Format: Paperback / softback, 290 pages, height x width: 240x168 mm, 11 Illustrations, color; 2 Illustrations,
black and white; X, 290 p. 13 illus., 11 illus. in color., 1 Paperback / softback
Series: Oberwolfach Seminars 49
Pub. Date: 09-Oct-2022
ISBN-13: 9783031057922
This book presents the notes from the seminar on wave phenomena given in 2019 at the Mathematical Research Center in Oberwolfach.
The research on wave-type problems is a fascinating and emerging field in mathematical research with many challenging applications in sciences and engineering. Profound investigations on waves require a strong interaction of several mathematical disciplines including functional analysis, partial differential equations, mathematical modeling, mathematical physics, numerical analysis, and scientific computing.
The goal of this book is to present a comprehensive introduction to the research on wave phenomena. Starting with basic models for acoustic, elastic, and electro-magnetic waves, topics such as the existence of solutions for linear and some nonlinear material laws, efficient discretizations and solution methods in space and time, and the application to inverse parameter identification problems are covered. The aim of this book is to intertwine analysis and numerical mathematics for wave-type problems promoting thus cooperative research projects in this field.
Space-time approximations for linear acoustic, elastic, and electro-magnetic wave equations.- Local wellposedness and long-time behavior of quasilinear Maxwell equations.- Error analysis of second-order time integration methods for discontinuous Galerkin discretizations of Friedrichs' systems.- An abstract framework for inverse wave problems with applications.
Format: Hardback, 544 pages, height x width: 235x155 mm, 24 Illustrations, color; 9 Illustrations,
black and white; XVI, 544 p. 33 illus., 24 illus. in color., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 396
Pub. Date: 06-Oct-2022
ISBN-13: 9789811947506
This volume presents modern trends in the area of symmetries and their applications based on contributions to the Workshop "Lie Theory and Its Applications in Physics" held in Sofia, Bulgaria (on-line) in June 2021.
Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a big interdisciplinary and interrelated field.
The topics covered in this Volume are the most modern trends in the field of the Workshop: Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, Exceptional quantum algebra for the standard model of particle physics, Gauge Theories and Applications, Structures on Lie Groups and Lie Algebras.
This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.
Plenary Talks: T. Kobayashi, Multiplicity in Restricting Minimal Representations.- Yang-Hui He, From the String Landscape to the Mathematical Landscape: a Machine-Learning Outlook.- I. Todorov, Octonionic Clifford Algebra for the Internal Space of the Standard Model.- P. Vitale, The Jacobi Sigma Model.- P. Aschieri, Levi-Civita Connections on Braided Algebras.- N. Bobev, Notes on AdS4 Holography and Higher-Derivative Supergravity.- T. Brzezinski, Homothetic Rota-Baxter Systems and Dyckm-Algebras.- M. Henkel, Quantum Dynamics Far from Equilibrium: a Case Study in the Spherical Model.- Hankyung Ko and V. Mazorchuk, On First Extensions in S -Subcategories of O.- Robert de Mello Koch and Sanjaye Ramgoolam, Higher Dimensional CFTs as 2D Conformally-Equivariant Topological Field Theories.- G. Manolakos, G. Patellis and G. Zoupanos, Reducing the N = 1, 10D E8 Gauge Theory over a Modified Flag Manifold.- String Theories, (Super-)Gravity, Cosmology: Andre Alves Lima, Galen M. Sotkov and Marian Stanishkov, Ramond States of the D1-D5 CFT Away from the Free Orbifold Point.