. David Logan
An Introduction to Nonlinear Partial Differential Equations Book PDF

Author : J. David Logan
Publisher : John Wiley & Sons
Page : 416 pages
File Size : 50,5 Mb
Release : 2008-04-11
Category : Mathematics
ISBN : 9780470225950

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An Introduction to Nonlinear Partial Differential Equations by J. David Logan Pdf

Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.

Intelligent Systems Modeling and Simulation II

Samsul Ariffin Abdul Karim
Intelligent Systems Modeling and Simulation II Book PDF

Author : Samsul Ariffin Abdul Karim
Publisher : Springer Nature
Page : 688 pages
File Size : 53,7 Mb
Release : 2022-10-12
Category : Technology & Engineering
ISBN : 9783031040283

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Intelligent Systems Modeling and Simulation II by Samsul Ariffin Abdul Karim Pdf

This book develops a new system of modeling and simulations based on intelligence system. As we are directly moving from Third Industrial Revolution (IR3.0) to Fourth Industrial Revolution (IR4.0), there are many emergence techniques and algorithm that appear in many sciences and engineering branches. Nowadays, most industries are using IR4.0 in their product development as well as to refine their products. These include simulation on oil rig drilling, big data analytics on consumer analytics, fastest algorithm for large-scale numerical simulations and many more. These will save millions of dollar in the operating costs. Without any doubt, mathematics, statistics and computing are well blended to form an intelligent system for simulation and modeling. Motivated by this rapid development, in this book, a total of 41 chapters are contributed by the respective experts. The main scope of the book is to develop a new system of modeling and simulations based on machine learning, neural networks, efficient numerical algorithm and statistical methods. This book is highly suitable for postgraduate students, researchers as well as scientists that have interest in intelligent numerical modeling and simulations.