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Author: Per Aage Brandt
Publisher: Peter Lang Publishing
ISBN: 9780820470061
Category : Cognition
Languages : en
Pages : 271
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Book Description
The essays in this book and develop a semiotic elaboration of the theory of mental spaces, a grounding hypothesis of semantic domains, and the methodologically necessary idea of a mental architecture corresponding to the neural organization of the brain.
Author: Per Aage Brandt
Publisher: Peter Lang Publishing
ISBN: 9780820470061
Category : Cognition
Languages : en
Pages : 271
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Book Description
The essays in this book and develop a semiotic elaboration of the theory of mental spaces, a grounding hypothesis of semantic domains, and the methodologically necessary idea of a mental architecture corresponding to the neural organization of the brain.
Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 1461215749
Category : Mathematics
Languages : en
Pages : 311
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Book Description
The analysis of Euclidean space is well-developed. The classical Lie groups that act naturally on Euclidean space-the rotations, dilations, and trans lations-have both shaped and guided this development. In particular, the Fourier transform and the theory of translation invariant operators (convolution transforms) have played a central role in this analysis. Much modern work in analysis takes place on a domain in space. In this context the tools, perforce, must be different. No longer can we expect there to be symmetries. Correspondingly, there is no longer any natural way to apply the Fourier transform. Pseudodifferential operators and Fourier integral operators can playa role in solving some of the problems, but other problems require new, more geometric, ideas. At a more basic level, the analysis of a smoothly bounded domain in space requires a great deal of preliminary spadework. Tubular neighbor hoods, the second fundamental form, the notion of "positive reach", and the implicit function theorem are just some of the tools that need to be invoked regularly to set up this analysis. The normal and tangent bundles become part of the language of classical analysis when that analysis is done on a domain. Many of the ideas in partial differential equations-such as Egorov's canonical transformation theorem-become rather natural when viewed in geometric language. Many of the questions that are natural to an analyst-such as extension theorems for various classes of functions-are most naturally formulated using ideas from geometry.
Author: Zoltán Kövecses
Publisher: Cambridge University Press
ISBN: 1108490875
Category : Language Arts & Disciplines
Languages : en
Pages : 211
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Book Description
Offers an extended, improved version of Conceptual Metaphor Theory (CMT), updating it in the context of current linguistic theory.
Author: Hans Triebel
Publisher: European Mathematical Society
ISBN: 9783037190197
Category : Mathematics
Languages : en
Pages : 276
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Book Description
Wavelets have emerged as an important tool in analyzing functions containing discontinuities and sharp spikes. They were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, earthquake prediction, and pure mathematics applications such as solving partial differential equations. This book develops a theory of wavelet bases and wavelet frames for function spaces on various types of domains. Starting with the usual spaces on Euclidean spaces and their periodic counterparts, the exposition moves on to so-called thick domains (including Lipschitz domains and snowflake domains). Specifically, wavelet expansions and extensions to corresponding spaces on Euclidean $n$-spaces are developed. Finally, spaces on smooth and cellular domains and related manifolds are treated. Although the presentation relies on the recent theory of function spaces, basic notation and classical results are repeated in order to make the text self-contained. This book is addressed to two types of readers: researchers in the theory of function spaces who are interested in wavelets as new effective building blocks for functions and scientists who wish to use wavelet bases in classical function spaces for various applications. Adapted to the second type of reader, the preface contains a guide on where to find basic definitions and key assertions.
Author: Gilles Fauconnier
Publisher: Cambridge University Press
ISBN: 9780521449496
Category : Language Arts & Disciplines
Languages : en
Pages : 250
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Book Description
Mental Spaces is the classic introduction to the study of mental spaces and conceptual projection, as revealed through the structure and use of language. It examines in detail the dynamic construction of connected domains as discourse unfolds. The discovery of mental space organization has modified our conception of language and thought: powerful and uniform accounts of superficially disparate phenomena have become available in the areas of reference, presupposition projection, counterfactual and analogical reasoning, metaphor and metonymy, and time and aspect in discourse. The present work lays the foundation for this research. It uncovers simple and general principles that lie behind the awesome complexity of everyday logic.
Author: Gregor Fels
Publisher: Springer Science & Business Media
ISBN: 0817644792
Category : Mathematics
Languages : en
Pages : 342
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Book Description
Driven by numerous examples from the complex geometric viewpoint New results presented for the first time Widely accessible, with all necessary background material provided for the nonspecialist Comparisons with classical Barlet cycle spaces are given Good bibliography and index
Author: Mikhail S. Agranovich
Publisher: Springer
ISBN: 3319146483
Category : Mathematics
Languages : en
Pages : 331
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Book Description
This book, which is based on several courses of lectures given by the author at the Independent University of Moscow, is devoted to Sobolev-type spaces and boundary value problems for linear elliptic partial differential equations. Its main focus is on problems in non-smooth (Lipschitz) domains for strongly elliptic systems. The author, who is a prominent expert in the theory of linear partial differential equations, spectral theory and pseudodifferential operators, has included his own very recent findings in the present book. The book is well suited as a modern graduate textbook, utilizing a thorough and clear format that strikes a good balance between the choice of material and the style of exposition. It can be used both as an introduction to recent advances in elliptic equations and boundary value problems and as a valuable survey and reference work. It also includes a good deal of new and extremely useful material not available in standard textbooks to date. Graduate and post-graduate students, as well as specialists working in the fields of partial differential equations, functional analysis, operator theory and mathematical physics will find this book particularly valuable.
Author: Cho-ho Chu
Publisher: World Scientific
ISBN: 9811214123
Category : Mathematics
Languages : en
Pages : 406
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Book Description
This timely book exposes succinctly recent advances in the geometric and analytic theory of bounded symmetric domains. A unique feature is the unified treatment of both finite and infinite dimensional symmetric domains, using Jordan theory in tandem with Lie theory. The highlights include a generalized Riemann mapping theorem, which realizes a bounded symmetric domain as the open unit ball of a complex Banach space with a Jordan structure. Far-reaching applications of this realization in complex geometry and function theory are discussed.This monograph is intended as a convenient reference for researchers and graduate students in geometric analysis, infinite dimensional holomorphy as well as functional analysis and operator theory.
Author: Simeon Reich
Publisher: World Scientific
ISBN: 1783260211
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems. In the last forty years, the generation theory of flows of holomorphic mappings has been of great interest in the theory of Markov stochastic branching processes, the theory of composition operators, control theory, and optimization. It transpires that the asymptotic behavior of solutions to evolution equations is applicable to the study of the geometry of certain domains in complex spaces.Readers are provided with a systematic overview of many results concerning both nonlinear semigroups in metric and Banach spaces and the fixed point theory of mappings, which are nonexpansive with respect to hyperbolic metrics (in particular, holomorphic self-mappings of domains in Banach spaces). The exposition is organized in a readable and intuitive manner, presenting basic functional and complex analysis as well as very recent developments./a
Author: Martin Dindoš
Publisher: American Mathematical Soc.
ISBN: 0821840436
Category : Mathematics
Languages : en
Pages : 78
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Book Description
The author studies Hardy spaces on $C1$ and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.
