Format: Paperback / softback, 378 pages, height x width: 235x155 mm, weight: 599 g,
1 Illustrations, color; 6 Illustrations, black and white; XIII, 378 p. 7 illus., 1 illus. in color.
Series: Springer Proceedings in Mathematics & Statistics 390
Pub. Date: 07-Oct-2023
ISBN-13: 9783031061721
This proceedings volume gathers selected, peer-reviewed papers presented at the 41st International Conference on Infinite Dimensional Analysis, Quantum Probability and Related Topics (QP41) that was virtually held at the United Arab Emirates University (UAEU) in Al Ain, Abu Dhabi, from March 28th to April 1st, 2021. The works cover recent developments in quantum probability and infinite dimensional analysis, with a special focus on applications to mathematical physics and quantum information theory. Covered topics include white noise theory, quantum field theory, quantum Markov processes, free probability, interacting Fock spaces, and more.
By emphasizing the interconnection and interdependence of such research topics and their real-life applications, this reputed conference has set itself as a distinguished forum to communicate and discuss new findings in truly relevant aspects of theoretical and applied mathematics, notably in the field of mathematical physics, as well as an event of choice for the promotion of mathematical applications that address the most relevant problems found in industry. That makes this volume a suitable reading not only for researchers and graduate students with an interest in the field but for practitioners as well.
PART I: Quantum Probability Methods.- The nonlinear and quadratic
quantization programs(Accardi et al.).- A pedagogical note on the computation
of relative entropy of two n-mode gaussian states(Parthasarathy).- Quantum
operators of the semicircle distributions(Popa et al.).- Quantum Probability
for Modeling Cognition, Decision Making, and Articial
Intelligence(Khrennikov).- PART II: Quantum Information Methods.- Note on
Complexity of Communication Processes (Watanabe).- Trace decreasing quantum
dynamical maps: Divisibility and entanglement dynamics(Filippov).- Compound
state, its conditionality and quantum mutual information(Matsuoka).- Block
Markov Chains on Trees(Souissi).- PART III: Quantum Dynamical
Systems.- Hilbert von Neumann Modules versus Concrete von Neumann
Modules(Skeide).- Absorption and xed points for semigroups of quantum
channels(Girotti).- Characterization of Gaussian Quantum Markov
Semigroups(Poletti).- A Mean-eld Laser Quantum Master Equation(Fagnola et
al.).- Unique ergodicity and weakly monotone Fock space(Crismale).- Part
IV: Innite Dimensional Analysis.- Solutions of innite dimensional partial
dierential equations(Draouil et al.).- On Some Properties of Solution Sets
of Discontinuous Quantum Stochastic Dierential Inclusions(Dikko).-Fractional
operators from vanishing Morrey to vanishing Campanato spaces in the variable
exponent setting on quasi-metric measure spaces(Rafeiro et al.).- Part
V: Operator Algebras.- Characterization of certain traces on von Neumann
algebras(Bikchentaev).- Actions of -Morphisms on Certain Projections of
C-Matrix Algebras(Shaheen).- Part VI: Stochastic Operators.- Compatible
Linear Lypunov Function for Innite Dimensional Volterra Quadratic Stochastic
Operators(Embong).- Bijectivity of a Class of Lotka-Volterra Operators Dened
on 2D-Simplex(Hee Pah et al.).- Dynamics of stochastic Cesaro
operators(Khakimov et al.).- The dynamics of a Volterra cubic
operator(Jamilov et al.).- The dynamics of superposition of non-Volterra
quadratic stochasticoperators S2(Jamilov et al.).- A quadratic worm
propagation model(Khudoyberdiev).
Format: Paperback / softback, 535 pages, height x width: 235x155 mm, weight: 836 g, XIII, 535 p., 1 Paperback / softback
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Pub. Date: 30-Nov-2023
ISBN-13: 9783031178399
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed.
Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis.
Each chapter of this volume finishes with a list of problems ? handy for understanding and self-study ? and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume.
By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Volume I - Theory: - Topology.- Measure Theory.- Banach Space Theory.- Function Spaces.- Multivalued Analysis.- Smooth and Nonsmooth Calculus.- Nonlinear Operators.- Variational Analysis.- References.
Format: Paperback / softback, 136 pages, height x width: 240x168 mm, weight: 262 g, 25 Tables, color; 1 Illustrations, black and white; XI, 136 p. 1 illus.
