Format: Hardback, 769 pages, height x width: 235x155 mm, 15 Illustrations, black and white; XVIII, 769 p. 15 illus., 1 Hardback
Series: Springer Monographs in Mathematics
Pub. Date: 04-Apr-2024
ISBN-13: 9783031500886
This monograph explores key principles in the modern theory of dynamic optimization, incorporating important advances in the field to provide a comprehensive, mathematically rigorous reference. Emphasis is placed on nonsmooth analytic techniques, and an in-depth treatment of necessary conditions, minimizer regularity, and global optimality conditions related to the Hamilton-Jacobi equation is given. New, streamlined proofs of fundamental theorems are incorporated throughout the text that eliminate earlier, cumbersome reductions and constructions. The first chapter offers an extended overview of dynamic optimization and its history that details the shortcomings of the elementary theory and demonstrates how a deeper analysis aims to overcome them. Aspects of dynamic programming well-matched to analytical techniques are considered in the final chapter, including characterization of extended-value functions associated with problems having endpoint and state constraints, inverse verification theorems, sensitivity relationships, and links to the maximum principle.This text will be a valuable resource for those seeking an understanding of dynamic optimization. The lucid exposition, insights into the field, and comprehensive coverage will benefit postgraduates, researchers, and professionals in system science, control engineering, optimization, and applied mathematics.
Preface.- Overview.- Set Convergence, Measurability, and Existence of
Minimizers.- Variational Principles.- Nonsmooth Analysis.- Subdifferential
Calculus.- Differential Inclusions.- The Maximum Principle.- The Generalized
Euler-Lagrange and Hamiltonian Inclusion Conditions.- Free End-Time
Problems.- The Maximum Principle for Problems with Pathwise Constraints.- The
Euler-Lagrange and Hamiltonian Inclusion Conditions in the Presence of State
Constraints.- Regularity of Minimizers.- Dynamic Programming.- Bibliography.-
Index.
Format: Hardback, 199 pages, height x width: 235x155 mm, 6 Tables, color; 7 Illustrations, color;
4 Illustrations, black and white; IV, 199 p. 11 illus., 7 illus. in color.,
Series: Research Perspectives Ghent Analysis and PDE Center 3
Pub. Date: 14-Feb-2024
ISBN-13: 9783031485787
This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics:
1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown.
2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.
Part I Geometric Analysis.- Analysis on noncompact manifolds and index
theory: Fredholm conditions and pseudodifferential operators.- Singular value
decomposition for the X-ray transforms on the reduced Heisenberg group, and a
two-radius theorem.- Nonlocal functionals with non-standard growth.- A
variational approach to the hot spots conjecture.- Endpoint Sobolev
inequalities for vector fields and cancelling operators.- Scattering of
Maxwell potentials on curved spacetimes.- Part II. Analysis and PDEs.- Remark
on the ill-posedness for KdV-Burgers equation in Fourier amalgam spaces.-
-convergence for the bi-Laplace-Beltrami equation on hypersurfaces.- Bounded
weak solutions with Orlicz space data: an overview.- Recent progress on the
mathematical theory of wave turbulence.- Laplace-Beltrami equation on
Lipschitz hypersurfaces in the generic Bessel potential spaces.- On the
convergence Fourier series and greedy algorithm by multiplicative system.-
Asymptotics of harmonic functions in the absence of monotonicity formulas.-
Semiregular non-commutative harmonic oscillators: Some spectral asymptotic
properties.- Global compactness, subcritical approximation of the
Sobolev quotient, and a related concentration result in the Heisenberg
group.- A note on Carleson-Hunt type theorems for Vilenkin-Fourier series.-
Self-similar gravitational collapse for polytropic stars.- Control of
parabolic equations with inverse square infinite potential wells.- On
geometric estimates for some problems arising from modeling pull-in voltage
in MEMS.- A note on fractional powers of the Hermite operator.- Non-standard
version of Egorov algebra of generalized functions.- Density conditions for
coherent state subsystems of nilpotent Lie groups.- Space-time mixed norm
estimates in Riemannian symmetric spaces of non-compact type.- Analysis on
compact symmetric spaces: eigenfunctions and nonlinear SchrOodinger
equations.- Part III Applied Mathematics.- On empirical Bayes approach to
inverse problems.- The interferon influence on the infection wave
propagation.- Machine learning-based analysis of human motions
for Parkinsons disease diagnostics.
Format: Hardback, 214 pages, height x width: 235x155 mm, XIV, 214 p.
Series: RSME Springer Series 12
Pub. Date: 05-Mar-2024
ISBN-13: 9783031502576
This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leechs original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Becks triple cohomology. It also establishes connections with Grillets cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general.
Functor Categories and Cohomology.- The D-Cohomology of Monoids.- Other
Cohomologies.- Cohomology and H-Coextensions.- Cohomology of Monoids with
Operators.- Cohomology and Monoidal Groupoids.- Concluding remarks.
