Jul 2024
Can be used as a one semester graduate course for mathematicians
Devoted to existence and uniqueness of weak solutions to nonlinear Fokker-Planck equations
Presents recent research material on nonlinear Fokker-Planck equations
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2353)
This book delves into a rigorous mathematical exploration of the well-posedness and long-time behavior of
weak solutions to nonlinear Fokker-Planck equations, along with their implications in the theory of probabilistically
weak solutions to McKean-Vlasov stochastic differential equations and the corresponding nonlinear Markov processes.
These are widely acknowledged as essential tools for describing the dynamics of complex systems in disordered media,
as well as mean-field models. The resulting stochastic processes elucidate the microscopic dynamics underlying
the nonlinear Fokker-Planck equations, whereas the solutions of the latter describe the evolving macroscopic probability
distributions.
The intended audience for this book primarily comprises specialists in mathematical physics, probability theory and PDEs.
It can also be utilized as a one-semester graduate course for mathematicians. Prerequisites for the readers include
a solid foundation in functional analysis and probability theory.
Aug 2024
Serves as a reference book for graduate/postgraduate research students to design new research projects
The primary audience includes researchers, mathematicians, modelers, and graduate students
Studies the theoretical aspects for a variety of coupled fractional differential systems involving Riemann-Liouville
This book studies the theoretical aspects for a variety of coupled fractional differential systems involving
Riemann-Liouville, Caputo, Ġ-Riemann--Liouville, Hilfer, Ġ--Hilfer, Hadamard, Hilfer--Hadamard, Erdelyi--Kober,
(k, Ġ)-Hilfer, generalized, Proportional, Ġ-Proportional, Hilfer--proportional, Ġ-Hilfer--proportional type fractional
derivative operators, subject to different types of nonlocal boundary conditions. The topic of fractional differential
systems is one of the hot and important topics of research as such systems appear in the mathematical modeling
of physical and technical phenomena. As the book contains some recent new work on the existence theory
for nonlocal boundary value problems of fractional differential systems, it is expected that it will attract
the attention of researchers, modelers and graduate students who are interested in doing their research
on fractional differential systems.
Conference proceedings
Aug 2024
Presents a timely overview of control theory and related topics, such as the stability of PDEs and the Calderon problem
Features leading researchers sharing recent results in several exciting and fast-moving areas
Collects chapters based on talks given at the 2023 conference gControl & Related Fieldsh, held in Seville, Spain
Part of the book series: Trends in Mathematics (TM)
This volume presents a timely overview of control theory and related topics, such as the reconstruction problem,
the stability of PDEs, and the Calderon problem. The chapters are based on talks given at the conference
"Control & Related Fieldsh held in Seville, Spain in March 2023. In addition to providing a snapshot of these areas,
chapters also highlight breakthroughs on more specific topics, such as:
Stabilization of an acoustic system
The Kramers-Fokker-Planck operator
Control of parabolic equations
Control of the wave equation
Advances in Partial Differential Equations and Control will be a valuable resource for both established researchers
as well as more junior members of the community.
Aug 2024
Gathers selection tests in number theory proposed to national IMO teams
Covers tests administered in various countries from 1968 to 2024
Ideal as preparation material for students aiming to compete in mathematical contests
Part of the book series: Problem Books in Mathematics (PBM)
This book gathers carefully chosen selection tests proposed to IMO (International Mathematical Olympiad)
teams across many countries. Offering a blend of original solutions and adaptations by the author,
this work is chronologically organized and provides a unique insight into the evolution of this mathematical contest.
The proposed problems touch on topics such as the Chinese remainder theorem, Diophantine equations,
Fermat's theorem, Euler's theorem, perfect squares, sequences of integers, and Pythagorean triples, to name
a few. A meticulously crafted index helps the reader navigate through the topics with ease.
This book serves as an invaluable preparation tool for both aspiring students and those passionate about mathematics
alike.
Aug 2024
Collects contributions from top experts in the fields of history of mathematics and history of mathematics education
Explores topics in Gert Schubring's research heritage
Coral Festschrift in honor of Gert Schubring's 80th birthday
Part of the book series: Trends in the History of Science (TRENDSHISTORYSCIENCE)
This book celebrates Gert Schubring's 80th birthday and honors his impactful contributions to the field of history
of mathematics and its education. Recognized with the prestigious Hans Freudenthal Award in 2019,
Schubring's academic work sets the tone for this volume.
The thoughtfully curated articles in this collection offer insightful studies on textbooks and biographies
of key figures in mathematics and mathematics education, contextualizing their significance within the broader
historical landscape, and providing the readers with a deeper understanding of the development of the
history of mathematics and its education. Researchers as well as curious readers and students will find
this collection to be a valuable resource in the field.
