Establishes a theory of classification and translation closedness of time scales
Explores its use in practical model scenarios, like Nicholson`s blowfiles
model, the Lasota-Wazewska model, the Keynesian-Cross model and others
Provides the theoretical background necessary for accurate mathematical
modeling in physics, chemical technology, population dynamics,
biotechnology and economics, neural networks and social sciences
This monograph establishes a theory of classification and translation closedness of time scales,
a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis.
The authors develop a theory of translation function on time scales that contains (piecewise)
almost periodic functions, (piecewise) almost automorphic functions and their related
generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost
automorphic functions, and more). Against the background of dynamic equations, these
function theories on time scales are applied to study the dynamical behavior of solutions for
various types of dynamic equations on hybrid domains, including evolution equations,
discontinuous equations and impulsive integro-differential equations. The theory presented
allows many useful applications, such as in the Nicholson`s blowfiles model; the LasotaWazewska model;
the Keynesian-Cross model; in those realistic dynamical models with a more
complex hibrid domain, considered under different types of translation closedness of time
scales; and in dynamic equations on mathematical models which cover neural networks. This
book provides readers with the theoretical background necessary for accurate mathematical
modeling in physics, chemical technology, population dynamics, biotechnology and economics,
neural networks, and social sciences
1st ed. 2020, XVI, 577 p. 17
illus., 8 illus. in color.
Hardcover
ISBN 978-3-030-38643-6
Product category : Monograph
Series : Developments in Mathematics
Introduces state-of-the-art techniques in computer science and network
analysis
Features new theoretical models and approaches for network analysis with
new efficient tools
Presents a range of application for network models and network analysis
This proceedings presents the result of the 8th International Conference in Network Analysis,
held at the Higher School of Economics, Moscow, in May 2018. The conference brought
together scientists, engineers, and researchers from academia, industry, and government.
Contributions in this book focus on the development of network algorithms for data mining
and its applications. Researchers and students in mathematics, economics, statistics, computer
science, and engineering find this collection a valuable resource filled with the latest research
in network analysis. Computational aspects and applications of large-scale networks in market
models, neural networks, social networks, power transmission grids, maximum clique problem,
telecommunication networks, and complexity graphs are included with new tools for efficient
network analysis of large-scale networks. Machine learning techniques in network settings
including community detection, clustering, and biclustering algorithms are presented with
applications to social network analysis.
1st ed. 2020, XIII, 244 p.
65 illus., 43 illus. in color.
Hardcover
ISBN 978-3-030-37156-2
Product category : Proceedings
Series : Springer Proceedings in Mathematics & Statistics
Covers hot topics in mathematical biology
Presents the latest results and envisages new challenges
Addresses topics of interest to both experienced researchers and young
scientists
This book disseminates the latest results and envisages new challenges in the application of
mathematics to various practical situations in biology, epidemiology, and ecology. It comprises
a collection of the main results presented at the Ninth Edition of the International Workshop
Dynamical Systems Applied to Biology and Natural Sciences DSABNS held from
7 to 9
February 2018 at the Department of Mathematics, University of Turin, Italy. While the principal
focus is ecology and epidemiology, the coverage extends even to waste recycling and a genetic
application. The topics covered in the 12 peer-reviewed contributions involve such diverse
mathematical tools as ordinary and partial differential equations, delay equations, stochastic
equations, control, and sensitivity analysis. The book is intended to help both in disseminating
the latest results and in envisaging new challenges in the application of mathematics to
various practical situations in biology, epidemiology, and ecology
1st ed. 2020, XII, 243 p. 70
illus., 40 illus. in color.
Hardcover
ISBN 978-3-030-41119-0
Product category : Contributed volume
Series : SEMA SIMAI Springer Series
With an Introduction to Regularity Structures
Provides a self-contained introduction to rough path analysis with many
exercises
Includes applications to stochastic partial differential equations
Covers the basics of the new theory of regularity structures
With many updates and additional exercises, the second edition of this book continues to
provide readers with a gentle introduction to rough path analysis and regularity structures,
theories that have yielded many new insights into the analysis of stochastic differential
equations, and, most recently, stochastic partial differential equations. Rough path analysis
provides the means for constructing a pathwise solution theory for stochastic differential
equations which, in many respects, behaves like the theory of deterministic differential
equations and permits a clean break between analytical and probabilistic arguments. Together
with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of
many classical results without having to rely on specific probabilistic properties such as
adaptedness or the martingale property. Essentially self-contained, this textbook puts the
emphasis on ideas and short arguments, rather than aiming for the strongest possible
statements. A typical reader will have been exposed to upper undergraduate analysis and
probability courses, with little more than Itﾃｴ-integration against Brownian motion required for
most of the text. From the reviews of the first edition: "Can easily be used as a support for a
graduate course ... Presents in an accessible way the unique point of view of two experts who
themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical
Reviews "It is easy to base a graduate course on rough paths on this
A researcher who
carefully works her way through all of the exercises will have a very good impression of the
current state of the art" - Nicolas Perkowski inZentralblatt MATH
Due 2020-07-08
2nd ed. 2020, X, 350 p. 3
illus.
