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Geometries In Interaction
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Book Synopsis Geometries in Interaction by : Y. Eliashberg
Download or read book Geometries in Interaction written by Y. Eliashberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades of the 20th century tremendous progress has been achieved in geometry. The discovery of deep interrelations between geometry and other fields including algebra, analysis and topology has pushed it into the mainstream of modern mathematics. This Special Issue of Geometric And Functional Analysis (GAFA) in honour of Mikhail Gromov contains 14 papers which give a wide panorama of recent fundamental developments in modern geometry and its related subjects. The book is a collection of important results and an enduring source of new ideas for researchers and students in a broad spectrum of directions related to all aspects of geometry and its applications to functional analysis, PDE, analytic number theory and physics. This is a reprint from GAFA, Vol. 5 (1995), No. 2., enlarged by a short biography of Mikhail Gromov and a list of his publications.
Book Synopsis Geometry of the Fundamental Interactions by : M. D. Maia
Download or read book Geometry of the Fundamental Interactions written by M. D. Maia and published by Springer Science & Business Media. This book was released on 2011-06-14 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles. Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field. This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.
Book Synopsis Interaction Geometry by : Rolfe A. Leary
Download or read book Interaction Geometry written by Rolfe A. Leary and published by . This book was released on 1976 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Geometry of Ecological Interactions by : Ulf Dieckmann
Download or read book The Geometry of Ecological Interactions written by Ulf Dieckmann and published by Cambridge University Press. This book was released on 2000-05-04 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of theoretical ecology has expanded dramatically in the last few years. This volume gives detailed coverage of the main developing areas in spatial ecological theory, and is written by world experts in the field. Integrating the perspective from field ecology with novel methods for simplifying spatial complexity, it offers a didactical treatment with a gradual increase in mathematical sophistication from beginning to end. In addition, the volume features introductions to those fundamental phenomena in spatial ecology where emerging spatial patterns influence ecological outcomes quantitatively. An appreciation of the consequences of this is required if ecological theory is to move on in the 21st century. Written for reseachers and graduate students in theoretical, evolutionary and spatial ecology, applied mathematics and spatial statistics, it will be seen as a ground breaking treatment of modern spatial ecological theory.
Book Synopsis Geometries in Interaction by : Y. Eliashberg
Download or read book Geometries in Interaction written by Y. Eliashberg and published by Springer Science & Business Media. This book was released on 1995-08-29 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains 14 papers (originally published in Geometric and Functional Analysis, v.5, no.2, 1995) which give a broad overview of recent fundamental developments in modern geometry and related subjects. Among the topics are aspects of long-time behavior of solutions of nonlinear Hamiltonian evolution equations; Lagrangian intersections in contact geometry; and Selberg's eigenvalue conjecture. Includes an exceedingly brief biography (3pp.) and a list of Gromov's (b.1943) publications. No index. Annotation copyright by Book News, Inc., Portland, OR
Book Synopsis Singularities and Their Interaction with Geometry and Low Dimensional Topology by : Javier Fernández de Bobadilla
Download or read book Singularities and Their Interaction with Geometry and Low Dimensional Topology written by Javier Fernández de Bobadilla and published by Springer Nature. This book was released on 2021-05-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.
