Format: Paperback / softback, 265 pages, height x width: 235x155 mm, 13 Illustrations, color;
5 Illustrations, black and white; XIV, 265 p. 18 illus., 13 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 378
Pub. Date: 24-Feb-2023
ISBN-13: 9783030874346
This book grew out of the Random Transformations and Invariance in Stochastic Dynamics conference held in Verona from the 25th to the 28th of March 2019 in honour of Sergio Albeverio. It presents the new area of studies concerning invariance and symmetry properties of finite and infinite dimensional stochastic differential equations.This area constitutes a natural, much needed, extension of the theory of classical ordinary and partial differential equations, where the reduction theory based on symmetry and invariance of such classical equations has historically proved to be very important both for theoretical and numerical studies and has given rise to important applications. The purpose of the present book is to present the state of the art of the studies on stochastic systems from this point of view, present some of the underlying fundamental ideas and methods involved, and to outline the main lines for future developments. The main focus is on bridging the gap between deterministic and stochastic approaches, with the goal of contributing to the elaboration of a unified theory that will have a great impact both from the theoretical point of view and the point of view of applications. The reader is a mathematician or a theoretical physicist. The main discipline is stochastic analysis with profound ideas coming from Mathematical Physics and Lie's Group Geometry. While the audience consists essentially of academicians, the reader can also be a practitioner with Ph.D., who is interested in efficient stochastic modelling.
Albeverio, S., De Vecchi, F.C.: Some recent developments on Lie Symmetry analysis of stochastic differential equations.- Applebaum, D., Ming, L.: Markov processes with jumps on manifolds and Lie groups.- Cordoni, F., Di Persio, L.: Asymptotic expansion for a Black-Scholes model with small noise stochastic jump diffusion interest rate.- Cruzeiro, A.B., Zambrini, J.C.: Stochastic geodesics.- DeVecchi, F.C., Gubinelli, M.: A note on supersymmetry and stochastic differential equations.- Ebrahimi-Fard, K, Patras, F.: Quasi shuffle algebras in non-commutative stochastic calculus.- Elworthy, K.D.: Higher order derivatives of heat semigroups on spheres and Riemannian symmetric spaces.- Gehringer, J., Li, X.M.: Rough homogenisation with fractional dynamics.- Holm, D.D., Luesink, E.: Stochastic geometric mechanics with diffeomorphisms.- Izydorczyk, L., Oudjane, N., Russo, F.: McKean Feynman-Kac probabilistic representations of non linear partial differential equations.- Lescot, P., Valade, L.: Bernestein processes, isovectors and machanics.- Marinelli, C., Scarpa, L.: On the positivity of local mild solutions to stochastic evolution equations.- Privault, N.: Invariance of Poisson point processes by moment identities with statistical applications.
Format: Paperback / softback, 267 pages, height x width: 235x155 mm, weight: 433 g,
28 Illustrations, color; 21 Illustrations, black and white; IX, 267 p. 49 illus., 28 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 379
Pub. Date: 04-Feb-2023
ISBN-13: 9789811662997
This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations. This book is a collection of selected papers presented at the international conference of Functional Differential Equations and Applications (FDEA-2019), 7th in the series, held at Ariel University, Israel, from August 22-27, 2019. Topics covered in the book include classical properties of functional differential equations as oscillation/non-oscillation, representation of solutions, sign properties of Green's matrices, comparison of solutions, stability, control, analysis of boundary value problems, and applications. The primary audience for this book includes specialists on ordinary, partial and functional differential equations, engineers and doctors dealing with modeling, and researchers in areas of mathematics and engineering.