- L. Anguelova, Primordial Black Hole Generation in a Two-field Inflationary Model.- D. Staicova, Late Time Cosmic Acceleration with Uncorrelated Baryon Acoustic Oscillations.- L. Ravera, On the Hidden Symmetries of D = 11 Supergravity.- F. Nieri, Defects at the Intersection: the Supergroup Side.- T. Masuda, A New S-matrix Formula and Extension of the State Space in Open String Field Theory.- E. Boffo, Dual Dilaton with R and Q Fluxes.- Representation Theory: E. Poletaeva, On 1-Dimensional Modules over the Super-Yangian of the Superalgebra Q(1).- N. I. Stoilova and Joris Van der Jeugt, A Klein Operator for Paraparticles.- G. Sengor and C. Skordis, Principal and Complementary Series Representations at the Late-Time Boundary of de Sitter.- S. Aoki, Janos Balog, T. Onogi, and S. Yokoyama, Bulk Reconstruction from a Scalar CFT at the Boundary by the Smearing with the Flow Equation.- Y. Wang and Chih-Hao Fu, Building Momentum Kernel from Shapovalov Form.- Ilia Smilga, Action of w0 on VL for Orthogonal and Exceptional Groups.- Ood Shabtai, Pairs of Spectral Projections of Spin Operators.- Integrable Systems: Jean-Emile Bourgine, Algebraic Engineering and Integrable Hierarchies.- Cestm ir Burdik and O. Navratil, Nested Bethe Ansatz for RTT-Algebra An.- O. Vaneeva, O. Magda and A. Zhalij, Lie Reductions and Exact Solutions of Generalized Kawahara Equations.- Y. Nasuda, Several Exactly Solvable Quantum Mechanical Systems and the SWKB Quantization Condition.- A. Pribytok, Automorphic Symmetries and AdSn Integrable Deformations.- Applications to Quantum Theory: M. Kirchbach, T. Popov, and J.-A. Vallejo, The Conformal-Symmetry-Color-Neutrality Connection in Strong Interaction.- I. Salom and N. Manojlovic, s (2) Gaudin Model with General Boundary Terms.- T. Barron and A. Kazachek, Entanglement of Mixed States in Kahler Quantization.- J. Alnefjord, A. Lifson, C. Reuschle, and M. Sjodahl, The Chirality-Flow Formalism for Standard Model Calculations.- F. Kuipers, Spacetime Stochasticity and Second Order Geometry.- Special Mathematical Results: P. Moylan, Velocity Reciprocity in Flat and Curved Space-Time.- S. Stoimenov and M. Henkel, Meta-Schrodinger Transformations.- Hulya Arg uz, The Quantum Mirror to the Quartic del Pezzo Surface.- A. Ganchev, Bidirectional Processes - in Category Theory, Physics, Engineering.- Gauge Theories and Applications: Richard S. Garavuso, Nonholomorphic Superpotentials in Heterotic Landau-Ginzburg Models.- F. Feruglio, Automorphic Forms and Fermion Masses.- T. Ishibashi, Wilson Lines and Their Laurent Positivity.- Maro Cvitan, Predrag Dominis Prester, Stefano Gregorio Giaccari, Mateo Paulisi c, and Ivan Vukovic, Gauging Higher-Spin-Like Symmetries Using the Moyal Product.- N. Ikeda and S. Sasaki, Integration of Double Field Theory Algebroids and Pre-rackoid in Doubled Geometry.- H. Mori, S. Sasaki, K. Shiozawa, Doubled Aspects of Algebroids and Gauge Symmetry in Double Field Theory.- C. Anghel and D. Cheptea, Lie Algebroids and Weight Systems.- Structures on Lie Groups and Lie Algebras: K. Arashi, Visible Actions of Certain Affine Transformation Groups of a Siegel Domain of the Second Kind.- A. Brus, Ji ri Hrivnak and L. Motlochova, Quantum Particle on Lattices in Weyl Alcoves.- A. Latorre and L. Ugarte, Abelian J-Invariant Ideals on Nilpotent Lie Algebras.- Alexis Langlois-Remillard, The Dihedral Dunkl-Dirac Symmetry Algebra with Negative Clifford Signature.- Tekin Karadag , Lie Structure on Hopf Algebra Cohomology.- Esther Garcia, Miguel Gomez Lozano, and Ruben Munoz Alcazar, Filtration Associated to an Abelian Inner Ideal and the Speciality of the Subquotient of a Lie Algebra.- Esther Garcia, Miguel Gomez Lozano, and Guillermo Vera de Salas, Nilpotent Inner Derivations in Prime Superalgebras.