Book Synopsis Shock-turbulence Interaction and Richtmyer-Meshkov Instability in Spherical Geometry by : Ankit Vijay Bhagatwala
Download or read book Shock-turbulence Interaction and Richtmyer-Meshkov Instability in Spherical Geometry written by Ankit Vijay Bhagatwala and published by Stanford University. This book was released on 2011 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The canonical problems of shock-turbulence interaction and Richtmyer-Meshkov instability (RMI) are central to understanding the hydrodynamic processes involved in Inertial Confinement Fusion (ICF). Over the last few decades, there has been considerable analytical, computational and experimental work on the planar versions of these problems. In spite of the problem of interest being spherical in nature, there have been few studies in any of the three areas for these problems. It is not clear a priori, that the conclusions drawn from planar versions of these problems carry over to the spherical domain. The research presented here represents a first attempt to understand the hydrodynamic processes involved in an Inertial Fusion Engine (IFE) from capsule implosion to interaction of the resulting shock waves with the chamber gases. To abstract the key hydrodynamic components from the complex physics involved in an IFE, three canonical problems are identified and simulated: Interaction of a blast wave with isotropic turbulence, interaction of a converging shock with isotropic turbulence and RMI in spherical geometry. The last problem is a hydrodynamic abstraction of the capsule implosion itself, while the first two problems attempt to model the late stage interaction of fusion induced shock waves with chamber gases. On the shock-turbulence front, the study primarily focuses on the effect of shock strength relative to background turbulence on vorticity dynamics, which forms the cornerstone of any turbulence simulation. The effect of turbulence on shock structure is also characterized. For the converging shock, the maximum compression achieved in presence of turbulence is compared with that for a pure shock. For spherical RMI, focus is on evolution of the mixing layer and growth in vorticity and turbulent kinetic energy for different incident shock Mach numbers. The effect of interface perturbation on maximum compression achieved, which is one of the most important metrics for feasible ICF, is also considered.
Book Synopsis Geometries of Nature, Living Systems and Human Cognition by :
Download or read book Geometries of Nature, Living Systems and Human Cognition written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Structures for Physics by : Bob Coecke
Download or read book New Structures for Physics written by Bob Coecke and published by Springer. This book was released on 2011-01-15 with total page 1034 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.
Book Synopsis Topology, Geometry, and Gauge Fields by : Gregory L. Naber
Download or read book Topology, Geometry, and Gauge Fields written by Gregory L. Naber and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.
Book Synopsis The Interaction of Analysis and Geometry by : Victor I. Burenkov
Download or read book The Interaction of Analysis and Geometry written by Victor I. Burenkov and published by American Mathematical Soc.. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004), this title includes topics such as geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion, and nonlinear potential theory."
Book Synopsis Interactions on Digital Tablets in the Context of 3D Geometry Learning by : David Bertolo
Download or read book Interactions on Digital Tablets in the Context of 3D Geometry Learning written by David Bertolo and published by John Wiley & Sons. This book was released on 2016-07-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last few years, multi-touch mobile devices have become increasingly common. However, very few applications in the context of 3D geometry learning can be found in app stores. Manipulating a 3D scene with a 2D device is the main difficulty of such applications. Throughout this book, the author focuses on allowing young students to manipulate, observe and modify 3D scenes using new technologies brought about by digital tablets. Through a user-centered approach, the author proposes a grammar of interactions adapted to young learners, and then evaluates acceptability, ease of use and ease of learning of the interactions proposed. Finally, the author studies in situ the pedagogic benefits of the use of tablets with an app based on the suggested grammar. The results show that students are able to manipulate, observe and modify 3D scenes using an adapted set of interactions. Moreover, in the context of 3D geometry learning, a significant contribution has been observed in two classes when students use such an application. The approach here focuses on interactions with digital tablets to increase learning rather than on technology. First, defining which interactions allow pupils to realize tasks needed in the learning process, then, evaluating the impact of these interactions on the learning process. This is the first time that both interactions and the learning process have been taken into account at the same time.
Book Synopsis Algebra, Geometry and Their Interactions by : Alberto Corso
Download or read book Algebra, Geometry and Their Interactions written by Alberto Corso and published by American Mathematical Soc.. This book was released on 2007 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume's papers present work at the cutting edge of current research in algebraic geometry, commutative algebra, numerical analysis, and other related fields, with an emphasis on the breadth of these areas and the beneficial results obtained by the interactions between these fields. This collection of two survey articles and sixteen refereed research papers, written by experts in these fields, gives the reader a greater sense of some of the directions in which this research is moving, as well as a better idea of how these fields interact with each other and with other applied areas. The topics include blowup algebras, linkage theory, Hilbert functions, divisors, vector bundles, determinantal varieties, (square-free) monomial ideals, multiplicities and cohomological degrees, and computer vision.
