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This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled "Einstein Equations: Physical and Mathematical Aspects of General Relativity". Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like: Quantum ergosphereGeneral relativistic Poynting-Robertson effect modellingNumerical relativityLength-contraction in curved spacetimeClassicality from an inhomogeneous universeEinstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

New fundamentals for designing future-oriented housing This book shows how architectural design can improve housing. It looks at 14 innovative multiunit dwelling projects through the lenses of current research on urban housing systems, driven by questions on social, environmental, and economic sustainability. Residential buildings designed for diverse cultural contexts are brought together and examined according to spatial antonyms: the individual and communal, the interior and exterior, and the determined and undetermined, to create a resource for future architectural practice. The book concentrates on design decisions and incorporates rich illustrations and conversations with architects and residents. It follows a series of talks curated by the Melbourne School of Design to extend the debate on the missing links between architectural practice and housing research. New fundamentals for designing future-oriented housing In-detail portraits of 14 impactful multi-unit dwelling projects by international architecture offices A rich set of illustrations created exclusively for this book

Cet ouvrage propose une contribution aux fondements de la théorie des espaces de Berkovich globaux. Cette approche récente à la géométrie analytique, qui mêle les théories classiques des espaces analytiques complexes et p-adiques, fournit un cadre géométrique naturel pour plusieurs théories arithmétiques, telle que la théorie d'Arakelov. Les auteurs suivent trois axes principaux, inexplorés au-delà de la dimension 1: catégorie, topologie et cohomologie. En particulier, ils introduisent une notion de domaine affinoïde surconvergent, pour lequel sont valables les analogues des théorèmes de Tate et de Kiehl.This monograph contributes to the foundations of the theory of global Berkovich spaces. This recent approach of analytic geometry, which blends the known theories of complex and p-adic analytic spaces, provides a natural geometric framework for several arithmetic theories, such as Arakelov geometry. The authors focus on three main themes which have yet to be investigated beyond dimension 1: category, topology, and cohomology. In particular, they introduce a notion of overconvergent affinoid domain where the analogues of Tate's and Kiehl's theorems hold.

This book collects papers related to the session ¿Harmonic Analysis and Partial Differential Equations¿ held at the 13th International ISAAC Congress in Ghent and provides an overview on recent trends and advances in the interplay between harmonic analysis and partial differential equations. The book can serve as useful source of information for 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.

"Schönheit hat nichts mit Geld oder Finanzen zu tun, sondern mit Kreativität und Liebe", sagt Anna Heringer und trifft damit den Nerv der Zeit - das belegen volle Hörsäle, internationale Auszeichnungen, wie z.B. der Aga Kahn Award 2007 oder der OBEL Award 2020 sowie Ausstellungen im MoMA, im MAM Sao Paulo und bei der Biennale in Venedig oder die Einladung zum TED Talk 2017. In Form Follows Love erzählt Anna Heringer der Autorin Dominique Gauzin-Müller von ihrem Werdegang als Architektin, dem Studium, ihren Erfahrungen während eines Workshops von Martin Rauch, ihrer Praxis im Globalen Süden, bis hin zu ihren aktuellen Projekten im Globalen Norden. Sie teilt mit uns dabei die Erkenntnis, dass Lehm nicht nur ein umweltfreundlicher Werkstoff ist, sondern damit beim Bauen im besten Fall sogar gesellschaftlich heilsame Prozesse angestoßen werden können. Essenzieller Text der auf Lehmbau spezialisierten Architektin Anna Heringer Wie Architektur Umwelt und Gesellschaft positiv verändern kann Bauen mit lokalen Ressourcen zur Erhaltung des ökologischen Gleichgewichts Erhältlich in Deutsch, Französisch und Englisch

This book presents the analysis of viscous flows in thin tube structures, and develops a multi-scale method for modeling blood flow. For the reader's convenience, the authors introduce all necessary notions and theorems from functional analysis and the classical theory of the Navier-Stokes equations. The problems of all asymptotic methods used in the book are explained as well, such as the dimension reduction and the boundary layer method. Through several numerical experiments, readers will discover that the proposed methods are more flexible than the theoretically predicted conditions. Multiscale Analysis of Viscous Flows in Thin Tube Structures will be a valuable resource for a wide range of readers, including applied mathematicians, specialists in bio-engineering, and biophysicists.

