Format: Paperback / softback, 200 pages, height x width: 235x155 mm, XIII, 200 p., 1 Paperback / softback
Series: Lecture Notes on Mathematical Modelling in the Life Sciences
Pub. Date: 23-Jan-2025
ISBN-13: 9783031777714
The book provides a self-contained and complete description of the long time evolution of the solutions to a class of one-dimensional reaction?diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation is the mathematical analysis of models for biological invasions. The model under study, while simple looking, is of current use in real-life situations. Interestingly, it arises in totally different contexts, such as the study of branching random walks in probability theory. While the model has attracted a lot of attention, and while many partial results about the time-asymptotic behaviour of its solutions have been proved over the last decades, some basic questions on the sharp asymptotics have remained unanswered. One ambition of this monograph is to close these gaps. In some of the situations that we envisage, the level sets organise themselves into an invasion front that is asymptotically linear in time, up to a correction that converges exponentially in time to a constant. In other situations that constitute the main and newest part of the work, the correction is asymptotically logarithmic in time. Despite these apparently different behaviours, there is an underlying common way of thinking that is underlined. At the end of each chapter, a long set of problems is proposed, many of them rather elaborate and suitable for master's projects or even the first question in a PhD thesis. Open questions are also discussed. The ideas presented in the book apply to more elaborate systems modelling biological invasions or the spatial propagation of epidemics. The models themselves may be multidimensional, but they all have in common a mechanism imposing the propagation in a given direction; examples are presented in the problems that conclude each chapter. These ideas should also be useful in the treatment of further models that we are not able to envisage for the time being. The book is suitable for graduate or PhD students as well as researchers.
1. Introduction.- 2. Cauchy Problem, Steady States, and Diffusive
Behaviour.- 3. Travelling Waves.- 4. Sharp Fisher-KPP Spreading.- 5. Sharp
ZFK Spreading.- 6. Spreading in Several Space Dimensions.- 7. Final Remarks.
Format: Hardback, 452 pages, height x width: 235x155 mm, XIX, 452 p., 1 Hardback
Pub. Date: 03-Dec-2024
ISBN-13: 9783031746222
This book is a concise, self-contained treatise on abstract algebra with an introduction to number theory, where students normally encounter rigorous mathematics for the first time. The authors build up things slowly, by explaining the importance of proofs. Number theory with its focus on prime numbers is then bridged via complex numbers and linear algebra, to the standard concepts of a course in abstract algebra, namely groups, representations, rings, and modules.
The interplay between these notions becomes evident in the various topics studied. Galois theory connects field extensions with automorphism groups. The group algebra ties group representations with modules over rings, also at the level of induced representations. Quadratic reciprocity occurs in the study of Fourier analysis over finite fields. Jordan decomposition of matrices is obtained by decomposition of modules over PIDs of complex polynomials. This latter example is just one of many stunning generalizations of the fundamental theorem of arithmetic, which in its various guises penetrates abstract algebra and figures multiple times in the extensive final chapter on modules.
Chapter 1. Number theory.
Chapter 2. Construction of numbers.
Chapter 3. Linear algebra.
Chapter 4. Groups.
Chapter 5. Representations of finite groups.
Chapter 6. Rings.
Chapter 7. Field extensions.
Chapter 8. Galois theory.
Chapter 9. Modules.
Chapter 10. Appendix.
Format: Hardback, 340 pages, height x width: 235x155 mm, 29 Illustrations, color; 40 Illustrations, black and white; X, 340 p. 63 illus., 29 illus. in color., 1 Hardback
Pub. Date: 21-Jan-2025
ISBN-13: 9783031762567
The book is a comprehensive compilation of diverse articles delving into various intriguing topics within the realm of geometry. Each article is refereed by prominent researchers in the field. The book contains research articles offering valuable insights and original results, making it a valuable resource for researchers in the field, as well as survey articles that review current developments and list open problems.
