• Mathematics

On the Topology and Future Stability of the Universe


Author: Hans Ringström
Publisher: OUP Oxford
ISBN: 0191669784
Category: Mathematics
Page: 736
View: 7439
The standard starting point in cosmology is the cosmological principle; the assumption that the universe is spatially homogeneous and isotropic. After imposing this assumption, the only freedom left, as far as the geometry is concerned, is the choice of one out of three permissible spatial geometries, and one scalar function of time. Combining the cosmological principle with an appropriate description of the matter leads to the standard models. It is worth noting that these models yield quite a successful description of our universe. However, even though the universe may, or may not, be almost spatially homogeneous and isotropic, it is clear that the cosmological principle is not exactly satisfied. This leads to several questions. The most natural one concerns stability: given initial data corresponding to an expanding model of the standard type, do small perturbations give rise to solutions that are similar to the future? Another question concerns the shape of the universe: what are the restrictions if we only assume the universe to appear almost spatially homogeneous and isotropic to every observer? The main purpose of the book is to address these questions. However, to begin with, it is necessary to develop the general theory of the Cauchy problem for the Einstein-Vlasov equations. In order to to make the results accessible to researchers who are not mathematicians, but who are familiar with general relativity, the book contains an extensive prologue putting the results into a more general context.

    • Mathematics

Spectral Theory and Differential Operators


Author: David Edmunds,Des Evans
Publisher: Oxford University Press
ISBN: 0198812051
Category: Mathematics
Page: 624
View: 8354
This book is an updated version of the classic 1987 monograph "Spectral Theory and Differential Operators".The original book was a cutting edge account of the theory of bounded and closed linear operators in Banach and Hilbert spaces relevant to spectral problems involving differential equations. It is accessible to a graduate student as well as meeting the needs of seasoned researchers in mathematics and mathematical physics. This revised edition corrects various errors, and adds extensive notes to the end of each chapter which describe the considerable progress that has been made on the topic in the last 30 years.

    • Science

Basic Concepts in Physics

From the Cosmos to Quarks
Author: Masud Chaichian,Hugo Perez Rojas,Anca Tureanu
Publisher: Springer Science & Business Media
ISBN: 3642195989
Category: Science
Page: 377
View: 4004
"Basic Concepts in Physics: From the Cosmos to Quarks" is the outcome of the authors' long and varied teaching experience in different countries and for different audiences, and gives an accessible and eminently readable introduction to all the main ideas of modern physics. The book’s fresh approach, using a novel combination of historical and conceptual viewpoints, makes it ideal complementary reading to more standard textbooks. The first five chapters are devoted to classical physics, from planetary motion to special relativity, always keeping in mind its relevance to questions of contemporary interest. The next six chapters deal mainly with newer developments in physics, from quantum theory and general relativity to grand unified theories, and the book concludes by discussing the role of physics in living systems. A basic grounding in mathematics is required of the reader, but technicalities are avoided as far as possible; thus complex calculations are omitted so long as the essential ideas remain clear. The book is addressed to undergraduate and graduate students in physics and will also be appreciated by many professional physicists. It will likewise be of interest to students, researchers and teachers of other natural sciences, as well as to engineers, high-school teachers and the curious general reader, who will come to understand what physics is about and how it describes the different phenomena of Nature. Not only will readers of this book learn much about physics, they will also learn to love it.

    • Mathematics

Hilbert Modular Forms and Iwasawa Theory


Author: Haruzo Hida
Publisher: Oxford University Press
ISBN: 019857102X
Category: Mathematics
Page: 402
View: 6215
Describing the applications found for the Wiles and Taylor technique, this book generalizes the deformation theoretic techniques of Wiles-Taylor to Hilbert modular forms (following Fujiwara's treatment), and also discusses applications found by the author.