This monograph meticulously examines the contributions of French mathematician Michel Chasles to 19th-century geometry. Through an in-depth analysis of Chasles' extensive body of work, the author examines six pivotal arguments which collectively reshape the foundations of geometry. Chasles introduces a novel form of polarity, termed "parabolic," to the graphic context, so expressing the metric properties by means of this specific polarity--a foundational argument. Beyond the celebrated "Chasles theorem," he extends his analysis to the movement of a rigid body, employing concepts derived from projective geometry. This approach is consistently applied across diverse domains. Chasles employs the same methodology to analyze systems of forces. The fourth argument examined by the author concerns the principle of virtual velocities, which can also be addressed through a geometric analysis. In the fifth chapter, Chasles' philosophy of duality is explained. It is grounded on theduality principles of projective geometry. Finally, the author presents Chasles' synthetic solution for the intricate problem of ellipsoid attraction--the sixth and concluding chapter. Throughout these explorations, Chasles engages in a dynamic scientific dialogue with leading physicists and mathematicians of his era, revealing diverse perspectives and nuances inherent in these discussions.Tailored for historians specializing in mathematics and geometry, this monograph also beckons philosophers of mathematics and science, offering profound insights into the philosophical, epistemological, and methodological dimensions of Chasles' groundbreaking contributions. Providing a comprehensive understanding of Chasles' distinctive perspective on 19th-century geometry, this work stands as a valuable resource for scholars and enthusiasts alike.

This monograph offers a self-contained introduction to the regularity theory for integro-differential elliptic equations, mostly developed in the 21st century. This class of equations finds relevance in fields such as analysis, probability theory, mathematical physics, and in several contexts in the applied sciences. The work gives a detailed presentation of all the necessary techniques, with a primary focus on the main ideas rather than on proving all the results in their greatest generality.The basic building blocks are presented first, with the study of the square root of the Laplacian, and weak solutions to linear equations. Subsequently, the theory of viscosity solutions to nonlinear equations is developed, and proofs are provided for the main known results in this context. The analysis finishes with the investigation of obstacle problems for integro-differential operators and establishes the regularity of solutions and free boundaries.A distinctive feature of this work lies in its presentation of nearly all covered material in a monographic format for the first time, and several proofs streamline, and often simplify, those in the original papers. Furthermore, various open problems are listed throughout the chapters.

The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and complicated refinements. Apart from the basic theory of equations in divergence form, it includes subjects as singular perturbations, homogenization, computations, asymptotic behavior of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes systems, p-Laplace type operators, large solutions, and mountain pass techniques. Just a minimum on Sobolev spaces has been introduced and work on integration on the boundary has been carefully avoided to keep the reader attention focused on the beauty and variety of these issues. The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original, and have not been published elsewhere. The book will be of interest to graduate students and researchers specializing in partial differential equations.

This monograph presents a mathematically rigorous and accessible treatment of the interaction between information, decision, control, and probability in single-agent and multi-agent systems. The book provides a comprehensive and unified theory of information structures for stochastic control, stochastic teams, stochastic games, and networked control systems.Part I of the text is concerned with a general mathematical theory of information structures for stochastic teams, leading to systematic characterizations and classifications, geometric and topological properties, implications on existence, approximations and relaxations, their comparison, and regularity of optimal solutions in information. Information structures in stochastic games are then considered in Part II, and the dependence of equilibrium solutions and behavior on information is demonstrated. Part III studies information design through information theory in networked control systems - both linear and nonlinear - and discusses optimality and stability criteria. Finally, Part IV introduces information and signaling games under several solution concepts, with applications to prior mismatch, cost mismatch and privacy, reputation games and jamming. This text will be a valuable resource for researchers and graduate students interested in control theory, information theory, statistics, game theory, and applied mathematics. Readers should be familiar with the basics of linear systems theory, stochastic processes, and Markov chains.