Angela Slavova: Dynamical Behaviour of Integro-Differential Equations arising in Nano-Structures.- Jiri Benedikt, Petr Girg, and Lukas Kotrla: Nonlinear Models of the Fluid Flow in Porous Media and Their Methods of StudyMikhail Chirkov and S.Sergey Rusakov: Modeling of Control of the Immune Response in the Acute Form of an Infectious Disease under Conditions of Uncertainty.- G.V. Demidenko and I.I. Matveeva: The Second Lyapunov Method for Time-Delay Systems.- S.V. Rusakov, V.G. Gilev, and A.Yu. Rakhmanov: Diffusion-Kinetic Model of Curing of Epoxy Polymer.- Vasyl Martsenyuk, Mikolaj Karpinski, Aleksandra Klos-Witkowska, and Andriy Sverstiuk: On Qualitative Research of Lattice Dynamical System of Two- and Three-Dimensional Biopixels Array.- Khusainov Denys and Bychkov Oleksii: Research on Solutions Stability for Dynamic Switched Time-Delay Systems.- Gershon Kresin and Tehiya Ben Yaakov: Some Extremal Problems for Solutions of the Modified Helmholtz Equation in the Half-Space.- Medea Iordanishvili, Tea Shavadze and Tamaz Tadumadze: Delay Optimization Problem for One Class of Functional Differential Equation.- Alexey Kolchev and Ivan Egoshin: Some Problems of Mathematical Modeling of Radiophysical Sounding Signals.- Roman Koplatadze and Ivan Egoshin: Oscillation Criteria for Higher-Order Linear Differential Equations.- Irina Astashova, Alexey Filinovskiy and Dmitriy: On Necessary Conditions of Optimality to the Extremal Problem for Parabolic Equations.- T. Lazebnik, S. Yanetz, and S. Bunimovich-Mendrazitsky: PDE Modeling of Bladder Cancer Treatment Using BCG Immunotherapy.- A.V. Podolskiy and T.A. Shaposhnikova: Homogenization of a Parabolic Equation for P-Laplace Operator in a Domain Perforated along (N - 1)-Dimensional Manifold with Dynamical Boundary Condition Specified On Perforations Boundary: Critical Case.- Seshadev Padhi: Positive Solutions of Cantilever Beam Equation Depending on Parameter.- Irina Volinsky, Alexander Domoshnitsky, Marina Bershadsky and Roman Shklyar: Marchuk's Models of Infection Diseases: New Developments.- Yaroslav Petrivskyi and Volodymyr Petrivskyi: Some Properties of the Solution of the Nonlinear Equation of Oscillations in Modeling the Magnetic Separation.- Sergey Labovskiy and Manuel Alves: Poisson Problem for a Functional Differential Equation: Positivity of a Quadratic Functional, Jacobi Condition.- Tatiana Korchemkina: On Asymptotic Behavior of the First Derivatives of Bounded Solutions to Second-Order Differential Equations with General Power-Law Nonlinearity.- Alexander Domoshnitsky, Oleg Kupervasser, Hennadii Kutomanov, and Roman Yavich: A Method for Stabilization of Ground Robot Path Controlled by Airborne Autopilot with Time Delay.- Dan Gamliel: Periodic Solutions for a Class of Impulsive Delay Differential Equations.
Format: Paperback / softback, 101 pages, height x width: 235x155 mm, 20 Tables, color;
16 Illustrations, color; 4 Illustrations, black and white; XIV, 101 p. 20 illus., 16 illus. in color.,
Series: SpringerBriefs in Physics
Pub. Date: 27-Mar-2023
ISBN-13: 9783031247811
This brief book introduces the Poisson-Boltzmann equation in three chapters that build upon one another, offering a systematic entry to advanced students and researchers. Chapter one formulates the equation and develops the linearized version of Debye-Huckel theory as well as exact solutions to the nonlinear equation in simple geometries and generalizations to higher-order equations. Chapter two introduces the statistical physics approach to the Poisson-Boltzmann equation. It allows the treatment of fluctuation effects, treated in the loop expansion, and in a variational approach. First applications are treated in detail: the problem of the surface tension under the addition of salt, a classic problem discussed by Onsager and Samaras in the 1930s, which is developed in modern terms within the loop expansion, and the adsorption of a charged polymer on a like-charged surface within the variational approach. Chapter three finally discusses the extension of Poisson-Boltzmann theory to explicit solvent. This is done in two ways: on the phenomenological level of nonlocal electrostatics and with a statistical physics model that treats the solvent molecules as molecular dipoles. This model is then treated in the mean-field approximation and with the variational method introduced in Chapter two, rounding up the development of the mathematical approaches of Poisson-Boltzmann theory. After studying this book, a graduate student will be able to access the research literature on the Poisson-Boltzmann equation with a solid background.
Derivation of the Poisson-Boltzmann equation.- Generalizations of the Poisson-Boltzmann equation.- Theory and its Confrontation with Experiment.
