Birkhäuser

This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.

The Breadth of Symplectic and Poisson Geometry
Jerrold E. Marsden, Tudor S. Ratiu
 Birkhäuser
 3 Juillet 2007
 9780817644192
One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Written in his honor, the invited papers in this volume reflect the active and vibrant research in these areas and are a tribute to Weinstein's ongoing influence.
The wellrecognized contributors to this text cover a broad range of topics: Induction and reduction for systems with symmetry, symplectic geometry and topology, geometric quantization, the Weinstein Conjecture, Poisson algebra and geometry, Dirac structures, deformations for Lie group actions, Kähler geometry of moduli spaces, theory and applications of Lagrangian and Hamiltonian mechanics and dynamics, symplectic and Poisson groupoids, and quantum representations. 
In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The MeyersElcart System); and determining whether there are any "full" interpolation results for linear operators between Morrey spaces. This book will serve as a useful reference to graduate students and researchers interested in Potential Theory, Harmonic Analysis, PDE, and/or Morrey Space Theory.

The work on Autonomic Road Transport Support (ARTS) presented here aims at meeting the challenge of engineering autonomic behavior in Intelligent Transportation Systems (ITS) by fusing research from the disciplines of traffic engineering and autonomic computing. Ideas and techniques from leading edge artificial intelligence research have been adapted for ITS over the last 30 years. Examples include adaptive control embedded in real time traffic control systems, heuristic algorithms (e.g. in SATNAV systems), image processing and computer vision (e.g. in automated surveillance interpretation). Autonomic computing which is inspired from the biological example of the body's autonomic nervous system is a more recent development. It allows for a more efficient management of heterogeneous distributed computing systems. In the area of computing, autonomic systems are endowed with a number of properties that are generally referred to as selfX properties, including selfconfiguration, selfhealing, selfoptimization, selfprotection and more generally selfmanagement. Some isolated examples of autonomic properties such as selfadaptation have found their way into ITS technology and have already proved beneficial. This edited volume provides a comprehensive introduction to Autonomic Road Transport Support (ARTS) and describes the development of ARTS systems. It starts out with the visions, opportunities and challenges, then presents the foundations of ARTS and the platforms and methods used and it closes with experiences from realworld applications and prototypes of emerging applications. This makes it suitable for researchers and practitioners in the fields of autonomic computing, traffic and transport management and engineering, AI, and software engineering. Graduate students will benefit from stateoftheart description, the study of novel methods and the case studies provided.

The theory of realvalued Sobolev functions is a classical part of analysis and has a wide range of applications in pure and applied mathematics. By contrast, the study of manifoldvalued Sobolev maps is relatively new. The incentive to explore these spaces arose in the last forty years from geometry and physics. This monograph is the first to provide a unified, comprehensive treatment of Sobolev maps to the circle, presenting numerous results obtained by the authors and others. Many surprising connections to other areas of mathematics are explored, including the MongeKantorovich theory in optimal transport, items in geometric measure theory, Fourier series, and nonlocal functionals occurring, for example, as denoising filters in image processing. Numerous digressions provide a glimpse of the theory of spherevalued Sobolev maps.
Each chapter focuses on a single topic and starts with a detailed overview, followed by the most significant results, and rather complete proofs. The "Complements and Open Problems" sections provide short introductions to various subsequent developments or related topics, and suggest newdirections of research. Historical perspectives and a comprehensive list of references close out each chapter. Topics covered include lifting, point and line singularities, minimal connections and minimal surfaces, uniqueness spaces, factorization, density, Dirichlet problems, trace theory, and gap phenomena.
Sobolev Maps to the Circle will appeal to mathematicians working in various areas, such as nonlinear analysis, PDEs, geometric analysis, minimal surfaces, optimal transport, and topology. It will also be of interest to physicists working on liquid crystals and the GinzburgLandau theory of superconductors. 
XIII Symposium on Probability and Stochastic Processes
Alfonso RochaArteaga, Sergio I. Lopez, Victor M. Rivero, Arno SiriJegousse
 Birkhäuser
 16 Octobre 2020
 9783030575137
This volume features a collection of contributed articles and lecture notes from the XIII Symposium on Probability and Stochastic Processes, held at UNAM, Mexico, in December 2017.It is split into two main parts: the first one presents lecture notes of the course provided by Mauricio Duarte, followed by its second part which contains research contributions of some of the participants.