1. Introduction.- 2. Interview with Athanase Papadopoulos.- 3. A
glance at S. Novikovs theory of multivalued Morse functions.- 4. A twisted
invariant of a compact Riemann surface.- 5. Directional moduli and
pseudoconvexity.- 6. Angle Defect for Super Triangles.- 7. Lipschitz and
quasiconformal mappings in cartography.- 8. Spherical representations of the
group of isometries of semi-homogeneous trees.- 9. Trees of fractions.-
10. Binary quadratic forms: modern developments.- 11. A Note on Reversibility
of Unipotent Matrices.- 12. Le complement superieur: On the poetics of
mathematics.- 13. Pythagorean Book II of the Elements restored and
Pythagorean Incommensurabilities reconstructed.
Format: Hardback, 472 pages, height x width: 235x155 mm, 25 Illustrations, color; 3 Illustrations,
black and white; XVII, 472 p. 28 illus., 25 illus. in color., 1 Hardback
Series: Algorithms and Computation in Mathematics 33
Pub. Date: 27-Jan-2025
ISBN-13: 9783031776830
This text presents a comprehensive and unified treatment of nonlinear filtering theory, with a strong emphasis on its mathematical underpinnings. It is tailored to meet the needs of a diverse readership, including mathematically inclined engineers and scientists at both graduate and post-graduate levels. What sets this book apart from other treatments of the topic is twofold. Firstly, it offers a complete treatment of filtering theory, providing readers with a thorough understanding of the subject. Secondly, it introduces updated methodologies and applications that are crucial in today’s landscape. These include finite-dimensional filters, the Yau-Yau algorithm, direct methods, and the integration of deep learning with filtering problems. The book will be an invaluable resource for researchers and practitioners for years to come.
With a rich historical backdrop dating back to Gauss and Wiener, the exposition delves into the fundamental principles underpinning the estimation of stochastic processes amidst noisy observations?a critical tool in various applied domains such as aircraft navigation, solar mapping, and orbit determination, to name just a few. Substantive exercises and examples given in each chapter provide the reader with opportunities to appreciate applications and ample ways to test their understanding of the topics covered. An especially nice feature for those studying the subject independent of a traditional course setting is the inclusion of solutions to exercises at the end of the book.
The book is structured into three cohesive parts, each designed to build the reader's understanding of nonlinear filtering theory. In the first part, foundational concepts from probability theory, stochastic processes, stochastic differential equations, and optimization are introduced, providing readers with the necessary mathematical background. The second part delves into theoretical aspects of filtering theory, covering topics such as the stochastic partial differential equation governing the posterior density function of the state, and the estimation algebra theory of systems with finite-dimensional filters. Moving forward, the third part of the book explores numerical algorithms for solving filtering problems, including the Yau-Yau algorithm, direct methods, classical filtering algorithms like the particle filter, and the intersection of filtering theory with deep learning.
Preface.- I. Preliminary knowledge.-
1. Probability theory.-
2. Stochastic processes.-
3. Stochastic differential equations.-
4. Optimization.- II. Filtering theory.-
5. The filtering equations.-
6. Estimation algebra.- III. Numerical algorithms.-
7. Yau-Yau algorithm.-
8. Direct methods.-
9. Classical filtering methods.-
10. Estimation algorithms based on deep learning.
Format: Hardback, 190 pages, height x width: 235x155 mm, X, 190 p., 1 Hardback
Series: Operator Theory: Advances and Applications 305
Pub. Date: 29-Jan-2025
ISBN-13: 9783031761805
This book is about function spaces aspects of polyanalytic functions, a topic that has gained a lot of attention in the past decades. This book fills a gap in literature and is written by a leading researcher in the field.
Rather than studying polyanalytic functions from a complex analysis point of view, it considers the (Lie)-algebraic part of the theory. Several generalizations are offered. The presented theory has many applications, including to quantum physics. An extensive introduction to the topic is provided, making the book accessible to specialists and newcomers ali
Foreword.- Preface.- Introduction.- I Spaces of polyanalytic type in one complex variable.- 1 Extended Fock-space construction approach.- 2 Complex plane C case.- 3 Unit disk D case.- 4 Upper half-plane ? case.- 5 Basis oriented approach.- 6 Approach based on pure isometries.- II Spaces of polyanalytic type in several complex variables.- 7 Multi-operator extended Fock-space construction.- 8 The Cn case.- 9 The unit ball Bn case.- 10 Hilbert spaces with generalized Gaussian measure on C2.- 11 The Siegel domain case.- Bibliography.- Index.