Book Synopsis Interactions of Classical and Numerical Algebraic Geometry by : Daniel James Bates
Download or read book Interactions of Classical and Numerical Algebraic Geometry written by Daniel James Bates and published by American Mathematical Soc.. This book was released on 2009-09-16 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference on Interactions of Classical and Numerical Algebraic Geometry, held May 22-24, 2008, at the University of Notre Dame, in honor of the achievements of Professor Andrew J. Sommese. While classical algebraic geometry has been studied for hundreds of years, numerical algebraic geometry has only recently been developed. Due in large part to the work of Andrew Sommese and his collaborators, the intersection of these two fields is now ripe for rapid advancement. The primary goal of both the conference and this volume is to foster the interaction between researchers interested in classical algebraic geometry and those interested in numerical methods. The topics in this book include (but are not limited to) various new results in complex algebraic geometry, a primer on Seshadri constants, analyses and presentations of existing and novel numerical homotopy methods for solving polynomial systems, a numerical method for computing the dimensions of the cohomology of twists of ideal sheaves, and the application of algebraic methods in kinematics and phylogenetics.
Book Synopsis Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics by : Coquereaux Robert
Download or read book Infinite Dimensional Geometry, Noncommutative Geometry, Operator Algebras And Fundamental Interactions - Proceedings Of The First Caribbean Spring School Of Mathematics And Theoretical Physics written by Coquereaux Robert and published by World Scientific. This book was released on 1995-06-28 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geocomputation with R by : Robin Lovelace
Download or read book Geocomputation with R written by Robin Lovelace and published by CRC Press. This book was released on 2019-03-22 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geocomputation with R is for people who want to analyze, visualize and model geographic data with open source software. It is based on R, a statistical programming language that has powerful data processing, visualization, and geospatial capabilities. The book equips you with the knowledge and skills to tackle a wide range of issues manifested in geographic data, including those with scientific, societal, and environmental implications. This book will interest people from many backgrounds, especially Geographic Information Systems (GIS) users interested in applying their domain-specific knowledge in a powerful open source language for data science, and R users interested in extending their skills to handle spatial data. The book is divided into three parts: (I) Foundations, aimed at getting you up-to-speed with geographic data in R, (II) extensions, which covers advanced techniques, and (III) applications to real-world problems. The chapters cover progressively more advanced topics, with early chapters providing strong foundations on which the later chapters build. Part I describes the nature of spatial datasets in R and methods for manipulating them. It also covers geographic data import/export and transforming coordinate reference systems. Part II represents methods that build on these foundations. It covers advanced map making (including web mapping), "bridges" to GIS, sharing reproducible code, and how to do cross-validation in the presence of spatial autocorrelation. Part III applies the knowledge gained to tackle real-world problems, including representing and modeling transport systems, finding optimal locations for stores or services, and ecological modeling. Exercises at the end of each chapter give you the skills needed to tackle a range of geospatial problems. Solutions for each chapter and supplementary materials providing extended examples are available at https://geocompr.github.io/geocompkg/articles/. Dr. Robin Lovelace is a University Academic Fellow at the University of Leeds, where he has taught R for geographic research over many years, with a focus on transport systems. Dr. Jakub Nowosad is an Assistant Professor in the Department of Geoinformation at the Adam Mickiewicz University in Poznan, where his focus is on the analysis of large datasets to understand environmental processes. Dr. Jannes Muenchow is a Postdoctoral Researcher in the GIScience Department at the University of Jena, where he develops and teaches a range of geographic methods, with a focus on ecological modeling, statistical geocomputing, and predictive mapping. All three are active developers and work on a number of R packages, including stplanr, sabre, and RQGIS.
Book Synopsis Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2 by : Raf Cluckers
Download or read book Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2 written by Raf Cluckers and published by Cambridge University Press. This book was released on 2011-09-22 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