Aug 2024
Extends Jordanfs results on maximal solvable subgroups
Discusses irreducible matrix groups, primitive permutation groups, and related topics
Suitable for graduate students and researchers in finite group theory and representation theory
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2346)
This book studies maximal solvable subgroups of classical groups over finite fields. It provides the first modern
account of Camille Jordan's classical results, and extends them, giving a classification of maximal irreducible
solvable subgroups of general linear groups, symplectic groups, and orthogonal groups over arbitrary finite fields.
A subgroup of a group G is said to be maximal solvable if it is maximal among the solvable subgroups of G.
The history of this notion goes back to Jordanfs Traite (1870), in which he provided a classification of maximal
solvable subgroups of symmetric groups. The main difficulty is in the primitive case, which leads to the problem
of classifying maximal irreducible solvable subgroups of general linear groups over a field of prime order.
One purpose of this monograph is expository: to give a proof of Jordanfs classification in modern terms.
More generally, the aim is to generalize these results to classical groups over arbitrary finite fields, and to provide
other results of interest related to irreducible solvable matrix groups.
The text will be accessible to graduate students and researchers interested in primitive permutation groups,
irreducible matrix groups, and related topics in group theory and representation theory.
The detailed introduction will appeal to those interested in the historical background of Jordanfs work.
Jul 2024
Provides the first comprehensive classification of normal 2-coverings of non-abelian simple groups
The first reference book to collect and consolidate existing research on normal 2-coverings and their applications
Showcases a wide range of applications of normal 2-coverings across different mathematical domains
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2352)
This book provides a complete and comprehensive classification of normal
2-coverings of non-abelian simple groups
and their generalizations. While offering readers a thorough understanding of these structures, and of the groups
admitting them, it delves into the properties of weak normal coverings. The focal point is the weak normal covering
number of a group G, the minimum number of proper subgroups required for every element of G to have a conjugate
within one of these subgroups, via an element of Aut(G). This number is shown to be at least 2 for every non-abelian
simple group and the non-abelian simple groups for which this minimum value is attained are classified. The discussion
then moves to almost simple groups, with some insights into their weak normal covering numbers. Applications span
algebraic number theory, combinatorics, Galois theory, and beyond. Compiling existing material and synthesizing
it into a cohesive framework, the book gives a complete overview of this fundamental aspect of finite group theory.
It will serve as a valuable resource for researchers and graduate students working on non-abelian simple groups,
Sep 2024
Explores topological techniques in delay and ordinary differential equations with a focus on continuum mechanics
Presents results related to problems of existence, multiplicity localization, bifurcation of solutions, and more
Uses topological methods, including degree theory, fixed point index theory, and classical fixed point theorems
Part of the book series: Advances in Mechanics and Mathematics (AMMA, volume 51)
Part of the book sub series: Advances in Continuum Mechanics (ACM)
This volume explores the application of topological techniques in the study of delay and ordinary differential equations
with a particular focus on continuum mechanics. Chapters, written by internationally recognized researchers
in the field, present results on problems of existence, multiplicity localization, bifurcation of solutions, and more.
Topological methods are used throughout, including degree theory, fixed point index theory, and classical and recent
fixed point theorems. A wide variety of applications to continuum mechanics are provided as well, such as chemostats,
non-Newtonian fluid flow, and flows in phase space. Topological Methods for Delay and Ordinary Differential Equations
will be a valuable resource for researchers interested in differential equations, functional analysis, topology,
and the applied sciences.
Aug 2024
presents intuitive explanations and elementary methods, making it ideal for students with diverse backgrounds
offers exercises that range from challenging students to reinforcing their learning of key concepts
clear guidance on navigating the content enables instructors to adapt the course to meet their students' needs
This textbook provides a concise introduction to the differential geometry of curves and surfaces in three-dimensional
space, tailored for undergraduate students with a solid foundation in mathematical analysis and linear algebra.
The book emphasizes the geometric content of the subject, aiming to quickly cover fundamental topics such
as the isoperimetric inequality and the Gauss?Bonnet theorem. This approach allows the author to extend beyond
the typical content of introductory books and include additional important geometric results, such as curves and surfaces
of constant width, the classification of complete surfaces of non-negative constant curvature,
and Hadamard's theorem on surfaces of non-positive curvature. This range of topics offers greater variety for
an introductory course.
Aug 2024
Provides new results on the arithmetic positivities of Arakelov geometry over adelic curves
Highlights connections with several classical topics in Arakelov geometry and Diophantine geometry
Includes detailed proofs and explanations
Part of the book series: Progress in Mathematics (PM, volume 355)
This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry
developed by the authors. It explores positivity conditions and establishes the Hilbert-Samuel formula
and the equidistribution theorem in the context of adelic curves. Connections with several classical topics in
Arakelov geometry and Diophantine geometry are highlighted, such as the arithmetic Hilbert-Samuel formula,
positivity of line bundles, equidistribution of small subvarieties, and theorems resembling the Bogomolov conjecture.
Detailed proofs and explanations are provided to ensure the text is accessible to both graduate students and
experienced researchers.