Format: Hardback, 187 pages, height x width: 235x155 mm, 31 Tables, color; 32 Illustrations,
color; 8 Illustrations, black and white; VIII, 187 p. 40 illus., 32 illus. in color.
Series: Trends in Mathematics
Pub. Date: 02-Oct-2023
ISBN-13: 9783031363344
This volume presents a timely overview of control theory and inverse problems, and highlights recent advances in these active research areas. The chapters are based on talks given at the spring school "Control & Inverse Problemsh held in Monastir, Tunisia in May 2022. In addition to providing a snapshot of these two areas, chapters also highlight breakthroughs on more specific topics, such as:
Controllability of dynamical systems
Information transfer in multiplier equations
Nonparametric instrumental regression
Control of chained systems
The damped wave equation
Control and Inverse Problems will be a valuable resource for both established
researchers as well as more junior members of the community.
Stabilization of one dimensional wave equation with variable potential and torque.- Controlling a dynamic system through reinforcement learning.- Landweber iterative method for an inverse source problem of space-fractional diffusion equations.- On the Spectrum Distribution of Parametric Second-order Delay Differential Equations. Perspectives in Partial Pole Placement.- Exact controllability of the linear Biharmonic Schrdinger equation with space-dependent coefficients.- Carleman estimate and application to the stabilization of a dissipative hyperbolic system.- On the transfer of information in multiplier equations.- A Global Carleman Estimates of the linearized sixth-order 1 D-Boussinesq equation Application.- Nonparametric instrumental regression via mollification.- Finite-time stabilization of some classes of infinite dimensional systems.- Dispersion on certain Cartesian products of graphs.- Tracking Control of Chained Systems: application to nonholonomic unicycle mobile robots.- A short elementary proof of the Gearhart-Pruss theorem for bounded semigroups.- Revisit the damped wave equation.
Format: Hardback, 270 pages, height x width: 235x155 mm, 64 Tables, color; 9 Illustrations, color;
114 Illustrations, black and white; X, 270 p. 123 illus., 9 illus. in color
Series: Trends in Mathematics
Pub. Date: 27-Sep-2023
ISBN-13: 9783031336805
Mark Vishik was one of the prominent figures in the theory of partial differential equations. His ground-breaking contributions were instrumental in integrating the methods of functional analysis into this theory.
In this book, friends and pupils of Mark Vishik remember his life and work. From his early years as a student to his connection with the Lwow school of Stephan Banach and to his later career as a respected teacher and mentor, Vishik's legacy is explored in detail. His research and pedagogical work influenced hundreds of undergraduate and graduate students, many of whom went on to become leading figures in their own right. The reader is introduced to a number of remarkable scientists whose lives intersected with Vishik's, including S. Banach, J. Schauder, I. N. Vekua, N. I. Muskhelishvili, L. A. Lyusternik, I. G. Petrovskii, S. L. Sobolev, I. M. Gelfand, M. G. Krein, A. N. Kolmogorov, N. I. Akhiezer, J. Leray, J.-L. Lions, L. Schwartz, L. Nirenberg, and others.
Part I Memoirs.- Notes about my Father. - Mark Iosifovich and Asia
Moiseevna: random reminiscences.- Meetings with Mark Iosifovich Vishik.- My
scientific advisor Mark Iosifovich Vishik. - M. I. Vishik in my life.- Un
grand mathematician, le Professeur Vishik.- Recollections of a former Mechmat
student.- A word about M. I. Vishik.- Mark Iosifovich Vishik.- Teacher and
Friend.- M. I. Vishik.- In Mark Vishik's own words.- Remembering Wladek
Lyantse.- Part II Science.- Symposium in honor of Professor Mark Vishik.
Berlin, 2001.- International Conference, Moscow, 2012.- The Scottish Book,
Problem 192.- General elliptic boundary value problems in bounded domains.-
On the Vishik-Lyusternik method.- Mark Vishik's work on quasilinear
equations.- Attractors for nonlinear nonautonomous equations.- Rigorous
results in space-periodic two-dimensional turbulence.- Attractors of
Hamiltonian nonlinear partial differential equations.- The true story of
Quatum Ergodic Theorem.- Bibliography of Mark Vishik.
Format: Paperback / softback, 91 pages, height x width: 235x155 mm, weight: 180 g, 13 Illustrations, color;
4 Illustrations, black and white; XV, 91 p. 17 illus., 13 illus. in color
Series: JSS Research Series in Statistics
Pub. Date: 18-Jul-2023
ISBN-13: 9789819941711
This book presents the latest results related to one- and two-way models for time series data. Analysis of variance (ANOVA) is a classical statistical method for IID data proposed by R.A. Fisher to investigate factors and interactions of phenomena. In contrast, the methods developed in this book apply to time series data. Testing theory of the homogeneity of groups is presented under a wide variety of situations including uncorrelated and correlated groups, fixed and random effects, multi- and high-dimension, parametric and nonparametric spectral densities. These methods have applications in several scientific fields. A test for the existence of interactions is also proposed. The book deals with asymptotics when the number of groups is fixed and sample size diverges. This framework distinguishes the approach of the book from panel data and longitudinal analyses, which mostly deal with cases in which the number of groups is large. The usefulness of the theory in this book is illustrated by numerical simulation and real data analysis. This book is suitable for theoretical statisticians and economists as well as psychologists and data analysts.
