https://doi.org/10.1142/12534 | October 2021
Pages: 220
ISBN: 978-981-124-651-7 (hardcover)
ISBN: 978-981-124-653-1 (ebook)
This book is concerned with functional methods (nonlinear semigroups of contractions, nonlinear m-accretive operators and variational techniques) in the theory of nonlinear partial differential equations of elliptic and parabolic type. In particular, applications to the existence theory of nonlinear parabolic equations, nonlinear Fokker-Planck equations, phase transition and free boundary problems are presented in details. Emphasis is put on functional methods in partial differential equations (PDE) and less on specific results.
Preface
Preliminaries
Monotone and Accretive Operators in Banach Spaces
Nonlinear Elliptic Boundary Value Problems
Nonlinear Dissipative Dynamics
Bibliography
Index
Specialists in the theory of partial differential equations and mathematical physics. This text is recommended also for an one semester graduate course on partial differential equations.
https://doi.org/10.1142/12545 | December 2021
Pages: 512
ISBN: 978-981-124-709-5 (hardcover)
ISBN: 978-981-124-756-9 (softcover)
Most branches of science involving random fluctuations can be approached by Stochastic Calculus. These include, but are not limited to, signal processing, noise filtering, stochastic control, optimal stopping, electrical circuits, financial markets, molecular chemistry, population dynamics, etc. All these applications assume a strong mathematical background, which in general takes a long time to develop. Stochastic Calculus is not an easy to grasp theory, and in general, requires acquaintance with the probability, analysis and measure theory.
The goal of this book is to present Stochastic Calculus at an introductory level and not at its maximum mathematical detail. The author's goal was to capture as much as possible the spirit of elementary deterministic Calculus, at which students have been already exposed. This assumes a presentation that mimics similar properties of deterministic Calculus, which facilitates understanding of more complicated topics of Stochastic Calculus.
The second edition contains several new features that improved the first edition both qualitatively and quantitatively. First, two more chapters have been added, Chapter 12 and Chapter 13, dealing with applications of stochastic processes in Electrochemistry and global optimization methods.
This edition contains also a final chapter material containing fully solved review problems and provides solutions, or at least valuable hints, to all proposed problems. The present edition contains a total of about 250 exercises.
This edition has also improved presentation from the first edition in several chapters, including new material.
A Few Introductory Problem
Basic Notions
Useful Stochastic Processes
Properties of Stochastic Processes
Stochastic Integration
Stochastic Differentiation
Stochastic Integration Techniques
Stochastic Differential Equations
Applications of Brownian Motion
Girsanov's theorem and Brownian Motion
Miscellaneous Applications
Applications to Electrochemistry
Methods of Global Optimization
Review Problems
Hints and Solutions
Advanced undergraduate and graduate level students in Science, Economics, and Business. It can be used by researchers and practitioners in both academia and industry.
https://doi.org/10.1142/12495 | December 2021
Pages: 800
ISBN: 978-981-124-502-2 (hardcover)
For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.
Introduction
Homology and Cohomology
de Rham Cohomology
Singular Homology and Cohomology
Simplicial Homology and Cohomology
Homology and Cohomology of CW Complexes
Poincare Duality
Presheaves and Sheaves; Basics
?ech Cohomology with Values in a Presheaf
Presheaves and Sheaves; A Deeper Look
Derived Functors, δ-Functors, and ∂-Functors
Universal Coefficient Theorems
Cohomology of Sheaves
Alexander and Alexander?Lefschetz Duality
Spectral Sequences
Bibliography
Index
Senior undergraduates of maths major who are familiar with some basic notions of linear algebra and abstract algebra, in particular the notion of a module. Also good for graduate students of abstract algebra courses.
https://doi.org/10.1142/12375 | December 2021
Pages: 168
ISBN: 978-981-124-051-5 (hardcover)
The book introduces the fundamentals and applications of the lattice Boltzmann method (LBM) for incompressible viscous flows. It is written clearly and easy to understand for graduate students and researchers.