The NLAGA's Biennial International Research Symposium (NLAGA-BIRS) is intended to gather African expertises in Nonlinear Analysis, Geometry and their Applications with their international partners in a four days conference where new mathematical results are presented and discussed. This book features the best papers presented during this Biennial. The different topics addressed are related to Partial Differential Equations, Differential inclusions, Geometrical Analysis of Optimal Shapes, Complex Analysis, Geometric Structures, Algebraic Geometry, Algebraic, Optimization, Optimal Control and Mathematical modeling. The main focus of the NLAGA project is to deepen and consolidate the development in West and Center Africa of Nonlinear Analysis, Geometry and their Applications, aimed at solving in particular real-world problems such as coastal erosion, urban network, pollution problems, and population dynamics.

This contributed volume presents recent advances as well as new directions in number theory and its applications. Algebraic and analytic number theory are the main focus with chapters showing how these areas are rapidly evolving. By gathering authors from over seven countries, readers will gain an international perspective on the current state of research as well as potential avenues to explore. Specific topics covered include: Algebraic Number TheoryElliptic curves and CryptographyHopf Galois theoryAnalytic and elementary number theory and applicationsNew Frontiers in Number Theory and Applications will appeal to researchers interested in gaining a global view of current research in number theory.

This book is devoted to the least gradient problem and its variants. The least gradient problem concerns minimization of the total variation of a function with prescribed values on the boundary of a Lipschitz domain. It is the model problem for studying minimization problems involving functionals with linear growth. Functions which solve the least gradient problem for their own boundary data, which arise naturally in the study of minimal surfaces, are called functions of least gradient.The main part of the book is dedicated to presenting the recent advances in this theory. Among others are presented an Euler-Lagrange characterization of least gradient functions, an anisotropic counterpart of the least gradient problem motivated by an inverse problem in medical imaging, and state-of-the-art results concerning existence, regularity, and structure of solutions. Moreover, the authors present a surprising connection between the least gradient problem and the Monge-Kantorovich optimal transport problem and some of its consequences, and discuss formulations of the least gradient problem in the nonlocal and metric settings. Each chapter is followed by a discussion section concerning other research directions, generalizations of presented results, and presentation of some open problems. The book is intended as an introduction to the theory of least gradient functions and a reference tool for a general audience in analysis and PDEs. The readers are assumed to have a basic understanding of functional analysis and partial differential equations. Apart from this, the text is self-contained, and the book ends with five appendices on functions of bounded variation, geometric measure theory, convex analysis, optimal transport, and analysis in metric spaces.

This text presents a collection of mathematical exercises with the aim of guiding readers to study topics in statistical physics, equilibrium thermodynamics, information theory, and their various connections. It explores essential tools from linear algebra, elementary functional analysis, and probability theory in detail and demonstrates their applications in topics such as entropy, machine learning, error-correcting codes, and quantum channels. The theory of communication and signal theory are also in the background, and many exercises have been chosen from the theory of wavelets and machine learning. Exercises are selected from a number of different domains, both theoretical and more applied. Notes and other remarks provide motivation for the exercises, and hints and full solutions are given for many. For senior undergraduate and beginning graduate students majoring in mathematics, physics, or engineering, this text will serve as a valuable guide as theymove on to more advanced work.

Metric algebraic geometry combines concepts from algebraic geometry and differential geometry. Building on classical foundations, it offers practical tools for the 21st century. Many applied problems center around metric questions, such as optimization with respect to distances.After a short dive into 19th-century geometry of plane curves, we turn to problems expressed by polynomial equations over the real numbers. The solution sets are real algebraic varieties. Many of our metric problems arise in data science, optimization and statistics. These include minimizing Wasserstein distances in machine learning, maximum likelihood estimation, computing curvature, or minimizing the Euclidean distance to a variety.This book addresses a wide audience of researchers and students and can be used for a one-semester course at the graduate level. The key prerequisite is a solid foundation in undergraduate mathematics, especially in algebra and geometry. This is an openaccess book.