Softcover
ISBN 978-3-030-41555-6
Product category : Graduate/advanced undergraduate textbook
Series : Universitext
This book offers an introduction to the research in several recently discovered and actively
developing mathematical and mathematical physics areas. It focuses on: 1)Feynman integrals
and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic
forms and applications to quantum gravity, 3) superconformal indices and elliptic
hypergeometric integrals, relatedinstanton partition functions, 4) moonshine, its arithmetic
aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the
elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the
topics covered are related to various partition functions emerging in different supersymmetric
and ordinary quantum field theories in curved space-times of different (d=2,3,窶ｦ,6) dimensions.
Presenting multidisciplinary methods (localization, Borcherds products, theory of special
functions, Cremona maps, etc) for treating a range of partition functions, the book is intended
forgraduate students and young postdocs interested in the interaction between quantum field
theory and mathematics related to automorphic forms, representation theory, number theory
and geometry, and mirror symmetry.
Due 2020-07-11
1st ed. 2020, X, 375 p. 23
illus.
Hardcover
ISBN 978-3-030-42399-5
Product category : Proceedings
Series : Moscow Lectures
With Theoretical Implications
Designed to enable the student an opportunity to engage in mathematical
problem solving at the highest level
Includes exercises at every level
Versatile pedagogical usage
When first published in 1959, this book was the basis of a two-semester course in complex
analysis for upper undergraduate and graduate students. J. S. Mac Nerney was a proponent of
the Socratic, or o-it-yourself・method of learning mathematics, in which
students are
encouraged to engage in mathematical problem solving, including theorems at every level
which are often regarded as oo difficult・for students to prove for themselves.
Accordingly,
Mac Nerney provides no proofs. What he does instead is to compose and arrange the
investigation in his own unique style, so that a contextual proof is always available to the
persistent student who enjoys a challenge. The central idea is to empower students by
allowing them to discover and rely on their own mathematical abilities. This text may be used
in a variety of settings, including: the usual classroom or seminar, but with the teacher acting
mainly as a moderator while the students present their discoveries, a small-group setting in
which the students present their discoveries to each other, and independent study. The Editors,
William E. Kaufman (who was Mac Nerney last PhD student) and Ryan C. Schwiebert,
have
composed the original typed Work into LaTeX ; they have updated the notation, terminology,
and some of the prose for modern usage, but the organization of content has been strictly
preserved. About this Book, some new exercises, and an index have also been added.
Due 2020-07-03
1st ed. 2020, XX, 90 p. 12
illus.
Softcover
ISBN 978-3-030-42084-0
Product category : Graduate/advanced undergraduate textbook
A Collection of Sneaky Tricks, Sly Substitutions, and Numerous Other
Stupendously Clever, Awesomely Wicked, and Devilishly Seductive
Maneuvers for Computing Hundreds of Perplexing Definite Integrals
From Physics, Engineering, and Mathematics (Plus Numerous Challenge
Problems with Complete, Detailed Solutions)
New edition with 25 added challenge problems and solutions and 25 new
worked examples
A "recipe book" with many valuable little-known integration techniques
Written with an accessible and easy-to-follow style by acclaimed popular
science author and engineering professor Paul Nahin
Includes rarely-taught problem solving techniques including Feynman's
favorite: differentiation under the integral
Features worked-out and thoroughly explained practice problems
What the point of calculating definite integrals since you can possibly
do them all? What
makes doing the specific integrals in this book of value aren the specific
answers wel obtain,
but rather the methods we use in obtaining those answers; methods you can
use for
evaluating the integrals you will encounter in the future. This book, now in its second edition, is
written in a light-hearted manner for students who have completed the first year of college or
high school AP calculus and have just a bit of exposure to the concept of a differential
equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a
book for you. New material in the second edition includes 25 new challenge problems and
solutions, 25 new worked examples, simplified derivations, and additional historical discussion.
Due 2020-07-23
2nd ed. 2020, XVI, 344 p.
43 illus.
Softcover
ISBN 978-3-030-43787-9
Product category : Undergraduate textbook
Series : Undergraduate Lecture Notes in Physics