Format: Hardback, 287 pages, height x width: 235x155 mm, 22 Illustrations, black and white; X, 287 p. 22 illus.,
Pub. Date: 08-Apr-2024
ISBN-13: 9789819991709
By combinatorial semigroups, we mean a general term of concepts, facts and methods which are produced in investigating of algebraic and combinatorial properties, constructions, classifications and interrelations of formal languages and automata, codes, finite and infinite words by using semigroup theory and combinatorial analysis. The main research objects in this field are the elements and subsets of the free semigroups and monoids and many combinatorial properties of these objects, which are closely related to algebraic theory of semigroups.
This book first introduces some basic concepts and notations in combinatorial semigroups. Since many contents involving the constructions of (generalized) disjunctive languages and regular languages are closely related to the algebraic theory of codes, some selected topics are introduced in the following chapter, including the method of defining codes by using dependence systems, the maximality and completeness of codes, and the detailed discussion of some special kinds of codes such as convex codes, semaphore codes and solid codes. Then the remaining chapters present the main topics of the book - regular languages, disjunctive languages, and their various kinds of generalizations.
This book might be useful to researchers in mathematics who are interested in combinatorial semigroups.
Preface.- Basic Concepts and Notations.- Some Common-Used Codes.-
Regular Languages.- Disjunctive Languages.- F-Disjunctive Languages.-
Relatively Disjunctive (Regular) Languages.- Generalized Disjunctive
Languages.- PS-Regular Languages.
Format: Paperback / softback, 362 pages, height x width: 240x168 mm, XIX, 362 p.,
Series: Frontiers in Mathematics
Pub. Date: 09-Mar-2024
ISBN-13: 9783031498848
The book gives the basic results of the theory of the spaces Ap of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian's theory of spaces Ap (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the -extensions of M. M. Djrbashian's two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane. The book can be useful for a wide range of readers. It can be a good handbook for Master, PhD students and Postdoctoral Researchers for enlarging their knowledge and analytical methods, as well as a useful resource for scientists who want to extend their investigation fields.
Introduction.- Part I Omega-Weighted Classes of Area Integrable Regular
Functions. - Preliminary Results.- Spaces Apw (D) in the Unit
Disc.- Spaces Apw (C) of Entire Functions. - Nevanlinna-Djrbashian Classes of
Functions Delta-Subharmonic in the Unit Disc. - Spaces Apw,(G+) in the
Halfplane.- Orthogonal Decomposition of Functions Subharmonic in the
Halfplane.- Nevanlinna-Djrbashian Classes in the Halfplane.- Part
II Delta-Subharmonic Extension of M.M. Djrbashian Factorization
Theory.- Extension of the Factorization Theory of M.M. Djrbashian.- Banach
Spaces of Functions Delta-Subharmonic in the Unit Disc.- Functions of
Omega-Bounded Type in the Halfplane.- Subclasses of Harmonic Functions with
Nonnegative Harmonic Majorants in the Halfplane.- Subclasses of
Delta-Subharmonic Functions of Bounded Type in the Halfplane.- Banach Spaces
of Functions Delta-Subharmonic in the Halfplane. - ADDENDUM.
Format: Hardback, 358 pages, height x width: 235x155 mm, 9 Tables, color; 9 Illustrations, color;
24 Illustrations, black and white; X, 358 p. 33 illus., 9 illus. in color.,
Series: Operator Theory: Advances and Applications 295
Pub. Date: 03-Apr-2024
ISBN-13: 9783031506123
This volume features presentations from the International Workshop on Operator Theory and its Applications that was held in Krakow, Poland, September 6-10, 2022. The volume reflects the wide interests of the participants and contains original research papers in the active areas of Operator Theory. These interests include weighted Hardy spaces, geometry of Banach spaces, dilations of the tetrablock contractions, Toeplitz and Hankel operators, symplectic Dirac operator, pseudodifferential and differential operators, singular integral operators, non-commutative probability, quasi multipliers, Hilbert transform, small rank perturbations, spectral constants, Banach-Lie groupoids, reproducing kernels, and the Kippenhahn curve. The volume includes contributions by a number of the world's leading experts and can therefore be used as an introduction to the currently active research areas in operator theory.
Weighted Hardy spaces over the unit ball: the freely noncommutative and
commutative settings.- Two aspects of small diameter properties.- Hilbert
Transform in the Cartwright De Branges Space.- A Note on the Dilation of a
Certain Family of Tetrablock Contractions.- Commuting Toeplitz operators and
moment maps on Cartan domains of type III.- Branching symplectic monogenics
using a Mickelsson Zhelobenko algebra.- On non-commutative spreadability.-
Small rank perturbations of H-expansive matrices.- On the Berger-Coburn
Phenomenon.- Quasi-Multipliers and Algebrizations of an Operator Space. III.-
Maximal Noncompactness of Singular Integral Operators on L2 Spaces with Some
Khvedelidze Weights.- Mellin pseudodifferential operators and singular
integral operators with complex conjugation.- On the dual representation of
the congruence kernels and the related Delsarte type transmutations of
multidimensional differential operators.- Toeplitz Operator with a Finite
Number of Horizontal Symbols Acting on the Poly-Fock Spaces.- On Abstract
Spectral Constants.- Geometric structures related to aW-algebra.-
Composition in reproducing kernel Hilbert spaces rebours.- Kippenhahns
construction revisited.- On de Finetti-type theorems.