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray's problem on existence of a solution to the boundary value problem for the stationary Navier--Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier--Stokes equations. This book will be the first major work on the Navier--Stokes equations to explore Leray's problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the reader's convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and Navier--Stokes systems are presented. For researchers in this active area, this book will be a valuable resource.

The book gives the basic results of the theory of the spaces Ap¿ of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ¿ permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian's theory of spaces Ap¿ (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the ¿-extensions of M. M. Djrbashian's two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane.The book can be useful for a wide range of readers. It can be a good handbook for Master, PhD students and Postdoctoral Researchers for enlarging their knowledge and analytical methods, as well as a useful resource for scientists who want to extend their investigation fields.

Many philosophers, physicists, and mathematicians have wondered about the remarkable relationship between mathematics with its abstract, pure, independent structures on one side, and the wilderness of natural phenomena on the other. Famously, Wigner found the "effectiveness" of mathematics in defining and supporting physical theories to be unreasonable, for how incredibly well it worked. Why, in fact, should these mathematical structures be so well-fitting, and even heuristic in the scientific exploration and discovery of nature? This book argues that the effectiveness of mathematics in physics is reasonable. The author builds on useful analogies of prime numbers and elementary particles, elementary structure kinship and the structure of systems of particles, spectra and symmetries, and for example, mathematical limits and physical situations. The two-dimensional Ising model of a permanent magnet and the proofs of the stability of everyday matter exemplify such effectiveness, and the power of rigorous mathematical physics. Newton is our original model, with Galileo earlier suggesting that mathematics is the language of Nature.

This volume presents modern developments in analysis, PDEs and geometric analysis by some of the leading worldwide experts, prominent junior and senior researchers who were invited to be part of the Ghent Analysis & PDE Center Methusalem Seminars from 2021 to 2022. The contributions are from the speakers of the Methusalem Colloquium, Methusalem Junior Seminar and Geometric Analysis Seminar. The volume has two main topics: 1. Analysis and PDEs. The volume presents recent results in fundamental problems for solving partial integro-differential equations in different settings such as Euclidean spaces, manifolds, Banach spaces, and many others. Discussions about the global and local solvability using micro-local and harmonic analysis methods, studies of new techniques and approaches arising from a physical perspective or the mathematical point of view have also been included. Several connected branches arising in this regard are shown. 2. Geometric analysis. The volume presents studies of modern techniques for elliptic and subelliptic PDEs that in recent times have been used to establish new results in differential geometry and differential topology. These topics involve the intrinsic research in microlocal analysis, geometric analysis, and harmonic analysis abroad. Different problems having relevant geometric information for different applications in mathematical physics and other problems of classification have been considered.

This volume explores state-of-the-art developments in theoretical and applied fluid mechanics with a focus on stabilization and control. Chapters are based on lectures given at the summer school "Fluids under Control", held in Prague from August 23-27, 2021. With its accessible and flexible presentation, readers will be motivated to deepen their understanding of how mathematics and physics are connected. Specific topics covered include: Stabilization of the 3D Navier-Stokes systemFlutter stabilization of flow-state systemsTurbulence controlDesign through analysis Fluids Under Control will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.

John Corcoran was a very well-known logician who worked on several areas of logic. He produced decisive works giving a better understanding of two major figures in the history of logic, Aristotle and Boole. Corcoran had a close association with Alfred Tarski, a prominent 20th-century logician. This collaboration manifested in Corcoran's substantial introduction to Tarski's seminal book, Logic, Semantics, Metamathematics (1956). Additionally, Corcoran's posthumous editorial involvement in 'What are logical notions?' (1986) breathed new life into this seminal paper authored by Tarski. His scholarly pursuits extended to the intricate explication of fundamental concepts in modern logic, including variables, propositions, truth, consequences, and categoricity. Corcoran's academic curiosity extended further to the intersection of ethics and logic, reflecting his contemplation of their interrelation. Beyond these theoretical contributions, Corcoran was deeply engaged in the pedagogical dimensions of logic instruction. This volume serves as a compilation of articles contributed by Corcoran's students, colleagues, and international peers. By encompassing a diverse range of subjects, this collection aptly mirrors Corcoran's wide-ranging interests, offering insights that not only deepen our understanding of his work but also advance the theoretical frameworks he explored.