Pages: 320
ISBN: 978-981-125-848-0 (hardcover)
A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.
The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter ?? intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.
Preface
Introduction
Sequences of Reaction-Diffusion Problems: Convergence:
Variational Convergence of Nonlinear Reaction-Diffusion Equations
Variational Convergence of Nonlinear Distributed Time Delays Reaction-Diffusion Equations
Variational Convergence of Two Components Nonlinear Reaction-Diffusion Systems
Variational Convergence of Integrodifferential Reaction-Diffusion Equations
Variational Convergence of a Class of Functionals Indexed by Young Measures
Sequences of Reaction-Diffusion Problems: Stochastic Homogenization:
Stochastic Homogenization of Nonlinear Reaction-Diffusion Equations
Stochastic Homogenization of Nonlinear Distributed Time Delays Reaction-Diffusion Equations
Stochastic Homogenization of Two Components Nonlinear Reaction-Diffusion Systems
Stochastic Homogenization of Integrodifferential Reaction-Diffusion Equations
Stochastic Homogenization of Non Diffusive Reaction Equations and Memory Effect
Appendices:
Gronwall Type Inequalities
Basic Notions on Variational Convergences
Ergodic Theory and Subadditive Processes
Large Deviations Principle
Measure Theory
Inf-Convolution and Parallel Sum
Bibliography
Notation
Index
Graduate students and researchers.
Series on Concrete and Applicable Mathematics: Volume 23
Pages: 450
ISBN: 978-981-125-664-6 (hardcover)
ISBN: 978-981-125-793-3 (softcover)
Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.
This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.
The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.
Vectors and Matrices
Vector Spaces and Inner-Product Spaces
Systems of Linear Equations and Inverses of Matrices
Determinants
Linear Mappings and Matrices
Eigenvalues, Invariant Subspaces, Canonical Forms
Special Matrices
Elements of Matrix Analysis
Readership: Written primarily for undergraduate and graduate students studying engineering, economics and business; can also be used in courses offered by the mathematics department, or by any kind of engineering and social sciences; can also be used by researchers in mathematics, economics, engineering; in addition, high school special courses, and teacher training courses can employ this textbook.
Pages: 300
ISBN: 978-1-80061-265-5 (hardcover)
ISBN: 978-1-80061-274-7 (softcover)
This book provides a gentle introduction to the foundations of Algebraic Geometry, starting from computational topics (ideals and homogeneous ideals, zero loci of ideals) up to increasingly intrinsic and abstract arguments, like "Algebraic Varieties", whose natural continuation is a more advanced course on the theory of schemes, vector bundles and sheaf-cohomology.
Valuable to students studying Algebraic Geometry and Geometry, A First Course in Algebraic Geometry and Algebraic Varieties contains around 60 solved exercises to help students thoroughly understand the theories introduced in the book. Proofs of the results are carried out in full details.
Many examples are discussed which reinforces the understanding of both the theoretical elements and their consequences as well as the possible applications of the material.
Preface
Basics on Commutative Algebra
Algebraic Affine Sets
Algebraic Projective Sets
Topological Properties. Algebraic Varieties
Regular and Rational Functions on Algebraic Varieties
Morphisms of Algebraic Varieties
Products of Algebraic Varieties
Rational maps of Algebraic Varieties
Completeness of Projective Varieties
Dimension of Algebraic Varieties
Fiber-Dimension. Semicontinuity
Tangent Spaces. Smoothness of Algebraic Varieties
Solutions to Exercises
Bibliography
Readership:
Advanced undergraduate students (specifically in their 3rd year of undergraduate study or their 1st year of postgraduate study) in the field of Algebraic Geometry; advanced Bachelor courses in Geometry or first courses Geometry during postgraduate study