Fractal Geometry and Stochastics VI
Ben Hambly, Uta Freiberg, Michael Hinz, Steffen Winter
 Birkhäuser
 23 Mars 2021
 9783030596491
This collection of contributions originates from the wellestablished conference series "Fractal Geometry and Stochastics" which brings together researchers from different fields using concepts and methods from fractal geometry.
Carefully selected papers from keynote and invited speakers are included, both discussing exciting new trends and results and giving a gentle introduction to some recent developments. The topics covered include Assouad dimensions and their connection to analysis, multifractal properties of functions and measures, renewal theorems in dynamics, dimensions and topology of random discrete structures, selfsimilar trees, phyperbolicity, phase transitions from continuous to discrete scale invariance, scaling limits of stochastic processes, stemistable distributions and fractional differential equations, and diffusion limited aggregation.
Representing a rich source of ideas and a good starting point for more advanced topics in fractal geometry, the volume will appeal to both established experts and newcomers. 
Geometric Flows on Planar Lattices
Andrea Braides, Margherita Solci
 Birkhäuser
 23 Mars 2021
 9783030699178
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gammaconvergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on twodimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.

This book expounds on the recent developments in applications of holomorphic functions in the theory of hypercomplex and antiHermitian manifolds as well as in the geometry of bundles. It provides detailed information about holomorphic functions in algebras and discusses some of the areas in geometry with applications. The book proves the existence of a onetoone correspondence between hypercomplex antiKähler manifolds and antiHermitian manifolds with holomorphic metrics, and also a deformed lifting to bundles. Researchers and students of geometry, algebra, topology and physics may find the book useful as a selfstudy guide.

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 wavetype 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. 
Nonlinear Analysis, Geometry and Applications
Diaraf Seck, Kinvi Kangni, Philibert Nang, Marie Salomon Sambou
 Birkhäuser
 20 Novembre 2020
 9783030573362
This book gathers nineteen papers presented at the first NLAGABIRS Symposium, which was held at the Cheikh Anta Diop University in Dakar, Senegal, on June 2428, 2019.The fourday 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 realworld 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. 
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudodifferential operators, partial differential equations, and timefrequency analysis. It is based on lectures given at the international conference "Fourier Analysis and PseudoDifferential Operators," June 2530, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series "Fourier Analysis and Partial Differential Equations."

Lattice Theory: Special Topics and Applications
George Gratzer, Friedrich Wehrung
 Birkhäuser
 27 Août 2014
 9783319064130
George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer.

This book traces the life of Cholesky (18751918), and gives his family history. After an introduction to topography, an English translation of an unpublished paper by him where he explained his method for linear systems is given, studied and replaced in its historical context. His other works, including two books, are also described as well as his involvement in teaching at a superior school by correspondence. The story of this school and its founder, Léon Eyrolles, are addressed. Then, an important unpublished book of Cholesky on graphical calculation is analyzed in detail and compared to similar contemporary publications. The biography of Ernest Benoit, who wrote the first paper where Cholesky´s method is explained, is provided. Various documents, highlighting the life and the personality of Cholesky, end the book.

Arithmetic LFunctions and Differential Geometric Methods
Pierre Charollois, Gerard Freixas I Montplet, Vincent Maillot
 Birkhäuser
 17 Mai 2021
 9783030652036
This book is an outgrowth of the conference Regulators IV: An International Conference on Arithmetic Lfunctions and Differential Geometric Methods that was held in Paris in May 2016. Gathering contributions by leading experts in the field ranging from original surveys to pure research articles, this volume provides comprehensive coverage of the front most developments in the field of regulator maps. Key topics covered are: Additive polylogarithms Analytic torsions ChabautyKim theory Local GrothendieckRiemannRoch theorems Periods Syntomic regulatorThe book contains contributions by M. Asakura, J. Balakrishnan, A. Besser, A. Best, F. Bianchi, O. Gregory, A. Langer, B. Lawrence, X. Ma, S. Müller, N. Otsubo, J. Raimbault, W. Raskin, D. Rssler, S. Shen, N. Triantafi llou, S. Ünver and J. Vonk.