I: Genetics and conservation biology.- Introductory remarks: Genetics and conservation biology.- Global issues of genetic diversity.- II: Genetic variation and fitness.- Introductory remarks.- Genetic variation and fitness: Conservation lessons from pines.- Genetic diversity and fitness in small populations.- Mutation load depending on variance in reproductive success and mating system.- Extinction risk by mutational meltdown: Synergistic effects between population regulation and genetic drift.- III: Inbreeding, population and social structure.- Introductory remarks.- Inbreeding: One word, several meanings, much confusion.- The genetic structure of metapopulations and conservation biology.- Effects of inbreeding in small plant populations: Expectations and implications for conservation.- The interaction of inbreeding depression and environmental stochasticity in the risk of extinction of small populations.- Genetic structure of a population with social structure and migration.- Guidelines in conservation genetics and the use of the population cage experiments with butterflies to investigate the effects of genetic drift and inbreeding.- IV: Molecular approaches to conservation.- Introductory remarks.- Rare alleles, MHC and captive breeding.- Andean tapaculos of the genus Scytalopus (Aves, Rhinocryptidae): A study of speciation using DNA sequence data.- Genetic distances and the setting of conservation priorities.- Multi-species risk analysis, species evaluation and biodiversity conservation.- V: Case studies.- Introductory remarks.- On genetic erosion and population extinction in plants: A case study in Scabiosa columbaria and Salvia pratensis.- Effects of releasing hatchery-reared brown trout to wild trout populations.- Genetics and demography of rare plants and patchily distributed colonizing species.- Response to environmental change: Genetic variation and fitness in Drosophila buzzatii following temperature stress.- Alternative life histories and genetic conservation.- The principles of population monitoring for conservation genetics.- VI: Genetic resource conservation.- Introductory remarks.- Optimal sampling strategies for core collections of plant genetic resources.- Conservation genetics and the role of botanical gardens.- Animal breeding and conservation genetics.- Scenarios.- Introductory remarks.- A: The genetic monitoring of primate populations for their conservation.- B: Heavy metal tolerance, plant evolution and restoration ecology.- C: Genetic conservation and plant agriculture.- D: Fragmented plant populations and their lost interactions.- E: Host-pathogen coevolution under in situ conservation.- Concluding remarks.

Parallel Completion Techniques.- The Computation of Gröbner Bases Using an Alternative Algorithm.- Symmetrization Based Completion.- On the Reduction of G-invariant Polynomials for an Arbitrary Permutation Groups G.- The Non-Commutaive Gröbner Freaks.- Alternatives in Implementing Noncommutative Gröbner Basis Systems.- String Rewriting and Gröbner Bases - A General Approach to Monoid and Group Rings.- Gröbner Fans and Projective Schemes.- Normalized Rewriting: A Unified View of Knuth-Bendix Completion and Gröbner Bases Computation.- New Directions for Syntactic Termination Orderings.- Two-sided Gröbner Bases in Iterated Ore Extensions.- Computing the Torsion Group of Elliptic Curves by the Method of Gröbner Bases.- Finding a Finite Group presentation Using Rewriting.- Deciding Degree-Four-Identities for Alternative Rings by Rewriting.

Structural optimization - a survey.- Mathematical optimization: an introduction.- Design optimization with the finite element program ANSYSR.- B&B: a FE-program for cost minimization in concrete design.- The CAOS system.- Shape optimization with program CARAT.- DYNOPT: a program system for structural optimization weight minimum design with respect to various constraints.- MBB-Lagrange: a computer aided structural design system.- The OASIS-ALADDIN structural optimization system.- The structural optimization system OPTSYS.- SAPOP: an optimization procedure for multicriteria structural design.- SHAPE: a structural shape optimization program.- STARS: mathematical foundations.