Format: Paperback , 384 pages, height x width: 235x155 mm, weight: 605 g,
2 Illustrations, black and white; XII, 384 p. 2 illus.,
Series: Linear Operators and Linear Systems 286
Pub. Date: 22-Dec-2022
ISBN-13: 9783030764753
This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis.
Signal processing constitutes a strong presence in several of the papers.
A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.
Editorial Introduction.- On Parseval Frames of Kernel Functions in de
Branges Spaces of Entire Vector Valued Functions.- Differential
Subordinations in Harmonic Mappings.- The Segal-Bargmann Transform in
Clifford Analysis.- On the Caratheodory-Fejer interpolation problem for
Stieltjes functions.- Harmonic Analysis of some arithmetical functions.-
Symmetric measures, continuous networks, and dynamics.- Multi Variable
Semicircular Processes From - Homomorphisms and Operators.- Representation
formulae for the determinant in a neighborhood of the identity.-
Parametrization of the Solution Set of a Matricial Truncated Hamburger Moment
Problem by a Schur Type Algorithm.- The Wiener algebra and singular
integrals.- Techniques to derive estimates for integral means and other
geometric quantities related to conformal mappings.- Complex Ternary Analysis
and Applications.
Format: Paperback / softback, 262 pages, height x width: 235x155 mm, weight: 415 g,
131 Illustrations, color; 65 Illustrations, black and white; VI, 262 p. 196 illus., 131 illus. in color.
Pub. Date: 18-Dec-2022
ISBN-13: 9783030880613
This volume is a collection of essays on complex symmetries. It is curated, emphasizing the analysis of the symmetries, not the various phenomena that display those symmetries themselves. With this, the volume provides insight to nonspecialist readers into how individual simple symmetries constitute complex symmetry. The authors and the topics cover many different disciplines in various sciences and arts.
Simple symmetries, such as reflection, rotation, translation, similitude, and a few other simple manifestations of the phenomenon, are all around, and we are aware of them in our everyday lives. However, there are myriads of complex symmetries (composed of a bulk of simple symmetries) as well. For example, the well-known helix represents the combination of translational and rotational symmetry. Nature produces a great variety of such complex symmetries. So do the arts.
The contributions in this volume analyse selected examples (not limited to geometric symmetries). These include physical symmetries, functional (meaning not morphological) symmetries, such as symmetries in the construction of the genetic code, symmetries in human perception (e.g., in geometry education as well as in constructing physical theories), symmetries in fractal structures and structural morphology, including quasicrystal and fullerene structures in stable bindings and their applications in crystallography and architectural design, as well as color symmetries in the arts.
The volume is rounded of with beautiful illustrations and presents a fascinating panorama of this interdisciplinary topic.
Gyoergy Darvas: Complex Symmetries, Introduction.- Douglas Dunham: Complex Symmetries in Repeating Hyperbolic Patterns.- Paul Hertz: Ignotheory: A Compositional System for Intermedia Art Based on Tiling Patterns and Labelled Graphs.- Ashish Kumar Upadhyay: Symmetries of Maps on Surfaces.- Koji Miyazaki and Motonaga Ishii: Symmetry in Projection of 4-dimensional Regular Polychora.- Guy Inchbald: Morphic Polytopes and Symmetries.- Takeshi Sugimoto: Inducing the Symmetries out of the Complexity: The Kepler Triangle and its Kin as a Model Problem.- Jim Lehman: Synchronizing the Isotropic Vctor Matrix with the Stellated Vector Matrix.- Andras Recski: An Analogy and Several Symmetries.- Dmitriy Gurevich: Discrete Lattices on the Single Bearing Spiral: From Geometry to Botany.- Simone Brasili and Riccardo Piergallini: Symmetry and Invariance: Interdisciplinary teaching.- Eleonora Stettner and Gyoergy Emese: Dilative Rotation, Dilative Reflection in Mathematics, Nature, Art, and Education.- Janos Szasz Saxon and Gabor Kis: Relationship of Symmetry and Combinatorics in the Poly-universe Game.- Marina Voinova: Symmetry in Arrow-like Salt Crystals.- Laszlo Szabados: Symmetries in Stellar, Galactic, and Extragalactic Astronomy.- Sergey V. Petoukhov, Elena S. Petukhova and Vladimir V. Verevkin: Symmetries and the Genetic, Code.- Kas Oosterhuis: Global Symmetry Local Asymmetry: In the Realized Buildings by the Innovation Studio ONL BV.- Katarzyna Szymanska-Stulka: Theme, Motive, Structure and Symmetry - Pentasonata by Andrzej Panufnik.- FreIlgen: Fluid Symmetry: Logical to Artists, Mesmerizing to Viewers.- Paul B. Re: Complex Symmetries in Reograms.- Patrice Jeener: Graphic Illustrations of Complex Symmetries.