Output Feedback Reinforcement Learning Control for Linear Systems
Zongli Lin, Syed Ali Asad Rizvi
 Birkhäuser
 29 Novembre 2022
 9783031158582
This monograph explores the analysis and design of modelfree optimal control systems based on reinforcement learning (RL) theory, presenting new methods that overcome recent challenges faced by RL. New developments in the design of sensor data efficient RL algorithms are demonstrated that not only reduce the requirement of sensors by means of output feedback, but also ensure optimality and stability guarantees. A variety of practical challenges are considered, including disturbance rejection, control constraints, and communication delays. Ideas from game theory are incorporated to solve output feedback disturbance rejection problems, and the concepts of low gain feedback control are employed to develop RL controllers that achieve global stability under control constraints.
Output Feedback Reinforcement Learning Control for Linear Systems will be a valuable reference for graduate students, control theorists working on optimal control systems, engineers, and applied mathematicians. 
Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology
Collectif
 Birkhäuser
 12 Décembre 2020
 9783030433802
This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas' students and past collaborators. Their articles attest and commemorate his lifelong contribution and influence to these fields.

Solvable Algebras of Pseudodifferential Operators
Boris Plamenevskii, Oleg Sarafanov
 Birkhäuser
 4 Mai 2023
 9783031283987
This book presents original research results on pseudodifferential operators.
C*algebras generated by pseudodifferential operators with piecewise smooth symbols on a smooth manifold are considered. For each algebra, all the equivalence classes of irreducible representations are listed; as a consequence, a criterion for a pseudodifferential operator to be Fredholm is stated, the topology on the spectrum is described, and a solving series is constructed.
Pseudodifferential operators on manifolds with edges are introduced, their properties are considered in details, and an algebra generated by the operators is studied.
An introductory chapter includes all necessary preliminaries from the theory of pseudodifferential operators and C*algebras. 
Optimal Control of Coupled Systems of Partial Differential Equations
Fredi Troltzsch, Jurgen Sprekels, Gunter Leugering, Karl Kunisch
 Birkhäuser
 3 Décembre 2009
 9783764389239
Beyond Lack of Compactness and Lack of Stability of a Coupled ParabolicHyperbolic FluidStructure System. A Continuous Adjoint Approach to Shape Optimization for Navier Stokes Flow. Recent Advances in the Analysis of Stateconstrained Elliptic Optimal Control Problems. Fast and Strongly Localized Observation for a perturbed Plate Equation. Representations, Composition, and Decomposition of C 1,1hypersurfaces. On Some Nonlinear Optimal Control Problems with Vectorvalued Affine Control Constraints. Weak Solutions to a Model for Crystal Growth from the Melt in Changing Magnetic Fields. Lavrentiev Proxregularization Methods for Optimal Control Problems with Pointwise State Constraints. Nonlinear Feedback Solutions for a Class of Quantum Control Problems. Optimal Feedback Synthesis for Bolza Control Problem Arising in Linearized Fluid Structure Interaction. Singlestep Oneshot Aerodynamic Shape Optimization. Shape Differentiability of Drag Functional for Compressible NavierStokes Equations. Nullcontrollability for a Coupled HeatFinitedimensional Beam System. Feedback Modal Control of Partial Differential Equations. Optimization Problems for Thin Elastic Structures. A New Nonlinear Semidefinite Programming Algorithm with an Application to Multidisciplinary Free Material Optimization. How to Check Numerically the Sufficient Optimality Conditions for Infinitedimensional Optimization Problems. Hidden Boundary Shape Derivative for the Solution to Maxwell Equations and Non Cylindrical Wave Equations.

