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:
Publisher: CUP Archive
ISBN:
Category :
Languages : en
Pages : 688
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Book Description
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: Bruce J. Zobel
Publisher: Springer Science & Business Media
ISBN: 3642740693
Category : Technology & Engineering
Languages : en
Pages : 376
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Book Description
Wood is the usual end product of a forestry operation. Because of its importance, numerous studies have been made relative to wood prop erties, the causes of wood variation, and how best to develop wood for desired products. There is voluminous literature related to these subjects, but it is neither well known nor appreciated by foresters because the publications are often not available or are not well understood by the forester or by those who use the wood. Frequently, the literature is confusing and contradictory, making it difficult for the nonspecialist to use what information is available. In order to produce and use wood efficiently, the variation pat terns within trees, among trees within species, and among species must be understood. This also requires some knowledge of the causes of variation and the effects of different wood properties upon utiliza tion. The information about variation patterns, their causes, and con trol and effect upon the product must be known by the tree grower, the tree breeder, and the tree harvester as well as by those who ultimately convert wood into a final, salable product.
Author: Phyllis B. Eveleth
Publisher: CUP Archive
ISBN: 9780521208062
Category : Family & Relationships
Languages : en
Pages : 520
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Book Description
Author: Benedikt Szmrecsanyi
Publisher: Cambridge University Press
ISBN: 1108491561
Category : Language Arts & Disciplines
Languages : en
Pages : 237
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Book Description
Variation studies is an increasingly popular area in linguistics, becoming embedded in curriculum design, conferences, and research. However, the field is at risk of fragmenting into different research communities with different foci. This pioneering book addresses this by establishing a canon of state-of-the-art quantitative methods to analyze grammatical variation from a comparative perspective. It explains how to use these methods to investigate large datasets in a responsible fashion, providing a blueprint for applying techniques from corpus linguistic, variationist, and dialectometric traditions in novel ways. It specifically explores the scope and limits of syntactic variability in a global language such as English, and investigates three grammatical alternations in nine varieties of English, exploring what we can learn about the grammatical choices that people make based on both observational and experimental data. Comprehensive yet accessible, it will be of interest to academic researchers and students of sociolinguistic, corpus linguistics, and World Englishes.
Author: Freddy Bugge Christiansen
Publisher: Princeton University Press
ISBN: 0691165890
Category : Science
Languages : en
Pages : 431
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Book Description
This textbook provides an authoritative introduction to both classical and coalescent approaches to population genetics. Written for graduate students and advanced undergraduates by one of the world's leading authorities in the field, the book focuses on the theoretical background of population genetics, while emphasizing the close interplay between theory and empiricism. Traditional topics such as genetic and phenotypic variation, mutation, migration, and linkage are covered and advanced by contemporary coalescent theory, which describes the genealogy of genes in a population, ultimately connecting them to a single common ancestor. Effects of selection, particularly genomic effects, are discussed with reference to molecular genetic variation. The book is designed for students of population genetics, bioinformatics, evolutionary biology, molecular evolution, and theoretical biology--as well as biologists, molecular biologists, breeders, biomathematicians, and biostatisticians. Contains up-to-date treatment of key areas in classical and modern theoretical population genetics Provides in-depth coverage of coalescent theory Discusses genomic effects of selection Gives examples from empirical population genetics Incorporates figures, diagrams, and boxed features throughout Includes end-of-chapter exercises Speaks to a wide range of students in biology, bioinformatics, and biostatistics
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: J. K. Chambers
Publisher: John Wiley & Sons
ISBN: 1119457084
Category : Language Arts & Disciplines
Languages : en
Pages : 628
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Book Description
Reflecting a multitude of developments in the study of language change and variation over the last ten years, this extensively updated second edition features a number of new chapters and remains the authoritative reference volume on a core research area in linguistics. A fully revised and expanded edition of this acclaimed reference work, which has established its reputation based on its unrivalled scope and depth of analysis in this interdisciplinary field Includes seven new chapters, while the remainder have undergone thorough revision and updating to incorporate the latest research and reflect numerous developments in the field Accessibly structured by theme, covering topics including data collection and evaluation, linguistic structure, language and time, language contact, language domains, and social differentiation Brings together an experienced, international editorial and contributor team to provides an unrivalled learning, teaching and reference tool for researchers and students in sociolinguistics