Format: Paperback / softback, 393 pages, height x width: 235x155 mm, weight: 734 g, 30 Tables,
color; 19 Illustrations, color; 21 Illustrations, black and white; XI, 393 p. 40 illus., 19 illus. in color.,
Series: Springer INdAM Series 48
Pub. Date: 23-Dec-2022
ISBN-13: 9783030829483
The volume covers most of the topics addressed and discussed during the Workshop INdAM "Recent advances in kinetic equations and applications", which took place in Rome (Italy), from November 11th to November 15th, 2019. The volume contains results on kinetic equations for reactive and nonreactive mixtures and on collisional and noncollisional Vlasov equations for plasmas. Some contributions are devoted to the study of phase transition phenomena, kinetic problems with nontrivial boundary conditions and hierarchies of models. The book, addressed to researchers interested in the mathematical and numerical study of kinetic equations, provides an overview of recent advances in the field and future research directions.
- Sharpening of Decay Rates in Fourier Based Hypocoercivity Methods. - Quantum Drift-Diffusion Equations for a Two-Dimensional Electron Gas with Spin-Orbit Interaction. - A Kinetic BGK Relaxation Model for a Reacting Mixture of Polyatomic Gases. - On Some Recent Progress in the Vlasov-Poisson-Boltzmann System with Diffuse Reflection Boundary. - The Vlasov Equation with Infinite Mass. - Mathematical and Numerical Study of a Dusty Knudsen Gas Mixture: Extension to Non-spherical Dust Particles. - Body-Attitude Alignment: First Order Phase Transition, Link with Rodlike Polymers Through Quaternions, and Stability. - The Half-Space Problem for the Boltzmann Equation with Phase Transition at the Boundary. - Recent Developments on Quasineutral Limits for Vlasov-Type Equations. - A Note on Acoustic Limit for the Boltzmann Equation. - Thermal Boundaries in Kinetic and Hydrodynamic Limits. - Control of Collective Dynamics with Time-Varying Weights. - Kinetic Modelling of Autoimmune Diseases. - A Generalized Slip-Flow Theory for a Slightly Rarefied Gas Flow Induced by Discontinuous Wall Temperature. - A Revisit to the Cercignani-Lampis Model: Langevin Picture and Its Numerical Simulation. - On the Accuracy of Gyrokinetic Equations in Fusion Applications.
Format: Paperback / softback, 239 pages, height x width: 235x155 mm,
weight: 397 g, XIII, 239 p., 1
Series: Springer Monographs in Mathematics
Pub. Date: 07-Jan-2023
ISBN-13: 9783030896621
Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension.
The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Preface.- Notation and Terminology. - I. Structure of Locally Reductive Lie Algebras.-
1. Finite-dimensional Lie algebras.-
2. Finite-dimensional Lie superalgebras.-
3. Root-reductive Lie algebras.-
4. Two generalizations.-
5. Splitting Borel subalgebras of sl(infinity), frak o (infinity), sp(infinity) and generalized flags.-
6. General Cartan, Borel and parabolic subalgebras of gl(infinity) and sl(infinity).- II. Modules over Locally Reductive Lie Algebras.-
7. Tensor modules of sl(infinity), frak o(infinity), sp (infinity).-
8. Weight modules.- 9.Generalized Harish-Chandra modules.- III. Geometric aspects. - 10.The Bott-Borel-Weil Theorem.- References.- Index of Notation.- Index.
Format: Hardback, 208 pages, height x width: 235x155 mm, weight: 506 g, XIV, 208 p., 1 Hardback
Pub. Date: 05-Feb-2023
ISBN-13: 9789811998799
This book is devoted to a new aspect of linear and nonlinear non-Fredholm operators and its applications. The domain of applications of theory developed here is potentially much wider than that presented in the book. Therefore, a goal of this book is to invite readers to make contributions to this fascinating area of mathematics.
