Format: Hardback, 200 pages, height x width: 235x155 mm, 22 Illustrations,
color; 4 Illustrations, black and white; XX, 200 p. 26 illus., 22 illus. in color., 1 Hardback
Series: Operator Theory: Advances and Applications 297
Pub. Date: 19-Jul-2024
ISBN-13: 9783031593963
This book is a tribute to the achievements of Ilya Spitkovsky in operator theory, pseudo-differential and integral equations,
factorization theory and many other related topics.
Ilya Spitkovsky started his career under the guidance of Mark Krein in Odessa, Ukraine. During these years, Ilyas rigorous
and clear style of doing mathematics matured. Since 1990 Ilya Spitkovsky has been a professor of mathematics at
the College of William and Mary in Williamsburg, Virginia, where he has taught a wide range of courses, including linear
algebra, real, complex, and functional analysis. He has authored more than 300 publications, including four research
monographs, and edited eight books of proceedings. Ilya Spitkovsky is currently a member of the editorial board of
five international journals. Since 2013 he is a professor of the Division of Science and Mathematics New York University
Abu Dhabi, UAE.
With this volume, the authors of the articles join the large family of people who congratulate Ilya Spitkovsky on
his anniversary. It is their wish that the contributions in this volume offer inspiring insights to researchers working
in these fields.
- Ilya Spitkovsky 70.- Ilya Spitkovskys pioneering work on massive
local spectra of Toeplitz operators.- The Reciprocal Schur Inequality.- On
Iterative Procedure for a Vectorial Wiener-Hopf Problem with Oscillating
Terms.- A direct proof of an inversion formula for Bezoutians.- A Numerical
Algorithm for Matrix Spectral Factorization on the Real Line.- On topological
aspects of numerical range.- On dilations of Fourier multipliers on weighted
Lebesgue spaces.- On the Algebras of Wiener-Hopf Operators with Continuous
Symbols Acting on Some Banach Function Spaces.- Algebras of Convolution Type
Operators with Piecewise Quasicontinuous and Piecewise Slowly Oscillating
Data onWeighted Lebesgue Spaces.- On solution to Riemann problem in
logarithmic cases.- Operator Projective Line and Its Transformations.-
Fredholm Determinants, Continued Fractions, Jost and Evans Functions for a
Jacobi Matrix Associated with the 2D-Euler Equations.- Factorization of
Partly Rational Matrix-Functions and its Application to the Solution of
R-linear Conjugation Problem.
Format: Hardback, 358 pages, height x width: 235x155 mm, 133 Illustrations,
black and white; XVI, 358 p. 133 illus., 1 Hardback
Series: Springer Proceedings in Mathematics & Statistics 459
Pub. Date: 03-Jul-2024
ISBN-13: 9783031595387
This book gathers peer-reviewed, selected contributions from participants of the 6th International Workshop
on Nonlinear and Modern Mathematical Physics (NMMP-2022), hosted virtually from June 1719, 2022.
Works contained in this volume cover topics like nonlinear differential equations, integrable systems,
Hamiltonian systems, inverse scattering transform, Painleve's analysis, nonlinear wave phenomena and applications,
numerical methods of nonlinear wave equations, quantum integrable systems, and more. In this book, researchers
and graduate students in mathematics and related areas will find new methods and tools that only recently have
been developed to solve nonlinear problems.
The sixth edition of the NMMP workshop was organized by Florida A&M University in Tallahassee, Florida, USA,
with support from the University of South Florida, Florida State University, Embry-Riddle Aeronautical University,
Savannah State University, Prairie View A&M University, and Beijing Jiaotong University. The aim was to bring
together researchers from around the world to present their findings and foster collaboration for future research.
1. A Hamiltonian set-up for 4-layer density stratified Euler fluids.-
2. Long wave propagation in canals with spatially varying cross-sections and currents.-
3. Factorization conditions for nonlinear second-order differential equations.-
4. Symbolic computation of solitary wave solutions and solitons through homogenization of degree.-
5. Propagation of bright solitons for KdV-type equations involving triplet
dispersion.-
6. A natural full-discretization of the Korteweg-de-Vries equation.-
7. Damped nonlinear Schrodinger equation with Stark effect.-
8. Effect of electrons drift velocity in nonlinear ion-acoustic solitons in a negative ion beam plasma.-
9. Darboux Transformation and Exact Solution for Novikov equation.-
10. Construction of multi-wave solutions of nonlinear equations with variable coefficients arising in fluid mechanics.-
12. Multiple lump and rogue wave solutions of a modified Benjamin-Ono equation 23.-
13. On the inclination of a parametric curve.-
14. Localized waves on the periodic background for the derivative nonlinear SchrOodinger equation.-
15. lp solution to the initial value problem of the discrete nonlinear SchrOodinger equation with complex potential.-
16. Darboux transformations for bi-integrable couplings of the AKNS system.
Format: Paperback / softback, 220 pages, height x width: 235x155 mm, 24
Illustrations,
black and white; X, 220 p. 24 illus., 1 Paperback / softback
Series: Lecture Notes in Mathematics 2351
Pub. Date: 08-Jul-2024
ISBN-13: 9783031590931
This book provides a comprehensive exploration of the theory of summability of formal power series with analytic
coefficients at the origin of Cn, aiming to apply it to formal solutions of partial differential equations (PDEs).