Format: Hardback, 490 pages, height x width: 235x155 mm, 22 Illustrations, color;
37 Illustrations, black and white; X, 490 p. 59 illus., 22 illus. in color., 1 Hardback
Series: Progress in Mathematics 357
Pub. Date: 10-Feb-2025
ISBN-13: 9789819784486
Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashis pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades.
The first volume of the Festschrift includes a survey article on Kobayashis innovative contributions to Mathematics, emphasizing their influence and introducing new perspectives across various fields. Original articles contained in Volume 1 focus on differential geometry with symmetries as well as algebraic and geometric aspects of representation theory of reductive Lie groups and related topics.
Contributions are by Velleda Baldoni, Dan Barbasch, Leticia Barchini, Sigiswald Barbier, Yves Benoist, Sam Claerebout, Michael Eastwood, Wee Teck Gan, William M. Goldman, Roger Howe, Kazuki Kannaka, Toshihisa Kubo, Hung Yean Loke, Jia-Jun Ma, Reiko Miyaoka, Kento Ogawa, Takayuki Okuda, Yoshiki Oshima, Paul-Emile Paradan, Annegret Paul, Michael Pevzner, Yiannis Sakellaridis, Atsumi Sasaki, Gordan Savin, Hideko Sekiguchi, Binyong Sun, Yuichiro Tanaka, Koichi Tojo, Peter Trapa, Mich?le Vergne, Joseph A. Wolf, Kayue Daniel Wong, and Chen-Bo Zhu.
The Mathematical Work of Toshiyuki Kobayashi (William M. Goldman, Kazuki
Kannaka, Toshihisa Kubo, Takayuki Okuda, Yoshiki Oshima, Michael Pevzner,
Atsumu Sasaki, Hideko Sekiguchi).- Tensor product of holomorphic discrete
series representations of U(p, q) and quivers (Velleda Baldoni and Mich?le
Vergne).- Genuine special unipotent representations of spin groups (Dan
Barbasch, Jia-Jun Ma, Binyong Sun, and Chen-Bo Zhu).- Admissible modules and
normality of classical nilpotent orbits (Dan Barbasch and Kayue Daniel
Wong).- A general approach to constructing minimal representations of Lie
supergroups (Sigiswald Barbier and Sam Claerebout).- A note on the orbits of
a symmetric subgroup in the flag variety (Leticia Barchini and Peter E.
Trapa).- On the rational symplectic group (Yves Benoist).- Conformal
Loxodromes (Michael Eastwood).- A family of Spin (8) dual pairs: the case of
real groups (Wee Teck Gan, Hung Yean Loke, Annegret Paul and Gordan
Savin).- The Oscillator Semigroup over Finite Fields (Roger
Howe).- Zariski-dense discontinuous surface groups for reductive symmetric
spaces (Kazuki Kannaka, Takayuki Okuda, and Koichi Tojo).- Geometry of light
wave fronts (Reiko Miyaoka).- A proof of Kobayashi's properness criterion
from a viewpoint of metric geometry (Kento Ogawa and Takayuki
Okuda).- Eigenvalues, singular values, and the O'Shea-Sjamaar Theorem
(Paul-Emile Paradan).- Transfer Operators and Hankel Transforms:
Horospherical Limits and Quantization (Yiannis Sakellaridis).- Invariant
measures on non-symmetric reductive real spherical homogeneous spaces of
rank-one type (Atsumu Sasaki).- A Note on Multiplicity-Freeness Property of
Cohomology Spaces (Yuichiro Tanaka).- On the Homogeneity Conjecture (Joseph
A. Wolf).
Format: Hardback, 540 pages, height x width: 235x155 mm, 2 Illustrations, color; 5 Illustrations,
black and white; X, 540 p. 7 illus., 2 illus. in color., 1 Hardback
Series: Progress in Mathematics 358
Pub. Date: 08-Feb-2025
ISBN-13: 9789819776610
Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashis pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades.
