Differentiability of Six Operators on Nonsmooth Functions and P-Variation PDF Download
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Author: R. M. Dudley
Publisher: Springer Science & Business
ISBN: 9783540659754
Category : Mathematics
Languages : en
Pages : 300
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Book Description
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.
Author: R. M. Dudley
Publisher: Springer Science & Business
ISBN: 9783540659754
Category : Mathematics
Languages : en
Pages : 300
Get Book Here
Book Description
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.
Author: Benedikt Hallgrímsson
Publisher: Elsevier
ISBN: 0080454461
Category : Science
Languages : en
Pages : 594
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Book Description
Darwin's theory of evolution by natural selection was based on the observation that there is variation between individuals within the same species. This fundamental observation is a central concept in evolutionary biology. However, variation is only rarely treated directly. It has remained peripheral to the study of mechanisms of evolutionary change. The explosion of knowledge in genetics, developmental biology, and the ongoing synthesis of evolutionary and developmental biology has made it possible for us to study the factors that limit, enhance, or structure variation at the level of an animals' physical appearance and behavior. Knowledge of the significance of variability is crucial to this emerging synthesis. Variation situates the role of variability within this broad framework, bringing variation back to the center of the evolutionary stage. - Provides an overview of current thinking on variation in evolutionary biology, functional morphology, and evolutionary developmental biology - Written by a team of leading scholars specializing on the study of variation - Reviews of statistical analysis of variation by leading authorities - Key chapters focus on the role of the study of phenotypic variation for evolutionary, developmental, and post-genomic biology
Author: Phyllis B. Eveleth
Publisher: CUP Archive
ISBN: 9780521208062
Category : Family & Relationships
Languages : en
Pages : 520
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Book Description
Author: Adam Sedgwick
Publisher:
ISBN:
Category : Heredity
Languages : en
Pages : 24
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Author: N. H. Bingham
Publisher: Cambridge University Press
ISBN: 9780521379434
Category : Mathematics
Languages : en
Pages : 518
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Book Description
A comprehensive account of the theory and applications of regular variation.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 208
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Book Description
Author: Theresa Biberauer
Publisher: Cambridge University Press
ISBN: 0521886953
Category : Language Arts & Disciplines
Languages : en
Pages : 375
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Book Description
Parametric variation in linguistic theory refers to the systematic grammatical variation permitted by the human language faculty. This book is a defence of the parametric approach to linguistic variation, set within the framework of the Minimalist Program.
Author:
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 416
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Book Description
Author: William Bateson
Publisher:
ISBN:
Category : Evolution (Biology)
Languages : en
Pages : 624
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Book Description
Author: James Joseph Sylvester
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 410
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Book Description
