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Author: Jindrich Zapletal
Publisher: Cambridge University Press
ISBN: 113946826X
Category : Mathematics
Languages : en
Pages : 7
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Book Description
Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.
Author: Jindrich Zapletal
Publisher: Cambridge University Press
ISBN: 113946826X
Category : Mathematics
Languages : en
Pages : 7
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Book Description
Descriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.
Author: James R. Holton
Publisher: Academic Press
ISBN: 0123848660
Category : Science
Languages : en
Pages : 554
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Book Description
During the past decade, the science of dynamic meteorology has continued its rapid advance. The scope of dynamic meteorology has broadened considerably. Much of the material is based on a two-term course for seniors majoring in atmospheric sciences. This book presents a cogent explanation of the fundamentals of meteorology and explains storm dynamics for weather-oriented meteorologists. It discusses climate dynamics and the implications posed for global change. The new edition has added a companion website with MATLAB exercises and updated treatments of several key topics. Provides clear physical explanations of key dynamical principles Contains a wealth of illustrations to elucidate text and equations, plus end-of-chapter problems Holton is one of the leading authorities in contemporary meteorology, and well known for his clear writing style Instructor's Manual available to adopters NEW IN THIS EDITION A companion website with MATLAB® exercises and demonstrations Updated treatments on climate dynamics, tropical meteorology, middle atmosphere dynamics, and numerical prediction
Author: Burt Totaro
Publisher: Cambridge University Press
ISBN: 113991605X
Category : Mathematics
Languages : en
Pages : 245
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Book Description
Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights into the Hodge conjecture and algebraic geometry more broadly. This book presents a coherent suite of computational tools for the study of group cohomology and algebraic cycles. Early chapters synthesize background material from topology, algebraic geometry, and commutative algebra so readers do not have to form connections between the literatures on their own. Later chapters demonstrate Peter Symonds's influential proof of David Benson's regularity conjecture, offering several new variants and improvements. Complete with concrete examples and computations throughout, and a list of open problems for further study, this book will be valuable to graduate students and researchers in algebraic geometry and related fields.
Author: Lawrence Sklar
Publisher: Oxford University Press, USA
ISBN: 9780198238492
Category : Knowledge, Theory of
Languages : en
Pages : 172
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Book Description
Skeptics have cast doubt on the idea that scientific theories give us a true picture of an objective world. Lawrence Sklar examines three kinds of skeptical arguments about scientific truth, and explores the important role they play within foundational science itself. Sklar demonstrates that these kinds of philosophical critique are employed within science, and reveals the clear difference between how they operate in a scientific context and more abstract philosophical contexts. The underlying theme of Theory and Truth is that science and philosophy are essential to one another. Sklar advances the claim that one cannot understand the methods of science without a comprehension of philosophy, and one cannot fruitfully pursue philosophy of science without understanding fundamental science as well.
Author: Paul J. Durack
Publisher: Elsevier Inc. Chapters
ISBN: 0128058773
Category : Science
Languages : en
Pages : 59
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Book Description
Long-term global ocean salinity variation provides an insight into water cycle change. This connection reflects changes to the evaporation and precipitation (E–P) fields along with terrestrial runoff, which comprises the global water cycle and sets the spatial pattern of salinity on the ocean surface. The dynamic nature of the global ocean ensures that along with E–P, temperature and circulation changes also play a role in driving patterns of salinity change. This chapter provides an introduction to the global water cycle, briefly outlines the history of ocean salinity observation, and introduces results that relate resolved salinity change to water cycle change. Because of sparse observational coverage, the use of climate models are necessary to investigate these relationships. Long-term changes to global ocean salinity suggest that an unambiguous and coherent water cycle change has occurred over the twentieth and early twenty-first centuries. Climate model simulations project that such changes will intensify in the twenty-first century in response to continued greenhouse gas emissions.
Author: Clarence W. Matthews
Publisher:
ISBN:
Category : Particle accelerators
Languages : en
Pages : 28
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Book Description
The motion of an idealized plasma ring under the influence of either or both steady and alternating magnetic fields is studied to determine the pertinent parameters and phenomena involved. The results show the velocities attainable in induced-electromotive-force accelerators and indicate various conditions which should be favorable for the operation of such accelerators.
Author: Kanishka Perera
Publisher: Cambridge University Press
ISBN: 1139851969
Category : Mathematics
Languages : en
Pages : 171
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Book Description
This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, p-Laplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research.
Author: Aleksandar Ivić
Publisher: Cambridge University Press
ISBN: 113978983X
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Hardy's Z-function, related to the Riemann zeta-function ζ(s), was originally utilised by G. H. Hardy to show that ζ(s) has infinitely many zeros of the form 1⁄2+it. It is now amongst the most important functions of analytic number theory, and the Riemann hypothesis, that all complex zeros lie on the line 1⁄2+it, is perhaps one of the best known and most important open problems in mathematics. Today Hardy's function has many applications; among others it is used for extensive calculations regarding the zeros of ζ(s). This comprehensive account covers many aspects of Z(t), including the distribution of its zeros, Gram points, moments and Mellin transforms. It features an extensive bibliography and end-of-chapter notes containing comments, remarks and references. The book also provides many open problems to stimulate readers interested in further research.
Author: János Kollár
Publisher: Cambridge University Press
ISBN: 1107311470
Category : Mathematics
Languages : en
Pages : 381
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Book Description
This book gives a comprehensive treatment of the singularities that appear in the minimal model program and in the moduli problem for varieties. The study of these singularities and the development of Mori's program have been deeply intertwined. Early work on minimal models relied on detailed study of terminal and canonical singularities but many later results on log terminal singularities were obtained as consequences of the minimal model program. Recent work on the abundance conjecture and on moduli of varieties of general type relies on subtle properties of log canonical singularities and conversely, the sharpest theorems about these singularities use newly developed special cases of the abundance problem. This book untangles these interwoven threads, presenting a self-contained and complete theory of these singularities, including many previously unpublished results.
Author: I. C. Jong
Publisher: Oxford University Press, USA
ISBN: 9780030263095
Category : Performing Arts
Languages : en
Pages : 530
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Book Description
See preceding entry. This companion text for a fundamental course in statics, usually offered in the sophomore or junior year in engineering curricula, emphasizes the application of principles to the analysis and solution of problems. Assumes background in algebra, geometry, trigonometry, and basic differential and integral calculus; college physics would be helpful. Annotation copyrighted by Book News, Inc., Portland, OR
