Bøger i Trends in Mathematics serien

This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed.The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.

The articles in this volume study various cohomological aspects of algebraic varieties:- characteristic classes of singular varieties;- geometry of flag varieties;- cohomological computations for homogeneous spaces;- K-theory of algebraic varieties;- quantum cohomology and Gromov-Witten theory.The main purpose is to give comprehensive introductions to the above topics through a series of "e;friendly"e; texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before.Contributors:Paolo AluffiMichel BrionAnders Skovsted BuchHaibao DuanAli Ulas Ozgur KisiselPiotr PragaczJorg SchurmannMarek SzyjewskiHarry Tamvakis

Generalized Deviations of Posets with Applications to Chain Conditions on Modules.- Stability Properties of Exchange Rings.- Good Conditions for the Total.- Semicentral Reduced Algebras.- On Generalizations of Injectivity.- Auslander-Gorenstein Rings for Beginners.- The Flat Cover Conjecture and Its Solution.- Some Results on Skew Polynomial Rings over a Reduced Ring.- Derived Equivalences and Tilting Theory.- CS-Property of Direct Sums of Uniform Modules.- Generalized Principally Injective Maximal Ideals.- The Module of Differentials of a Noncommutative Ring Extension.- Dual Bimodules and Nakayama Permutations.- The Coinduced Functor and Homological Properties of Hopf Modules.- Hopf Algebra Coaction and Its Application to Group-Graded Rings.- Non-Commutative Valuation Rings and Their Global Theories.- On the Maximal t-Corational Extensions of Modules.- On Values of Cyclotomic Polynomials.- Generalized Jordan Derivations.- On Quasi-Frobenius Rings.- Theories of Harada in Artinian Rings and Applications to Classical Artinian Rings.- On Some Dimensions of Modular Lattices and Matroids.- On Torsion-free Modules over Valuation Domains.- Hecke Orders, Cellular Orders and Quasi-Hereditary Orders.- Some Kind of Duality.- On Inertial Subalgebras of Certain Rings.- Some Recent Results on Hopficity, Co-hopficity and Related Properties.- Some Studies on QcF-coalgebras.- Finitely Pseudo-Frobenius Rings.- Surjectivity of Linkage Maps.- Infinite Quivers and Cohomology Groups.- Open Problems.

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal­ ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen­ tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter­ action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol­ ume treats various aspects of CR geometry and the Bergman kernel/ pro­ jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

This volume is an outcomeof invited lecturesdelivered at the Ring Theory Section of the 23rd Ohio State-DenisonConferencein May 1996. It also contains articles by some invited mathematicianswho could not attend the conference. These peer-refereedarticles showcasethe latest developmentsand trends in classicalRing Theory, highlighting the cro- fertilization of new techniquesand ideaswith the existing ones. Providing a wide variety of methodologies,this volume should be valuable both to graduatestudentsas well as to specialistsin Ring Theory. We would like to thank our colleagueswho investeda lot of their time to make the conferencea great success. In particular, our thanks go to ProfessorsTom Dowling, Dan Sanders,SurinderSehgal,Ron Solomonand Sergio R. L6pez-Permouthfor their help. The financial support for the Conference,provided by the Departmentof Mathematics,The Ohio State University, and MathematicsResearchInstitute, Columbus, is gratefully acknowleged. Many thanksgo to Dean Violet I. Meek for her commitment to the promotion of researchby her continuousencouragement of such efforts and for providing financial support from the Lima campusof The Ohio StateUniversity. We havereceivedimmensecooperationfrom all the refereeswho, meticulouslyand in a very short time, provided us with their reports in spite of their busy schedules. We expressour sincerethanks to all of them. Finally, we thank Ms. Cindy White for her excellent job in typing parts of this volume. We are pleasedto dedicatethis volume to ProfessorBruno J. Miiller on the occasionof his retirementfor his many contributionsto the Theory of Rings and Modules. As this volume was going to presswe have learned that ProfessorCarl Faith is retiring this year.

This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays.

The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory.

This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.

This book gathers nineteen papers presented at the first NLAGA-BIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 24¿28, 2019.The four-day symposium brought together African experts on nonlinear analysis and geometry and their applications, as well as their international partners, to present and discuss mathematical results in various areas. The main goal of the NLAGA project is to advance and consolidate the development of these mathematical fields in West and Central Africa with a focus on solving real-world problems such as coastal erosion, pollution, and urban network and population dynamics problems.The book addresses a range of topics related to partial differential equations, geometrical analysis of optimal shapes, geometric structures, optimization and optimal transportation, control theory, and mathematical modeling.

The book consists of articles based on the XXXVIII Biäowie¿a Workshop on Geometric Methods in Physics, 2019. The series of Biäowie¿a workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, with applications to classical and quantum physics.For the past eight years, the Biäowie¿a Workshops have been complemented by a School on Geometry and Physics, comprising series of advanced lectures for graduate students and early-career researchers. The extended abstracts of the five lecture series that were given in the eighth school are included. The unique character of the Workshop-and-School series draws on the venue, a famous historical, cultural and environmental site in the Biäowie¿a forest, a UNESCO World Heritage Centre in the east of Poland: lectures are given in the Nature and Forest Museum and local traditions are interwoven with the scientific activities.The chapter ¿Toeplitz Extensions in Noncommutative Topology and Mathematical Physics¿ is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones.

The book consists of articles based on the XXXVII Bialowieza Workshop on Geometric Methods in Physics, 2018.

This volume explores the connections between mathematical modeling, computational methods, and high performance computing, and how recent developments in these areas can help to solve complex problems in the natural sciences and engineering.

Local smoothing of Fourier integral operators and Hermite functions.- On () -classes on the Engel group.- Gelfand triples for the Kohn-Nirenberg quantization on homogeneous Lie groups.- A multiplicity result for a non-homogeneous subelliptic problem with Sobolev exponent.- The Dixmier trace and the noncommutative residue for multipliers on compact manifolds.- On the focusing energy-critical 3D quintic inhomogeneous NLS.- Lifespan of solutions to nonlinear Schr├╢dinger equations with general homogeneous nonlinearity of the critical order.- Spectral theory for magnetic Schr├╢dinger operators in exterior domains with exploding and oscillating long-range potentials.- Simple proof of the estimate of solutions to Schr├╢dinger equations with linear and sub-linear potentials in modulation spaces.- Remark on asymptotic order for the energy critical nonlinear damped wave equation to the linear heat equation via the Strichartz estimates.- On uniqueness for the generalized Choquard equation.- Characterization of the ground state to the intercritical NLS with a linear potential by the virial functional.- Well-posedness for a generalized Klein-Gordon-Schr├╢dinger equations.

With contributions by numerous experts

Wave phenomena are ubiquitous in nature. Their mathematical modeling, simulation and analysis lead to fascinating and challenging problems in both analysis and numerical mathematics. These challenges and their impact on significant applications have inspired major results and methods about wave-type equations in both fields of mathematics.The Conference on Mathematics of Wave Phenomena 2018 held in Karlsruhe, Germany, was devoted to these topics and attracted internationally renowned experts from a broad range of fields. These conference proceedings present new ideas, results, and techniques from this exciting research area.

The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme ΓÇ£Bridging the Gap Between Mathematical Modelling and Policy SupportΓÇ¥ on October 10th and 11th 2018. ISESO 2018 was organized by the KIT, the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart.

This book contains both expository articles and original research in the areas of function theory and operator theory. The book is intended for all researchers in the fields of function theory, operator theory and complex analysis in one or several variables.