Structure and Equivalence
Structure and Equivalence

Author: Neil Dewar

Publisher: Cambridge University Press

Published: 2022-03-17

Total Pages: 82

ISBN-13: 1108910467

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This Element explores what it means for two theories in physics to be equivalent (or inequivalent), and what lessons can be drawn about their structure as a result. It does so through a twofold approach. On the one hand, it provides a synoptic overview of the logical tools that have been employed in recent philosophy of physics to explore these topics: definition, translation, Ramsey sentences, and category theory. On the other, it provides a detailed case study of how these ideas may be applied to understand the dynamical and spatiotemporal structure of Newtonian mechanics - in particular, in light of the symmetries of Newtonian theory. In so doing, it brings together a great deal of exciting recent work in the literature, and is sure to be a valuable companion for all those interested in these topics.

Cross-Cultural Research Methods in Psychology
Cross-Cultural Research Methods in Psychology

Author: David Matsumoto

Publisher: Cambridge University Press

Published: 2010-10-11

Total Pages:

ISBN-13: 1139493140

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Cross-cultural research is now an undeniable part of mainstream psychology and has had a major impact on conceptual models of human behavior. Although it is true that the basic principles of social psychological methodology and data analysis are applicable to cross-cultural research, there are a number of issues that are distinct to it, including managing incongruities of language and quantifying cultural response sets in the use of scales. Cross-Cultural Research Methods in Psychology provides state-of-the-art knowledge about the methodological problems that need to be addressed if a researcher is to conduct valid and reliable cross-cultural research. It also offers practical advice and examples of solutions to those problems and is a must-read for any student of culture.

Adapting Tests in Linguistic and Cultural Situations
Adapting Tests in Linguistic and Cultural Situations

Author: Dragoş Iliescu

Publisher: Cambridge University Press

Published: 2017-11-02

Total Pages: 711

ISBN-13: 1107110122

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This book provides a practical but scientifically grounded step-by-step approach to the adaptation of tests in linguistic and cultural contexts.

Equivalence, Invariants and Symmetry
Equivalence, Invariants and Symmetry

Author: Peter J. Olver

Publisher: Cambridge University Press

Published: 1995-06-30

Total Pages: 546

ISBN-13: 9780521478113

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Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space
Gyros, Clocks, Interferometers...: Testing Relativistic Gravity in Space

Author: C. Lämmerzahl

Publisher: Springer Science & Business Media

Published: 2001-03-13

Total Pages: 507

ISBN-13: 3540412360

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Many new tests of gravity and, in particular, of Einstein's general relativity theory will be carried out in the near future: The Lense--Thirring effect and the equivalence principle will be tested in space; moreover, gravitational waves will be detected, and new atomic interferometers and clocks will be built for measurements in gravitational and inertial fields. New high-precision devices have made these experiments feasible. They will contribute to a better understanding of gravitational physics. Both experimental developments and the theoretical concepts are collected in this volume. Exhaustive reviews give an overall insight into the subject of experimental gravitation.

The Logical Structure of Mathematical Physics
The Logical Structure of Mathematical Physics

Author: Joseph D. Sneed

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 325

ISBN-13: 9401030669

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This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For example, in classical particle mechanics, mass and force playa theoretical role while position plays a non-theoretical role. Some attention is given to showing how this distinction can be drawn and describing precisely the way in which the theoretical and non-theoretical elements function in the claims of the theory. An attempt is made to say, rather precisely, what a theory of mathematical physics is and how you tell one such theory from anothe- what the identity conditions for these theories are.

On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks
On the Local Structure of Morita and Rickard Equivalences between Brauer Blocks

Author: Lluis Puig

Publisher: Birkhäuser

Published: 2012-12-06

Total Pages: 256

ISBN-13: 3034886934

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Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect. In 1959 he discovered the defect group, and in 1964 Dade determined the blocks with cyclic defect groups. In 1978 Alperin and Broué discovered the Brauer category, and Broué and the author determined the blocks having a nilpotent Brauer category. In 1979, the author discovered the source algebra which determines all the other current invariants, representing faithfully the block – and found its structure in the nilpotent blocks. Recently, the discovery by Rickard that all blocks with the same cyclic defect group and the same Brauer category have the same homotopic category focussed great interest on the new, loose relationship between blocks called Rickard equivalence. This book describes the source algebra of a block from the source algebra of a Rickard equivalent block and the source of the Rickard equivalence.

Handbook of Process Algebra
Handbook of Process Algebra

Author: J.A. Bergstra

Publisher: Elsevier

Published: 2001-03-16

Total Pages: 1357

ISBN-13: 0080533671

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Process Algebra is a formal description technique for complex computer systems, especially those involving communicating, concurrently executing components. It is a subject that concurrently touches many topic areas of computer science and discrete math, including system design notations, logic, concurrency theory, specification and verification, operational semantics, algorithms, complexity theory, and, of course, algebra.This Handbook documents the fate of process algebra since its inception in the late 1970's to the present. It is intended to serve as a reference source for researchers, students, and system designers and engineers interested in either the theory of process algebra or in learning what process algebra brings to the table as a formal system description and verification technique. The Handbook is divided into six parts spanning a total of 19 self-contained Chapters. The organization is as follows. Part 1, consisting of four chapters, covers a broad swath of the basic theory of process algebra. Part 2 contains two chapters devoted to the sub-specialization of process algebra known as finite-state processes, while the three chapters of Part 3 look at infinite-state processes, value-passing processes and mobile processes in particular. Part 4, also three chapters in length, explores several extensions to process algebra including real-time, probability and priority. The four chapters of Part 5 examine non-interleaving process algebras, while Part 6's three chapters address process-algebra tools and applications.

The Logic in Philosophy of Science
The Logic in Philosophy of Science

Author: Hans Halvorson

Publisher: Cambridge University Press

Published: 2019-07-11

Total Pages: 305

ISBN-13: 1107110998

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Reconsiders the role of formal logic in the analytic approach to philosophy, using cutting-edge mathematical techniques to elucidate twentieth-century debates.