This volume explores A.P. Morse's (19111984) development of a formal language for writing mathematics, his application of that language in set theory and mathematical analysis, and his unique perspective on mathematics. The editor brings together a variety of Morse's works in this compilation, including Morse's book A Theory of Sets, Second Edition (1986), in addition to material from another of Morse's publications, Web Derivatives, and notes for a course on analysis from the early 1950's. Because Morse provided very little in the way of explanation in his written works, the editor's commentary serves to outline Morse's goals, give informal explanations of Morse's formal language, and compare Morse's often unique approaches to more traditional approaches. Minor corrections to Morse's previously published works have also been incorporated into the text, including some updated axioms, theorems, and definitions. The editor's introduction thoroughly details the corrections and changes made and provides readers with valuable insight on Morse's methods.
A.P. Morse's Set Theory and Analysis will appeal to graduate students and researchers interested in set theory and analysis who also have an interest in logic. Readers with a particular interest in Morse's unique perspective and in the history of mathematics will also find this book to be of interest. 
Advances in the Theory of Varieties of Semigroups
Edmond W. H. Lee
 Birkhäuser
 8 Avril 2023
 9783031164972
This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this indepth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author's own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.

Michele Sce's Works in Hypercomplex Analysis
Irene Sabadini, Fabrizio Colombo, Daniele C. Struppa
 Birkhäuser
 24 Octobre 2020
 9783030502164
This book presents English translations of Michele Sce's most important works, originally written in Italian during the period 19551973, on hypercomplex analysis and algebras of hypercomplex numbers. Despite their importance, these works are not very well known in the mathematics community because of the language they were published in. Possibly the most remarkable instance is the socalled FueterSce mapping theorem, which is a cornerstone of modern hypercomplex analysis, and is not yet understood in its full generality.This volume is dedicated to revealing and describing the framework Sce worked in, at an exciting time when the various generalizations of complex analysis in one variable were still in their infancy. In addition to faithfully translating Sce's papers, the authors discuss their significance and explain their connections to contemporary research in hypercomplex analysis. They also discuss many concrete examples that can serve as a basis for further research. The vast majority of the results presented here will be new to readers, allowing them to finally access the original sources with the benefit of comments from fellow mathematicians active in the field of hypercomplex analysis. As such, the book offers not only an important chapter in the history of hypercomplex analysis, but also a roadmap for further exciting research in the field.

What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals?
You'll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the "analysis of the infinite." A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis. 
Ruggiero Boscovich's Theory of Natural Philosophy
Luca Guzzardi
 Birkhäuser
 31 Août 2020
 9783030520939
Drawing on published works, correspondence and manuscripts, this book offers the most comprehensive reconstruction of Boscovich's theory within its historical context. It explains the genesis and theoretical as well as epistemological underpinnings in light of the Jesuit tradition to which Boscovich belonged, and contrasts his ideas with those of Newton, Leibniz, and their legacy. Finally, it debates crucial issues in earlymodern physical science such as the concept of force, the particlelike structure of matter, the idea of material points and the notion of continuity, and shares novel insights on Boscovich's alleged influence on later developments in physics.
With its attempt to reduce all natural forces to one single law, Boscovich's Theory of Natural Philosophy, published in 1758, left a lasting impression on scientists and philosophers of every age regarding the fundamental unity of physical phenomena. The theory argues that every pair of material points is subject to one mutual force  and always the same force  which is their propensity to be mutually attracted or repelled, depending on their distance from one another. Furthermore, the action of this unique force is visualized through a famous diagram that fascinated generations of scientists. But his understanding of key terms of the theory  such as the notion of force involved and the very idea of a material point  is only ostensibly similar to our current conceptual framework. Indeed, it needs to be clarified within the plurality of contexts in which it has emerged rather than being considered in view of later developments.The book is recommended for scholars and students interested in the ideas of the early modern period, especially historians and philosophers of science, mathematicians and physicists with an interest in the history of the discipline, and experts on Jesuit science and philosophy.