This second volume of the Festschrift contains original articles on analytic methods in representation theory of reductive Lie groups and related topics.
Contributions are by Salem Ben Sa?d, Valentina Casarino, Paolo Ciatti, Jean-Louis Clerc, Jan Frahm, Joachim Hilgert, Toshihisa Kubo, Khalid Koufany, Quentin Labriet, Karl-Hermann Neeb, Yury Neretin, Gestur Olafsson, Bent ?rsted, Toshio Oshima, Birgit Speh, Jorge Vargas, and Clemens Weiske.
The source operator method: an overview (Salem Ben Said, Jean-Louis
Clerc and Khalid Koufany).- Some mixed norm bounds for the spectral
projections of the Heisenberg sublaplacian (Valentina Casarino and Paolo
Ciatti).- Four variations on the Rankin-Cohen brackets (Jean-Louis Clerc).-
Restricting holomorphic discrete series representations to a compact dual
pair (Jan Frahm and Quentin Labriet).- Nets of standard subspaces on
non-compactly causal symmetric spaces (Jan Frahm, Karl-Hermann Neeb, and
Gestur Olafsson).- Heisenberg parabolically induced representations of
Hermitian Lie groups, Part II: Next-to-minimal representations and branching
rules (Jan Frahm, Clemens Weiske and Genkai Zhang).- Quantum-Classical
Correspondences for Locally Symmetric Spaces (Joachim Hilgert).-
Classification of K-type formulas for the Heisenberg ultrahyperbolic operator
s for ?? ??(??, ) and tridiagonal determinants for
local Heun functions (Toshihisa Kubo and Bent ?rsted).- Gauss--Berezin
integral operators, spinors over orthosymplectic supergroups, and Lagrangian
super-Grassmannians (Yury A. Neretin).- Towards Gan-Gross-Prasad type
conjecture for discrete series representations of symmetric spaces (Bent
?rsted and Birgit Speh).- Pseudo-dual pairs and branching of Discrete Series
(Bent ?rsted and Jorge A. Vargas).- Integral transformations of
hypergeometric functions with several variables (Toshio Oshima).
Format: Hardback, 540 pages, height x width: 235x155 mm, X, 540 p., 1 Hardback
Series: Progress in Mathematics 359
Pub. Date: 11-Feb-2025
ISBN-13: 9789819776658
Symmetry in Geometry and Analysis is a Festschrift honoring Toshiyuki Kobayashi. The three volumes feature 35 selected contributions from invited speakers of twin conferences held in June 2022 in Reims, France, and in September 2022 in Tokyo, Japan. These contributions highlight the profound impact of Prof. Kobayashis pioneering ideas, groundbreaking discoveries, and significant achievements in the development of analytic representation theory, noncommutative harmonic analysis, and the geometry of discontinuous groups beyond the Riemannian context, among other areas, over the past four decades.
This third volume of the Festschrift contains original articles on branching problems in representation theory of reductive Lie groups and related topics.
Contributions are by Ali Baklouti, Hidenori Fujiwara, Dmitry Gourevitch, Masatoshi Kitagawa, Salma Nasrin, Yoshiki Oshima, and Petr Somberg.
A solution to Duflo's polynomial problem for nilpotent Lie groups
restricted representations (Ali Baklouti and Hidenori Fujiwara).-
Multiplicities and associated varieties in representation theory of reductive
groups (Dmitry Gourevitch).-Kobayashis Conjectures on the Discrete
Decomposability (Masatoshi Kitagawa).- Kobayashis multiplicity-one theorems
in branching laws and orbit philosophy beyond tempered representations (Salma
Nasrin).- Discrete branching laws of derived functor modules (Yoshiki
Oshima).- Rankin-Cohen brackets for orthogonal Lie algebras and bilinear
conformally equivariant differential operators (Petr Somberg).