Introduction.- One-way fixed effects model.- One-way fixed effects model for high-dimensional time series.- One-way fixed and random effects models for correlated groups.- Two-way random effects model for correlated cells.- Optimal test for one-way random effects model.- Numerical analysis.- Empirical data analysis.
Format: Hardback, 294 pages, height x width: 235x155 mm, 95 Illustrations, color;
9 Illustrations, black and white; XIV, 294 p. 104 illus., 95 illus. in color
Series: Statistics and Computing
Pub. Date: 04-Oct-2023
ISBN-13: 9783031302756
This textbook introduces the fundamental concepts and methods of statistical learning. It uses Python and provides a unique approach by blending theory, data examples, software code, and exercises from beginning to end for a profound yet practical introduction to statistical learning.
The book consists of three parts: The first one presents data in the framework of probability theory, exploratory data analysis, and unsupervised learning. The second part on inferential data analysis covers linear and logistic regression and regularization. The last part studies machine learning with a focus on support-vector machines and deep learning. Each chapter is based on a dataset, which can be downloaded from the book's homepage.
In addition, the book has the following features:
Chapter 1: Fundamentals of Data.
Chapter 2: Exploratory Data Analysis.
Chapter 3: Unsupervised Learning.- Part II: Inferential Data Analyses.
Chapter 4: Linear Regression.
Chapter 5: Logistic Regression.
Chapter 6: Regularization.- Part III: Machine Learning.
Chapter 7: Support-Vector Machines.
Chapter 8: Deep Learning.
Format: Hardback, 364 pages, height x width: 235x155 mm, 141 Illustrations, color;
3 Illustrations, black and white; IX, 364 p. 144 illus., 141 illus. in color
Pub. Date: 07-Sep-2023
ISBN-13: 9789819937714
This book highlights the latest developments on the numerical methods for inverse scattering problems associated with acoustic, electromagnetic, and elastic waves. Inverse scattering problems are concerned with identifying unknown or inaccessible objects by wave probing data, which makes possible many industrial and engineering applications including radar and sonar, medical imaging, nondestructive testing, remote sensing, and geophysical exploration. The mathematical study of inverse scattering problems is an active field of research. This book presents a comprehensive and unified mathematical treatment of various inverse scattering problems mainly from a numerical reconstruction perspective. It highlights the collaborative research outputs by the two groups of the authors yet surveys and reviews many existing results by global researchers in the literature. The book consists of three parts respectively corresponding to the studies on acoustic, electromagnetic, and elastic scattering problems. In each part, the authors start with in-depth theoretical and computational treatments of the forward scattering problems and then discuss various numerical reconstruction schemes for the associated inverse scattering problems in different scenarios of practical interest. In addition, the authors provide an overview of the existing results in the literature by other researchers. This book can serve as a handy reference for researchers or practitioners who are working on or implementing inverse scattering methods. It can also serve as a graduate textbook for research students who are interested in working on numerical algorithms for inverse scattering problems.
Introduction.- Direct Acoustic Scattering Problems.- Numerical Inverse
Acoustic Scattering Problems.- Direct Electromagnetic Scattering Problems.-
Numerical Inverse Electromagnetic Scattering Problems.- Direct Elastic
Scattering Problems.- Numerical Inverse Elastic Scattering Problems.-
Miscellaneous topics.- Others.
Format: Hardback, 141 pages, height x width: 240x168 mm, weight: 450 g, 8 Illustrations, color;
58 Illustrations, black and white; XIV, 141 p. 66 illus., 8 illus. in color.
Series: Synthesis Lectures on Operations Research and Applications
Pub. Date: 09-Jul-2023
ISBN-13: 9783031357183
This book presents a new search paradigm for solving the Traveling Salesman Problem (TSP). The intrinsic difficulty of the TSP is associated with the combinatorial explosion of potential solutions in the solution space. The author introduces the idea of using the attractor concept in dynamical systems theory to reduce the search space for exhaustive search for the TSP. Numerous examples are used to describe how to use this new search algorithm to solve the TSP and its variants including: multi-objective TSP, dynamic TSP, and probabilistic TSP. This book is intended for readers in the field of optimization research and application.
Introduction.- The Traveling Salesman Problem (TSP).- The Nature of Heuristic Local Search.- he Attractor-Based Search System.- Solving Multi-objective TSP.- Solving Dynamic TSP.- Solving Probabilistic TSP.- Conclusion.
Format: Paperback / softback, 213 pages, height x width: 240x168 mm, XI, 213 p., 1 Paperback / softback
Series: Frontiers in Mathematics
Pub. Date: 18-Sep-2023
ISBN-13: 9783031371486
This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle.
Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
Chapter.
1. PreliminariesChapter.
2. Why boundary regularity?Chapter.
3.
Continuous extension of holomorphic mappingsChapter.
4. Boundary smoothness
of holomorphic mappingsChapter.
5. Proper holomorphic mappingsChapter.
6.
Uniformization of domains with large automorphism groupsChapter.
7. Local
equivalence of real analytic hypersurfacesChapter.
8. Geometry of real
hypersurfaces: analytic continuationChapter.
9. Segre varietiesChapter.
10.
Holomorphic correspondencesChapter.
11. Extension of proper holomorphic
mappingsChapter.
12. Extension in C2AppendixBibliographyIndex