1st ed. 2019, Approx. 340 p.
Printed book
Hardcover
Series: Springer Proceedings in Mathematics & Statistics
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for
nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact
of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of
the fields to which he has made contributions of fundamental significance. This publication was
conceived during a conference in 2016 at NYU Shanghai that coincided with Chuck's 70th
birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II.
Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles
in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate
students and researchers who seek initiation and inspiration in Probability Theory and
Statistical Physics
Due 2019-11-27
1st ed. 2019, Approx. 260 p.
Hardcover
ISBN 978-981-15-0297-2
Series: Springer Proceedings in Mathematics & Statistics
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for
nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact
of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of
the fields to which he has made contributions of fundamental significance. This publication was
conceived during a conference in 2016 atNYU Shanghaithat coincided with Chuck's 70th
birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II.
Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles
in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate
students and researchers who seek initiation and inspiration in Probability Theory and
Statistical Physics.
Due 2019-11-23
1st ed. 2019, Approx. 325 p.
Printed book
Hardcover
ISBN 978-981-15-0301-6
Series: Springer Proceedings in Mathematics & Statistics
Charles M. (Chuck) Newman has been a leader in Probability Theory and Statistical Physics for
nearly half a century. This three-volume set is a celebration of the far-reaching scientific impact
of his work. It consists of articles by Chuck’s collaborators and colleagues across a number of
the fields to which he has made contributions of fundamental significance. This publication was
conceived during a conference in 2016 atNYU Shanghaithat coincided with Chuck's 70th
birthday. The sub-titles of the three volumes are: I. Spin Glasses and Statistical Mechanics II.
Brownian Web and Percolation III. Interacting Particle Systems and Random Walks The articles
in these volumes, which cover a wide spectrum of topics, will be especially useful for graduate
students and researchers who seek initiation and inspiration in Probability Theory and
Statistical Physics.
Due 2019-12-08
1st ed. 2019, Approx. 670 p.
Hardcover
ISBN 978-3-030-30293-1
Provides a self-contained and constructive approach to noncommutative
differential geometry, which connects to the earlier approach to
noncommutative geometry of Alain Connes in a complementary way
Contains a wide range of examples drawn from quantum groups, algebra and
mathematical physics
Includes a final chapter on concrete models of quantum spacetime as well as
a chapter on quantum groups and their differential structures
Includes 81 exercises with solutions
This book provides a comprehensive account of a modern generalisation of differential
geometry in which coordinates need not commute. This requires a reinvention of differential
geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than
to actual points. Such a theory is needed for the geometry of Hopf algebras or quantum
groups, which provide key examples, as well as in physics to model quantum gravity effects in
the form of quantum spacetime. The mathematical formalism can be applied to any algebra
and includes graph geometry and a Lie theory of finite groups. Even the algebra of 2 x 2
matrices turns out to admit a rich moduli of quantum Riemannian geometries. The approach
taken is a `bottom up’ one in which the different layers of geometry are built up in succession,
starting from differential forms and proceeding up to the notion of a quantum `Levi-Civita’
bimodule connection, geometric Laplacians and, in some cases, Dirac operators.The book also
covers elements of Connes’ approach to the subject coming from cyclic cohomology and
spectral triples. Other topics include various other cohomology theories, holomorphic structures
and noncommutative D-modules. A unique feature of the book is its constructive approach and
its wealth of examples drawn from a large body of literature in mathematical physics, now put
on a firm algebraic footing. Including exercises with solutions, it can be used as a textbook for
advanced courses as well as a reference for researchers.
Due 2020-02-01
Approx. 525 p.
Hardcover
ISBN 978-3-030-31162-9
First of a two volume series intended to give a systematic presentation of the
theory of cycle spaces in complex geometry
Foundational material is presented with only introductory complex analysis
being assumed
Explains the subject in a clear manner which is accessible to graduate
students in mathematics as well as research mathematicians.
