Format: Hardback, 401 pages, height x width: 235x155 mm, 34 Illustrations, black and white; XI, 401 p. 34 illus., 1 Hardback
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Pub. Date: 14-Apr-2024
ISBN-13: 9783031541216
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and complicated refinements. Apart from the basic theory of equations in divergence form, it includes subjects as singular perturbations, homogenization, computations, asymptotic behavior of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes systems, p-Laplace type operators, large solutions, and mountain pass techniques. Just a minimum on Sobolev spaces has been introduced and work on integration on the boundary has been carefully avoided to keep the reader attention focused on the beauty and variety of these issues.
The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original, and have not been published elsewhere. The book will be of interest to graduate students and researchers specializing in partial differential equations.
Part I Basic Techniques.- Hilbert Space Techniques.- A Survey of
Essential Analysis.- Weak Formulation of Elliptic Problems.- Elliptic
Problems in Divergence Form.- Singular Perturbation Problems.- Problems in
Large Cylinders.- Periodic Problems.- Homogenization.- Eigenvalues.-
Numerical Computations.- Part II More Advanced Theory.- Nonlinear Problems.-
L-estimates.- Linear Elliptic Systems.- The Stationary Navier--Stokes
System.- Some More Spaces.- Regularity Theory.- p-Laplace Type Equations.-
The Strong Maximum Principle.- Problems in the Whole Space.- Large
Solutions.- Mountain Pass Techniques.
Format: Hardback, 490 pages, height x width: 235x155 mm, 25 Tables, color; 26 Illustrations, color; 1 Illustrations, black and white; X, 490 p. 27 illus., 26 illus. in color., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 11-May-2024
ISBN-13: 9783031541032
This book is the first comprehensive presentation of a central topic of stochastic geometry: random mosaics that are generated by Poisson processes of hyperplanes. It thus connects a basic notion from probability theory, Poisson processes, with a fundamental object of geometry. The independence properties of Poisson processes and the long-range influence of hyperplanes lead to a wide range of phenomena which are of interest from both a geometric and a probabilistic point of view. A Poisson hyperplane tessellation generates many random polytopes, also a much-studied object of stochastic geometry. The book offers a variety of different perspectives and covers in detail all aspects studied in the original literature. The work will be useful to graduate students (advanced students in a Master program, PhD students), and professional mathematicians. The book can also serve as a reference for researchers in fields of physics, computer science, economics or engineering.
Format: Hardback, 360 pages, height x width: 235x155 mm, 2 Illustrations, color; 20 Illustrations, black and white; X, 360 p. 22 illus., 2 illus. in color., 1 Hardback
Series: Progress in Mathematics 350
Pub. Date: 06-May-2024
ISBN-13: 9783031542411
This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality.
The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries.
A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.
Table of Contents
The square root of the Laplacian.- Linear integro-differential
equations.- Fully nonlinear equations.- Obstacle problems.
Format: Hardback, 699 pages, height x width: 235x155 mm, 238 Illustrations, black and white; XIV, 699 p. 238 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 446
Pub. Date: 20-May-2024
ISBN-13: 9783031529641
This volume gathers selected papers presented at the ICMSQUARE 2023 - 12th International Conference on Mathematical Modeling in Physical Sciences held in Belgrade, Serbia from August 2831, 2023. This proceedings offers a compilation of cutting-edge research, which aims to advance the knowledge and development of high-quality research in mathematical fields related to physics, chemistry, biology, medicine, economics, environmental sciences, and more. Annually held since 2012, the ICMSQUARE conference serves as a platform for the exchange of ideas and discussions on the latest technological trends in these fields. This book is an invaluable resource for researchers, academicians, and professionals in these areas seeking to stay up-to-date with the latest developments in mathematical modeling.