    • Computers

From the Web to the Grid and Beyond

Computing Paradigms Driven by High-Energy Physics
Author: René Brun,Frederico Carminati,Giuliana Galli-Carminati
Publisher: Springer Science & Business Media
ISBN: 3642231578
Category: Computers
Page: 360
View: 4451
Born after World War II, large-scale experimental high-energy physics (HEP) has found itself limited ever since by available accelerator, detector and computing technologies. Accordingly, HEP has made significant contributions to the development of these fields, more often than not driving their innovations. The invention of the World Wide Web at CERN is merely the best-known example out of many. This book is the first comprehensive account to trace the history of this pioneering spirit in the field of computing technologies. It covers everything up to and including the present-day handling of the huge demands imposed upon grid and distributed computing by full-scale LHC operations—operations which have for years involved many thousands of collaborating members worldwide and accordingly provide the original and natural testbed for grid computing concepts. This book takes the reader on a guided tour encompassing all relevant topics, including programming languages, software engineering, large databases, the Web, and grid- and cloud computing. The important issue of intellectual property regulations for distributed software engineering and computing is also addressed. Aptly, the book closes with a visionary chapter of what may lie ahead. Approachable and requiring only basic understanding of physics and computer sciences, this book is intended for both education and research.

    • Political Science

Banach and Locally Convex Algebras


Author: Aleksandr I͡Akovlevich Khelemskiĭ
Publisher: Oxford University Press
ISBN: 0198535783
Category: Political Science
Page: 446
View: 1125
A reference textbook that summarizes the algebra of analysis" that includes some mention of the contemporary trends in the development of history. This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. In its description of general theory and in the examples it considers it is faithful to earlier traditions in the subject but differs from those books in being based on an approach through homological algebra. This approach leads Helemskii to consider topics not covered at this level in any other book. These topics include: complemented and uncomplemented ideal; projective and weak tensor products of banach algebras; Taylors multivariable holomorphic functional calculus; the Wedderburn decomposition of Banach algevras; a whole chapter on the homology of Banach algebras."

    • Mathematics

The general theory of integration


Author: Ralph Henstock
Publisher: Oxford University Press on Demand
ISBN: 9780198535669
Category: Mathematics
Page: 262
View: 6119
Written by one of the subject's foremost experts, this is the first book on division space integration theory. It is intended to present a unified account of many classes of integrals including the Lebesgue-Bochner, Denjoy-Perron gauge, Denjoy-Hincin, Cesaro-Perron, and Marcinkiewicz-Zygmund integrals. Professor Henstock develops here the general axiomatic theory of Riemann-type integration from first principles in such a way that familiar classes of integrals (such as Lebesgue and Wiener integrals) are subsumed into the general theory in a systematic fashion. In particular, the theory seeks to place Feynman integration on a secure analytical footing. By adopting an axiomatic approach, proofs are, in general, simpler and more transparent than have previously appeared. The author also shows how one proof can prove corresponding results for a wide variety of integrals. As a result, this book will be the central reference work in this subject for many years to come.

    • Mathematics

The Cauchy Problem in General Relativity


Author: Hans Ringström
Publisher: European Mathematical Society
ISBN: 9783037190531
Category: Mathematics
Page: 294
View: 5576
"The general theory of relativity is a theory of manifolds equipped with Lorentz metrics and fields which describe the matter content. Einstein's equations equate the Einstein tensor (a curvature quantity associated with the Lorentz metric) with the stress energy tensor (an object constructed using the matter fields). In addition, there are equations describing the evolution of the matter. Using symmetry as a guiding principle, one is naturally led to the Schwarzschild and Friedmann-Lemaãitre-Robertson-Walker solutions, modelling an isolated system and the entire universe respectively. In a different approach, formulating Einstein's equations as an initial value problem allows a closer study of their solutions. This book first provides a definition of the concept of initial data and a proof of the correspondence between initial data and development. It turns out that some initial data allow non-isometric maximal developments, complicating the uniqueness issue. The second half of the book is concerned with this and related problems, such as strong cosmic censorship. The book presents complete proofs of several classical results that play a central role in mathematical relativity but are not easily accessible to those wishing to enter the subject. Prerequisites are a good knowledge of basic measure and integration theory as well as the fundamentals of Lorentz geometry. The necessary background from the theory of partial differential equations and Lorentz geometry is included."--Publisher's description.