It offers three characterizations of summability and discusses their applications to PDEs, which play a pivotal
role in understanding physical, chemical, biological, and ecological phenomena.
Determining exact solutions and analyzing properties such as dynamic and asymptotic behavior are major challenges
in this field. The book compares various summability approaches and presents simple applications to PDEs,
introducing theoretical tools such as Nagumo norms, Newton polygon, and combinatorial methods. Additionally,
it presents moment PDEs, offering a broad class of functional equations including classical, fractional,
and q-difference equations. With detailed examples and references, the book caters to readers familiar with
the topics seeking proofs or deeper understanding, as well as newcomers looking for comprehensive tools to
grasp the subject matter. Whether readers are seeking precise references or aiming to deepen their knowledge,
this book provides the necessary tools to understand the complexities of summability theory and its applications
to PDEs.
- Part I Asymptotic expansions.- Taylor expansions.- Gevrey formal power
series.- Gevrey asymptotics.- Part II Summability.- k-summability: definition
and first algebraic properties.- First characterization of the k-summability:
the successive derivatives.- Second characterization of the k-summability:
the Borel-Laplace method.- Part III Moment summability.- Moment functions and
moment operators.- Moment-Borel-Laplace method and summability.- Linear
moment partial differential equations.
Conference proceedings
Aug 2024
Reflects the latest developments in analysis and applied mathematics and their interdisciplinary applications
Provides visions of professional experts in the field of analysis and applied mathematics
Includes real-world applications and emphasis on computational skills
Part of the book series: Trends in Mathematics (TM, volume 6)
Part of the book sub series: Research Perspectives Ghent Analysis and PDE Center (RPGAPC)
This book presents extended abstracts of the Analysis and Applied Mathematics seminar organized jointly
by Bahce?ehir University, Istanbul, Turkey, Ghent Analysis & PDE Center, Ghent University, Ghent, Belgium
and the Institute Mathematics & Math. Modeling, Almaty, Kazakhstan. The book is of value to professional
mathematicians as well as advanced students in the fields of analysis and applied mathematics.
The goal of the seminar is to provide a forum for researchers and scientists from different regions to communicate
their recent developments and to present their original results in various fields of analysis and applied mathematics.
All of the articles contain new results and are peer-reviewed. The volume reflects the latest developments in
the area of analysis and applied mathematics and their interdisciplinary applications.
Jul 2024
Overview
The first textbook on C*-algebra theory with a view toward noncommutative geometry
Accessible to graduates, advanced undergraduates, & mathematicians who wish to learn more about
noncommutative geometry
Discusses and works out computations for a plethora of concrete noncommutative spaces
Part of the book series: Birkhauser Advanced Texts Basler Lehrbucher (BAT)
This is the first textbook on C*-algebra theory with a view toward Noncommutative Geometry. Moreover,
it fills a gap in the literature, providing a clear and accessible account of the geometric picture of K-theory
and its relation to the C*-algebraic picture. The text can be used as the basis for a graduate level or a capstone
course with the goal being to bring a relative novice up to speed on the basic ideas while offering a glimpse
at some of the more advanced topics of the subject. Coverage includes C*-algebra theory, K-theory, K-homology,
Index theory and Connes’ Noncommuntative Riemannian geometry.
Aimed at graduate level students, the book is also a valuable resource for mathematicians who wish to deepen their
understanding of noncommutative geometry and algebraic K-theory. A wide range of important examples are
introduced at the beginning of the book. There are lots of excellent exercises and any student working through
these will benefit significantly. Prerequisites include a basic knowledge of algebra, analysis, and a bit of functional
analysis. As the book progresses, a little more mathematical maturity is required as the text discusses smooth
manifolds, some differential geometry and elliptic operator theory, and K-theory. The text is largely self-contained
though occasionally the reader may opt to consult more specialized material to further deepen their understanding
of certain details.
Aug 2024
Presents cross-connections of geometry of circles and spherical geometry from various points of view
Motivates readers to derive own new results
Includes solutions to selected exercises
Part of the book series: Birkhauser Advanced Texts Basler Lehrbucher (BAT)
About this book
This textbook focuses on the geometry of circles, spheres, and spherical geometry. Various classic themes are used
as introductory and motivating topics.
The book begins very simply for the reader in the first chapter discussing the notions of inversion and stereographic
projection. Here, various classical topics and theorems such as Steiner cycles, inversion, Soddy's hexlet, stereographic
projection and Poncelet's porism are discussed. The book then delves into Bend formulas and the relation of radii of
circles, focusing on Steiner circles, mutually tangent four circles in the plane and other related notions.
Next, some fundamental concepts of graph theory are explained. The book then proceeds to explore orthogonal-cycle
representation of quadrangulations, giving detailed discussions of the Brightwell-Scheinerman theorem (an extension
of the Koebe-Andreev-Thurston theorem), Newton’s 13-balls-problem, Casey’s theorem (an extension of Ptolemy’s
theorem) and its generalizations. The remainder of the book is devoted to spherical geometry including a chapter focusing
on geometric probability on the sphere.
The book also contains new results of the authors and insightful notes on the existing literature, bringing the reader
closer to the research front. Each chapter concludes with related exercises of varying levels of difficulty.
Solutions to selected exercises are provided.
This book is suitable to be used as textbook for a geometry course or alternatively as basis for a seminar for both
advanced undergraduate and graduate students alike.