Format: Hardback, 434 pages, height x width: 235x155 mm, 3 Illustrations, black and white; XVI, 434 p. 3 illus
Series: Theoretical and Mathematical Physics
Pub. Date: 17-Apr-2023
ISBN-13: 9783031219276
This book presents a modern view of anomalies in quantum field theories. It is divided into six parts. The first part is preparatory covering an introduction to fermions, a description of the classical symmetries, and a short introduction to conformal symmetry. The second part of the book is devoted to the relation between anomalies and cohomology. The third part deals with perturbative methods to compute gauge, diffeomorphism and trace anomalies. In the fourth part the same anomalies are calculated with non-perturbative heat-kernel-like methods. Part five is devoted to the family's index theorem and its application to chiral anomalies, and to the differential characters and their applications to global anomalies. Part six is devoted to special topics including a complete calculation of trace and diffeomorphism anomalies of a Dirac fermion in a MAT background in two dimensions, Wess-Zumino terms in field theories, sigma models, their local and global anomalies and their cancelation, and finally the analysis of the worldsheet, sigma model, and target space anomalies of string and superstring theories. The book is targeted to researchers and graduate students.
I. Basic tools I Fermions 2 Classical and BRST symmetries 3 Conformal symmetry II. Anomalies and cohomology 4 Effective actions and anomalies 5 Cohomological analysis of anomalies III. Perturbative methods for anomalies 6 Feynman diagrams and regularizations 7 Perturbative diffeomorphism and trace anomalies IV. Non-perturbative methods. (A) heat kernel 8 Functional non-perturbative methods 9 Explicit non-perturbative derivations 10 Metric-axial-tensor (MAT) background V. Non-perturbative methods. (B) Index theorem 11 Geometry of anomalies 12 Anomalies as obstructions: the Atiyah-Singer family's index theorem 13 Global anomalies VI. Special topics 14 MAT in 2d 15 Wess-Zumino terms 16 Sigma model anomalies 17 Anomalies and (super)string theories
Format: Hardback, 190 pages, height x width: 235x155 mm, 13 Tables, color;
13 Illustrations, color; 1 Illustrations, black and white; X, 190 p. 14 illus., 13 illus. in color.
Series: SISSA Springer Series 4
Pub. Date: 07-Apr-2023
ISBN-13: 9783031241505
This volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to higher dimensional varieties) from different aspects: the historical development that led to the theory of algebraic surfaces and the classification theorem of algebraic surfaces by Castelnuovo and Enriques; the use of such a classical geometric approach, as the one introduced by Castelnuovo, to study linear systems of hypersurfaces; and the algebraic methods used to find implicit equations of parametrized algebraic curves and surfaces, ranging from classical elimination theory to more modern tools involving syzygy theory and Castelnuovo-Mumford regularity. Since our subject has a long and venerable history, this book cannot cover all the details of this broad topic, theory and applications, but it is meant to serve as a guide for both young mathematicians to approach the subject from a classical and yet computational perspective, and for experienced researchers as a valuable source for recent applications.
Chapter
1. The $P_{12}$-Theorem: the Classification of surfaces and its historical development, written by Fabrizio Catanese. The first chapter explains the main steps and the strategy of the classification of algebraic surfaces, with a view to higher dimensional geometry, and with a historical discussion of the achievement of the classification, starting from the work of Castelnuovo and Enriques and encompassing the many developments which took place in the 20th century. It contains the first full treatment of the so-called P_{12}-theorem by Castelnuovo and Enriques, including a novel critical analysis.Chapter
2. Linear systems of hypersurfaces and beyond, written by Elisa Postinghel. The second chapter treats the dimensionality problem for linear systems of plane curves and of hypersurfaces of projective n-spaces with assigned multiple points. It offers a survey on the progress made towards this and related questions over a 120 year time span. The ideas presented stem from work of G. Castelnuovo and of B. Segre and are coupled with more modern tools from toric geometry, the theory of Mori dream spaces and sheaf cohomology.
Chapter
3. Implicit representations of algebraic curves and surfaces, written by Laurent Buse. The last chapter deals with a basic issue in geometry: one may easily find the intersection of a curve with a surface in three dimensional space if the surface is given via an implicit description through an equation. If the surface is given parametrically, the solution of the problem goes through the implicitization of the surface. This problem belongs to the classical elimination theory, and has seen an impetuous development in the last 30 years through new methods from homological and commutative algebra.