Persistence Theory: From Quiver Representations to Data Analysis


Author: Steve Y. Oudot
Publisher: American Mathematical Soc.
ISBN: 1470434431
Category:
Page: 218
View: 5282
Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

    • Science

Springer Handbook of Spacetime


Author: Abhay Ashtekar,Vesselin Petkov
Publisher: Springer
ISBN: 3642419925
Category: Science
Page: 950
View: 8007
The Springer Handbook of Spacetime is dedicated to the ground-breaking paradigm shifts embodied in the two relativity theories, and describes in detail the profound reshaping of physical sciences they ushered in. It includes in a single volume chapters on foundations, on the underlying mathematics, on physical and astrophysical implications, experimental evidence and cosmological predictions, as well as chapters on efforts to unify general relativity and quantum physics. The Handbook can be used as a desk reference by researchers in a wide variety of fields, not only by specialists in relativity but also by researchers in related areas that either grew out of, or are deeply influenced by, the two relativity theories: cosmology, astronomy and astrophysics, high energy physics, quantum field theory, mathematics, and philosophy of science. It should also serve as a valuable resource for graduate students and young researchers entering these areas, and for instructors who teach courses on these subjects. The Handbook is divided into six parts. Part A: Introduction to Spacetime Structure. Part B: Foundational Issues. Part C: Spacetime Structure and Mathematics. Part D: Confronting Relativity theories with observations. Part E: General relativity and the universe. Part F: Spacetime beyond Einstein.

    • Philosophy

The Oxford Handbook of Philosophy of Physics


Author: Robert Batterman
Publisher: Oxford University Press
ISBN: 0195392043
Category: Philosophy
Page: 688
View: 4467
This Oxford Handbook provides an overview of many of the topics that currently engage philosophers of physics. It surveys new issues and the problems that have become a focus of attention in recent years. It also provides up-to-date discussions of the still very important problems that dominated the field in the past. In the late 20th Century, the philosophy of physics was largely focused on orthodox Quantum Mechanics and Relativity Theory. The measurement problem, the question of the possibility of hidden variables, and the nature of quantum locality dominated the literature on the quantum mechanics, whereas questions about relationalism vs. substantivalism, and issues about underdetermination of theories dominated the literature on spacetime. These issues still receive considerable attention from philosophers, but many have shifted their attentions to other questions related to quantum mechanics and to spacetime theories. Quantum field theory has become a major focus, particularly from the point of view of algebraic foundations. Concurrent with these trends, there has been a focus on understanding gauge invariance and symmetries. The philosophy of physics has evolved even further in recent years with attention being paid to theories that, for the most part, were largely ignored in the past. For example, the relationship between thermodynamics and statistical mechanics—-once thought to be a paradigm instance of unproblematic theory reduction—-is now a hotly debated topic. The implicit, and sometimes explicit, reductionist methodology of both philosophers and physicists has been severely criticized and attention has now turned to the explanatory and descriptive roles of "non-fundamental,'' phenomenological theories. This shift of attention includes "old'' theories such as classical mechanics, once deemed to be of little philosophical interest. Furthermore, some philosophers have become more interested in "less fundamental'' contemporary physics such as condensed matter theory. Questions abound with implications for the nature of models, idealizations, and explanation in physics. This Handbook showcases all these aspects of this complex and dynamic discipline.

    • Mathematics

Thermoelasticity with Finite Wave Speeds


Author: Józef Ignaczak,Martin Ostoja-Starzewski
Publisher: Oxford University Press
ISBN: 0199541647
Category: Mathematics
Page: 413
View: 1909
Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier-type heat conduction, yet this book, which aims to provide a point of reference in the field, is the first monograph on the subject since the 1970s. It focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on theories with one or two relaxation times. While the resulting field equations are linear partial differential ones, the complexity of the theories is due to the coupling of mechanical with thermal fields. The mathematical aspects of the theories - existence and uniqueness theorems, domain of influence theorems, convolutional variationalprinciples - as well as the methods for various initial/boundary value problems are explained and illustrated in detail and several applications of generalized thermoelasticity are reviewed.