The book is organized as follows. In Chapter 1, the SRT- and MRT-LBM schemes are derived from the discrete Boltzmann equation for lattice gases and the relation between the LBM and the Navier-Stokes equation is explained by using the asymptotic expansion (not the Chapman-Enskog expansion). Chapter 2 presents the lattice kinetic scheme (LKS) which is an extension method of the LBM and can save memory because of needlessness for storing the velocity distribution functions. In addition, an improved LKS which can stably simulate high Reynolds number flows is presented. In Chapter 3, the LBM combined with the immersed boundary method (IB-LBM) is presented. The IB-LBM is well suitable for moving boundary flows. In Chapter 4, the two-phase LBM is explained from the point of view of the difficulty in computing two-phase flows with large density ratio. Then, a two-phase LBM for large density ratios is presented. In Appendix, sample codes (available for download) are given for users.
program_LBM_eng_fortran (10 KB)
program_LBM_eng_cpp (12 KB)
program_LBM_eng_python (28 KB)
Contents:
Lattice Boltzmann Method (LBM)
Lattice Kinetic Scheme (LKS)
Immersed Boundary-Lattice Boltzmann Method (IB-LBM)
Two-Phase Lattice Boltzmann Method (Two-Phase LBM)
Readership: Advanced undergraduate and graduate students, researchers and practitioners in the fields of fluid mechanics, engineering, computer science, and physics.
Series on Knots and Everything: Volume 72
https://doi.org/10.1142/12563 | January 2022
Pages: 700
ISBN: 978-981-124-742-2 (hardcover)
Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8?10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.
Preface (Graham Ellsbury)
Laws of Form ? A Survey of Ideas (Louis H Kauffman)
The Calculus of Indications ? a Candidate for the Pregeometry of Spacetime? (Graham Ellsbury)
Laws of Form and the Riemann Hypothesis (James M Flagg, Louis H Kauffman and Divyamaan Sahoo)
The Use of Boundary Logic (William Bricken)
The BF Calculus: A Complete Four-Valued Extension to Laws of Form (Art Collings)
The BF Calculus and the Square Root of Negation (Louis H Kauffman and Art Collings)
Modulators and Imaginary Values (Louis H Kauffman)
How to Count to Two ? A Memoire (Nathaniel Hellerstein)
Pervasive Simplicity-Investigations of the 'Primary Algebra' of Laws of Form (George Burnett-Stuart)
Laws of Form and Plato's Theory of Forms (Bernie Lewin)
Writing the Mark (Akeem Helming)
Conservative extensions of Laws of Form to deal with Engineering of Languages Semantic ? How Laws of Form bridges the gap from Language to Cognition (Phillipe Michelin)
Klein Bottle Logophysics, the Primeval Distinction, Semiosis, Perception and the Topology of Consciousness (Diego Lucio Rapoport)
First Philosophy and the First Distinction: Ontology and Phenomenology of Laws of Form (Randolph Dible)
From Conceptual Distinction to Spatial Diversity ? Reconstruction of a Hidden Story (Christina Weiss)
Laws of Form as a Unity of Layered Knowledges from Light! Within Void into the Mark of Distinction and Beyond: System E2 (Jack Engstrom)
Distinctions and Common Ground in Collective Epistemology (Fred Cummins)
A Sociological Reading of George Spencer-Brown's Laws of Form (Dirk Baecker)
Ways of Illumination (Philip Franses)
Forms of Uncertainty: The Startup (Florian Grote)
Laws of Form ? Laws of Narrative ? Laws of Story (Leon Conrad)
O (Divyamaan Sahoo)
The Omasters ? Letters and Compositions with Regard to Enlightenment and G Spencer-Brown (Cliff Barney)
Two Men of Distinction ? Parallels in the World Views of George Spencer-Brown and Douglas Harding (Tom Short)
The Names of Spencer-Brown (Vanilla Beer)
Academic and scientific readers: undergraduate and graduate students and researchers in mathematics, logic, computer science, cybernetics, philosophy, linguistics, physics and natural sciences. General readers: persons interested in the above fields.
https://doi.org/10.1142/12456 | February 2022
Pages: 200
ISBN: 978-981-124-384-4 (hardcover)
This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Godel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.
Propositional Logic
Predicate Logic
Models of Predicate Logic
Boolean Algebras
Computability
Decidable and Undecidable Theories
Algorithmic Randomness
Nonstandard Numbers
Foundations of Geometry
Advanced undergraduate or beginning graduate students interested in mathematical logic, mathematics, computer science, and philosophy.