Unique exposition by two leading experts
The book consists of a presentation from scratch of cycle space methodology incomplex
geometry. Applications in various contexts are given. A significant portionof the book is devoted
to material which is important in the general area of complexanalysis. In this regard, a
geometric approach is used to obtain fundamental results such as the local parameterization
theorem, Lelong' s Theorem and Remmert's direct image theorem. Methods involving cycle
spaces have been used in complex geometry for some forty years. The purpose of the book is
to systematically explain these methods in a way which is accessible to graduate students in
mathematics as well as to research mathematicians. After the background material which is
presented in the initial chapters, families of cycles are treated in the last most important part
of the book. Their topological aspects are developed in a systematic way and some basic,
important applications of analytic families of cycles are given. The construction of the cycle
space as a complex space, along with numerous important applications, is given in the second
volume. The present book is a translation of the French version that was published in 2014 by
the French Mathematical Society
Due 2019-11-25
1st ed. 2019, XIV, 465 p. 27
illus., 10 illus. in color.
Hardcover
ISBN 978-3-030-31410-1
Develops carefully the foundations of calculus of multivector fields and
differential forms
Explains advanced material in a self-contained and down-to-earth way, e.g.
Clifford algebra, spinors, differential forms and index theorems
Touches on modern research areas in analysis
Contains a novel treatment of Hodge decompositions based on first-order
differential operators
This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a
focus on conveying to the reader the geometricunderstandingof these abstract objects.
Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford
algebra offers the ideal tool for studying spacetime isometries and Mobius maps in arbitrary
dimensions. The book carefully develops the basic calculus of multivector fields and differential
forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes’s theorem as
compared to standard literature. It touches on recent research areas in analysis and explains
how the function spaces of multivector fields are split into complementary subspaces by the
natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the
analysis is done on bounded domains in Euclidean space, with a focus on analysis at the
boundary. The book also includes a derivation of newDirac integral equationsfor solving
Maxwell scattering problems, which hold promise for future numerical applications. The last
section presents down-to-earth proofs of index theorems for Dirac operators on compact
manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is
primarily intended for graduate and PhD students of mathematics. It is also recommended for
more advanced undergraduate students, as well as researchers in mathematics interested in
an introduction to geometric analysis.
Pages: 350
ISBN: 978-981-121-122-5 (hardcover)
A population is a summation of all the organisms of the same group or species, which live in a particular geographical area, and have the capability of interbreeding. The main mathematical problem for a given population is to carefully examine the evolution (time dependent dynamics) of the population. The mathematical methods used in the study of this problem are based on probability theory, stochastic processes, dynamical systems, nonlinear differential and difference equations, and (non-)associative algebras.
A state of a population is a distribution of probabilities of the different types of organisms in every generation. Type partition is called differentiation (for example, sex differentiation which defines a bisexual population). This book systematically describes the recently developed theory of (bisexual) population, and mainly contains results obtained since 2010.
The book presents algebraic and probabilistic approaches in the theory of population dynamics. It also includes several dynamical systems of biological models such as dynamics generated by Markov processes of cubic stochastic matrices; dynamics of sex-linked population; dynamical systems generated by a gonosomal evolution operator; dynamical system and an evolution algebra of mosquito population; and ocean ecosystems.
The main aim of this book is to facilitate the reader's in-depth understanding by giving a systematic review of the theory of population dynamics which has wide applications in biology, mathematics, medicine, and physics.
Preface
Introduction
Algebraic Preliminaries
Genetic Algebras
Algebras of Bisexual Population
Flows of Finite Dimensional Algebras
Markov Processes of Cubic Stochastic Matrices
Cubic Stochastic Operators and Processes
Dynamics Generated by Quadratic Stochastic Operator
Dynamics of Sex-Linked Population
Dynamical Systems Generated by a Gonosomal Evolution Operator
A Discrete-Time Dynamical System and an Evolution Algebra of Mosquito Population
On Ocean Ecosystem Discrete Time Dynamics Generated by l-Volterra Operators
Post-graduate students, academics and researchers in the field of population dynamics and its applications.