    • Physics

Physics Briefs

Physikalische Berichte
Author: N.A
Publisher: N.A
ISBN: N.A
Category: Physics
Page: N.A
View: 4628

    • Science

The Singular Universe and the Reality of Time


Author: Roberto Mangabeira Unger,Lee Smolin
Publisher: Cambridge University Press
ISBN: 1107074061
Category: Science
Page: 566
View: 2629
Roberto Mangabeira Unger and Lee Smolin argue for a revolution in our cosmological ideas. Ideal for non-scientists, physicists and cosmologists.

    • Mathematics

Differential Equations and Mathematical Biology, Second Edition


Author: D.S. Jones,Michael Plank,B.D. Sleeman
Publisher: CRC Press
ISBN: 9781420083583
Category: Mathematics
Page: 462
View: 1169
Deepen students’ understanding of biological phenomena Suitable for courses on differential equations with applications to mathematical biology or as an introduction to mathematical biology, Differential Equations and Mathematical Biology, Second Edition introduces students in the physical, mathematical, and biological sciences to fundamental modeling and analytical techniques used to understand biological phenomena. In this edition, many of the chapters have been expanded to include new and topical material. New to the Second Edition A section on spiral waves Recent developments in tumor biology More on the numerical solution of differential equations and numerical bifurcation analysis MATLAB® files available for download online Many additional examples and exercises This textbook shows how first-order ordinary differential equations (ODEs) are used to model the growth of a population, the administration of drugs, and the mechanism by which living cells divide. The authors present linear ODEs with constant coefficients, extend the theory to systems of equations, model biological phenomena, and offer solutions to first-order autonomous systems of nonlinear differential equations using the Poincaré phase plane. They also analyze the heartbeat, nerve impulse transmission, chemical reactions, and predator–prey problems. After covering partial differential equations and evolutionary equations, the book discusses diffusion processes, the theory of bifurcation, and chaotic behavior. It concludes with problems of tumor growth and the spread of infectious diseases.

    • Mathematics

Mathematical Reviews


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2978

    • Mathematics

Projective Representations of the Symmetric Groups

Q-functions and Shifted Tableaux
Author: Peter Norman Hoffman,J. F. Humphreys
Publisher: Oxford University Press
ISBN: 9780198535560
Category: Mathematics
Page: 304
View: 3723
This book is the first completely detailed and self-contained presentation of the wealth of information now known on the projective representations of the symmetric and alternating groups.

    • Education

Writing Mathematically

The Discourse of 'Investigation'
Author: Candia Morgan
Publisher: Routledge
ISBN: 113570953X
Category: Education
Page: 288
View: 303
School mathematics curricula internationally tend to emphasise problem-solving and have led to the development of opportunities for children to do maths in a more open, creative way. This has led to increased interest in 'performance-based' assessment, which involves children in substantial production of written language to serve as 'evidence' of their mathematical activity and achievement. However, this raises two important questions. Firstly, does this writing accurately present children's mathematical activity and ability? Secondly, do maths teachers have sufficient linguistic awareness to support their students in developing skills and knowledge necessary for writing effectively in their subject area? The author of this book takes a critical perspective on these questions and, through an investigation of teachers' readings and evaluations of coursework texts, identifies the crucial issues affecting the accurate assessment of school mathematics.

    • Mathematics

Sasakian Geometry


Author: Charles Boyer,Krzysztof Galicki
Publisher: Oxford University Press
ISBN: 9780198564959
Category: Mathematics
Page: 613
View: 4439
This book offers an extensive modern treatment of Sasakian geometry, which is of importance in many different fields in geometry and physics.

    • Mathematics

Compact Manifolds with Special Holonomy


Author: Dominic D. Joyce
Publisher: Oxford University Press on Demand
ISBN: 9780198506010
Category: Mathematics
Page: 436
View: 1636
This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.