First, it is worth noting that linear Fredholm operators, one of the most important classes of linear maps in mathematics, were introduced around 1900 in the study of integral operators. These linear Fredholm operators between Banach spaces share, in some sense, many properties with linear maps between finite dimensional spaces. Since the end of the previous century there has been renewed interest in linear ? nonlinear Fredholm maps from a topological degree point of view and its applications, following a period of gstagnation" in the mid-1960s. Now, linear and nonlinear Fredholm operator theory and the solvability of corresponding equations both from the analytical and topological points of view are quite well understood.
Also noteworthy is, that as a by-product of our results, we have obtained an important tool for modelers working in mathematical biology and mathematical medicine, namely, the necessary conditions for preserving positive cones for systems of equations without Fredholm property containing local ? nonlocal diffusion as well as terms for transport and nonlinear interactions.
1 Auxiliary Materials.- 2 Solvability in the sense of sequences: non-Fredholm operators.- 3 Solvability of some integro-differential equations with mixed diffusion.- 4 Existence of solutions for some non-Fredholm integro-differential equations with mixed diffusion.- 5 Non-Fredholm Schroedinger type operators.
Format: Hardback, 189 pages, height x width: 235x155 mm, weight: 471 g,
1 Illustrations, black and white; X, 189 p. 1 illus.,
Pub. Date: 07-Feb-2023
ISBN-13: 9783031237614
This book investigates Lorentzian structures in the four-dimensional space-time, supplemented either by a covector field of the time-direction or by a scalar field of the global time. Furthermore, it proposes a new metrizable model of gravity. In contrast to the usual General Relativity theory, where all ten components of the symmetric pseudo-metric are independent variables, the gravity model presented here essentially depends only on a single four-covector field, and is restricted to have only three-independent components. However, the author proves that the gravitational field, governed by the proposed model and generated by some massive body, resting and spherically symmetric in some coordinate system, is given by a pseudo-metric that coincides with the well known Schwarzschild metric from General Relativity. The Maxwell equations and electrodynamics are also investigated in the framework of the proposed model. In particular, the covariant formulation of electrodynamics of moving dielectrics and para/diamagnetic media is derived.
1. Preliminary introduction.-
2. Basic definitions and statements of the main results.- 2.1. Generalized-Lorentz's structures with time-direction and global time.- 2.1.1. Pseudo-Lorentzian coordinate systems.- 2.2. Kinematical Lorentz's structure with global time.- 2.3. Kinematical and Dynamical generalized-Lorentz structures with time direction.- 2.4. Lagrangian of the motion of a classical point particle in a given pseudo-metric with time direction.- 2.5. Lagrangian of the electromagnetic field in a given pseudo-metric.- 2.6. Correlated pseudo-metrics.- 2.7. Kinematically correlated models of the genuine gravity.- 2.8. Lagrangian for dynamical time-direction and its limiting case.- 2.9 Lagrangian of the genuine gravity.-
3. Mass, charge and Lagrangian densities and currents of the system of classical point particles.-
4. The total simplified Lagrangian in (2.9.23), (2.9.24), for the limiting case of (2.9.20) in a cartesian coordinate system.-
5. The Euler-Lagrange for the Lagrangian of the motion of a classical point particle in a cartesian coordinate system.-
6. The Euler-Lagrange for the Lagrangian of the gravitational and Electromagnetic fields in (4.0.71) in a cartesian coordinate system.- 6.1. The Euler-Lagrange for the Lagrangian in (4.1.71) in a cartesian coordinate system.-
7. Gravity field of spherically symmetric massive resting body in a coordinate system which is cartesian and inertial simultaneously.- 7.1. Certain curvilinear coordinate system in the case of stationary radially symmetric gravitational field and relation to the Schwarzschild metric.-
8. Newtonian gravity as an approximation of (6.0.52).- 8.1. Newtonian gravity as an approximation of (6.1.52).-
9. Polarization and magnetization.- 9.1 Polarization and magnetization in a cartesian coordinate system.-
10. Detailed proves of the stated Theorems, Propositions and Lemmas.-
11. Appendix: some technical statements.