Format: Hardback, 490 pages, height x width: 235x155 mm, 134 Illustrations, black and white; XVIII, 490 p. 134 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 448
Pub. Date: 13-May-2024
ISBN-13: 9783031529689
This proceedings volume convenes selected, revised papers presented at the 52nd Southeastern International Conference on Combinatorics, Graph Theory and Computing (SEICCGTC 2021), virtually held at Florida Atlantic University in Boca Raton, USA, on March 8-12, 2021. As has been a tradition since its inception in 1970, this edition once more brought together mathematicians, practitioners, and scientists around novel findings in combinatorics, graph theory and computing, and their interactions.
The lectures and works presented at the Conference have proven to be of great interest to other scientists and analysts employing these mathematical sciences in their professional activities in business, industry, and government. Such an environment promotes a better understanding of the roles of modern applied mathematics, combinatorics, and computer science. Many works have demonstrated that disciplines have increasingly contributed to each other. With this series of Conferences, the gaps between the fields tend to decrease even further.
This volume is of particular interest for the community of pure and applied mathematicians in academia, industry, and government, working in combinatorics and graph theory, as well as related areas of computer science and the interactions among these fields. Its findings can also benefit a general audience of practitioners and students from related fields
Format: Hardback, 438 pages, height x width: 235x155 mm, 90 Illustrations, color; 10 Illustrations, black and white; VIII, 438 p. 100 illus., 90 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 449
Pub. Date: 13-May-2024
ISBN-13: 9783031532115
This book convenes peer-reviewed, selected papers presented at the Tenth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Saints Constantine and Helena, Bulgaria, July 1720, 2023. Contributions are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis.
In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them to solve real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations.
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Format: Hardback, 242 pages, height x width: 235x155 mm, 46 Illustrations, black and white; VIII, 242 p. 46 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 450
Pub. Date: 16-May-2024
ISBN-13: 9783031530623
This volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almer?a, Spain, in July 2022. The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field. Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interestfor researchers, the volume will also be an invaluable resource for newcomers.
W. Fajardo, O. Lezama, C. Payares, A. Reyes and C. Rodr?guez,
Introduction to Algebraic Analysis on Ore Extensions.- S. Breaz and G. C.
Modoi, Derived equivalences induced by good silting complexes.- M. Cerqua and
A. Facchini, Pre-Lie algebras, their multiplicative lattice, and idempotent
endomorphisms.- G. Nadareishvili, Relative homological algebra for bivariant
K-theory.- S. Posur, An abelian ambient category for behaviors in algebraic
systems theory.- M. Prest, Definable categories and monoidal categories.- J.
Trlifaj, Flat Mittag-Leffler Modules, and their Relative and restricted
versions.
Format: Paperback / softback, 206 pages, height x width: 235x155 mm, 2 Illustrations, black and white; X, 206 p. 2 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2343
Pub. Date: 06-May-2024
ISBN-13: 9783031544606
This monograph provides a comprehensive treatment of the classification of small fusion systems, that is, fusion systems with few essential subgroups. It demonstrates a broad range of techniques from local group theory and fusion systems, several of which can be applied in more general settings. Addressing research problems that have not been treated in the past, it is the first text to explicitly use the amalgam method in this context.
Fusion systems offer an enticing way to unify various p-local methods employed in group theory, representation theory and homotopy theory; but as abstract constructions they are still somewhat mysterious. This book paves the way to a broad and systematic study of these categories by applying the amalgam method, thus modernizing a methodology widely used to understand the local structure of finite groups. With this comes an introduction to several vital techniques in local group theory, a generous survey of the structure and modular representation theory of some important families of finite groups, and a demonstration of the value of combinatorial methods in finite group theory and fusion systems.
Primarily aimed at researchers active in fusion systems and group amalgams, the book will also be of interest to anyone working with finite groups and their modular representations, group actions on trees, or classifying spaces. The inclusion of preliminary chapters outlining the theoretical prerequisites make it ideal for a short lecture course or as a reading group text for early career researchers and graduate students.