Series: Synthesis Lectures on Mathematics & Statistics
Pub. Date: 08-Dec-2023
ISBN-13: 9783031149719
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
Metric Spaces.- Extension of Metric Spaces.- Fixed Point Theorems on
Extended Metric Spaces.
Format: Paperback / softback, 76 pages, height x width: 235x155 mm, 1 Illustrations, black and white; VIII, 76 p. 1 illus.
Pub. Date: 22-Feb-2024
ISBN-13: 9789819978786
This book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems.
Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful.
Chapter 1. Introduction.
Chapter 2. Viscosity Solutions.
Chapter 3. Stochastic Tug-of-War Game.
Chapter 4. Cancellation Method for Regularity of the Tug-of-War with Noise.
Chapter 5. Mean Value Characterizations.
Chapter 6. Further Regularity Methods.
Chapter 7. Open Problems and Comments.
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Format: Paperback / softback, 302 pages, height x width: 235x155 mm, weight: 492 g, 16 Tables, color; 1 Illustrations, black and white; XV, 302 p. 1 illus.,
Series: SISSA Springer Series 3
Pub. Date: 15-Dec-2023
ISBN-13: 9783031115011
This book is based on a series of lectures given by the author at SISSA, Trieste, within the PhD courses Techniques in enumerative geometry (2019) and Localisation in enumerative geometry (2021). The goal of this book is to provide a gentle introduction, aimed mainly at graduate students, to the fast-growing subject of enumerative geometry and, more specifically, counting invariants in algebraic geometry. In addition to the more advanced techniques explained and applied in full detail to concrete calculations, the book contains the proofs of several background results, important for the foundations of the theory. In this respect, this text is conceived for PhD students or research beginners in the field of enumerative geometry or related areas. This book can be read as an introduction to Hilbert schemes and Quot schemes on 3-folds but also as an introduction to localisation formulae in enumerative geometry. It is meant to be accessible without a strong background in algebraic geometry; however, three appendices (one on deformation theory, one on intersection theory, one on virtual fundamental classes) are meant to help the reader dive deeper into the main material of the book and to make the text itself as self-contained as possible.
1 Introduction.- 2 Counting in algebraic geometry.- 3 Background
material.- 4 Informal introduction to Grassmannians.- 5 Relative
Grassmannians, Quot, Hilb.- 6 The Hilbert scheme of points.- 7 Equivariant
Cohomology.- 8 The Atiyah-Bott localisation formula.- 9 Applications of the
localisation formula.- 10 The toy model for the virtual fundamental class and
its localization.- 11 Degree 0 DT invariants of a local Calabi-Yau 3-fold.-
12 DT/PT correspondence and a glimpse of GromovWitten theory .- Appendix A:
Deformation Theory.- Appendix B: Intersection Theory.- Appendix C: Perfect
obstruction theories and virtual classes.
Format: Paperback / softback, 300 pages, height x width: 235x155 mm, weight: 486 g, 2 Tables, color; 1 Illustrations, black and white; XIII, 300 p. 1 illus
Series: Studies in Universal Logic
Pub. Date: 02-Dec-2023
ISBN-13: 9783031223327
How should we think about the meaning of the words that make up our language? How does reference of these terms work, and what is their referent when these are connected to abstract objects rather than to concrete ones? Can logic help to address these questions? This collection of papers aims to unify the questions of syntax and semantics of language, which span across the fields of logic, philosophy and ontology of language. The leading motif of the presented selection is the differentiation between linguistic tokens (material, concrete objects) on the one hand and linguistic types (ideal, abstract objects) on the other. Through a promenade among articles that span over all of the Author’s career, this book addresses the complex philosophical question of the ontology of language by following the crystalline conceptual tools offered by logic. At the core of Wybraniec-Skardowska’s scholarship is the idea that language is an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. The application throughout the book of tools of classical logic and set theory results fosters the emergence of a general formal logical theory of syntax, semantics and of the pragmatics of language, which takes into account the duality token-type in the understanding of linguistic expressions. Via a functional approach to language itself, logic appears as ontologically neutral with respect to existential assumptions relating to the nature of linguistic expressions and their extra-linguistic counterparts.
The book is addressed to readers both at the graduate and undergraduate level, but also to a more general audience interested in getting a firmer grip on the interplay between reality and the language we use to describe and understand it.