Graduate Studies in Mathematics, Volume: 199
2019; 305 pp; Hardcover
MSC: Primary 60; 62; 65; 82;
Print ISBN: 978-1-4704-4933-9
This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics. It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path integrals, random fields, statistical physics, chemical kinetics, and rare events). The book strikes a nice balance between mathematical formalism and intuitive arguments, a style that is most suited for applied mathematicians. Readers can learn both the rigorous treatment of stochastic analysis as well as practical applications in modeling and simulation. Numerous exercises nicely supplement the main exposition.
Undergraduate and graduate students and researchers interested in stochastic processes, stochastic analysis, and applications.
Mathematical Surveys and Monographs,Volume: 238
2019; Hardcover
MSC: Primary 14; 94; 11;
Print ISBN: 978-1-4704-4865-3
Algebraic Geometry Codes: Advanced Chapters is devoted to the theory of algebraic geometry codes, a subject related to several domains of mathematics. On one hand, it involves such classical areas as algebraic geometry and number theory; on the other, it is connected to information transmission theory, combinatorics, finite geometries, dense packings, and so on. The book gives a unique perspective on the subject. Whereas most books on coding theory start with elementary concepts and then develop them in the framework of coding theory itself within, this book systematically presents meaningful and important connections of coding theory with algebraic geometry and number theory. Among many topics treated in the book, the following should be mentioned: curves with many points over finite fields, class field theory, asymptotic theory of global fields, decoding, sphere packing, codes from multi-dimensional varieties, and applications of algebraic geometry codes.
The book is the natural continuation of Algebraic Geometric Codes: Basic Notions by the same authors. The concise exposition of the first volume is included as an appendix.
Graduate students and researchers interested in algebraic geometry of curves and applications to coding theory.
Due 2019-05-20
1st ed. 2019, X, 274 p. 100
illus., 96 illus. in color.
Printed book
Hardcover
ISBN 978-3-030-13422-8
Presents a new quadrature formula for the fractional Fourier transform
Many examples are addressed to illustrate the power of the new formula
Most of the algorithms presented, are implemented in standard packages as
MATLAB or MATHEMATICA
Present the XFT matrix as a finite-dimensional transformation
This book has two main objectives, the first of which is to extend the power of numerical
Fourier analysis and to show by means of theoretical examples and numerous concrete
applications that when computing discrete Fourier transforms of periodic and non periodic
functions, the usual kernel matrix of the Fourier transform, the discrete Fourier transform
(DFT), should be replaced by another kernel matrix, the eXtended Fourier transform (XFT),
since the XFT matrix appears as a convergent quadrature of a more general transform, the
fractional Fourier transform. In turn, the bookfs second goal is to present the XFT matrix as a
finite-dimensional transformation that links certain discrete operators in the same way that the
corresponding continuous operators are related by the Fourier transform, and to show that the
XFT matrix accordingly generates sequences of matrix operators that represent continuum
operators, and which allow these operators to be studied from another perspective.
Due 2019-05-22
1st ed. 2019, X, 115 p.
Printed book
Softcover
ISBN 978-3-030-13053-4
First book presenting the research area ggeomathematicsh
Includes a short description on recent research activities
Presents GEM ? International Journal on Geomathematics
The authors introduce geomathematics as an active research area to a wider audience. Chapter
1 presents an introduction to the Earth as a system to apply scientific methods. Emphasis is
laid on transfers from virtual models to reality and vice versa. In the second chapter
geomathematics is introduced as a new scientific area which nevertheless has its roots in
antiquity. The modern conception of geomathematics is outlined from different points of view
and its challenging nature is described as well as its interdisciplinarity. Geomathematics is
shown as the bridge between the real world and the virtual world. The complex mathematical
tools are shown from a variety of fields necessary to tackle geoscientific problems in the
mathematical language. Chapter 3 contains some exemplary applications as novel exploration
methods. Particular importance is laid on the change of language when it comes to translate
measurements to mathematical models. New solution methods like the multiscale mollifier
technique are presented. Further applications discussed are aspects of reflection seismics.
Chapter 4 is devoted to the short description of recent activities in geomathematics. The
Appendix (Chapter 5) is devoted to the GEM ? International Journal on Geomathematics
founded ten years ago. Besides a detailed structural analysis of the editorial goals an index of
all papers published in former issues is given
Due 2019-07-14
1st ed. 2019, Approx. 300 p.
Printed book
Hardcover
ISBN 978-3-030-14639-9
Includes photographs by Serguei Shimorin
Provides a vivid account of Serguei Shimorin's scientific life and legacy
Features personal recollections
This book contains both expository articles and original research in the areas of function theory
and operator theory. The contributions include extended versions of some of the lectures by
invited speakers at the conference in honor of the memory of Serguei Shimorin at the MittagLeffler
Institute in the summer of 2018. The book is intended for all researchers in the fields
of function theory, operator theory and complex analysis in one or several variables. The
expository articles reflecting the current status of several well-established and very dynamical
areas of research will be accessible and useful to advanced graduate students and young
researchers in pure and applied mathematics, and also to engineers and physicists using
complex analysis methods in their investigations
Due 2019-06-301st ed. 2019, Approx. 900 p.
Printed book
Hardcover
ISBN 978-3-030-15241-3
The contributors are well-established researchers in respective fields
The book presents theory, methods, and applications in a balanced manner
Presents the basic developments concerning of recent mathematical
advances in mathematical analysis in full details
This book explores several important aspects of recent developments in the interdisciplinary
applications of mathematical analysis (MA), and highlights how MA is now being employed in
many areas of scientific research.Each of the 23 carefully reviewed chapters was written by
experienced expert(s) in respective field, andwill enrich readersf understanding of the respective
research problems, providing them with sufficient background to understand the theories,
methods and applications discussed. The bookfs main goal is to highlight the latest trends and
advances, equipping interested readers to pursue further research of their own. Given its scope,
the book will especially benefit graduate and PhD students, researchers in the applied
sciences, educators, and engineers with an interest in recent developments in the
interdisciplinary applications of mathematical analysis