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Central Equation of Thermoelasticity with Finite Wave Speeds

Józef Ignaczak and Martin Ostoja‐Starzewski

in Thermoelasticity with Finite Wave Speeds

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199541645
eISBN:
9780191716164
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199541645.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

This chapter focuses on a central equation of thermoelasticity with finite wave speeds, i.e. a partial differential equation which, most remarkably, has a similar form for both theories. Given next ... More


Appendix: Deligne’s Fibre Functor

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0031
Subject:
Mathematics, Number Theory

This chapter takes up the proof of Theorem 3.1. It shows that N ↦ ω‎(N) := H⁰(𝔸¹/k¯, j0!N) is a fiber functor on the Tannakian category Ƿsubscript geom of those perverse sheaves on 𝔾ₘ/k¯ satisfying ... More


INTERACTION BETWEEN ELLIPTIC PROBLEMS AND PARTITION PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0011
Subject:
Mathematics, Applied Mathematics

This chapter introduces the one-dimensional version of problems defined on functions of bounded variations. It is shown that for general energies, the surface and volume terms of the energy can ... More


AFM image artefacts

Peter Eaton and Paul West

in Atomic Force Microscopy

Published in print:
2010
Published Online:
May 2010
ISBN:
9780199570454
eISBN:
9780191722851
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199570454.003.0006
Subject:
Physics, Atomic, Laser, and Optical Physics

AFM, like any other measurement technique, is prone to artefacts. These can arise due to the AFM probe, the scanner, the instrument electronics, from the laboratory environment, or from many outer ... More


Characteristic Functions

James Davidson

in Stochastic Limit Theory: An Introduction for Econometricians

Published in print:
1994
Published Online:
November 2003
ISBN:
9780198774037
eISBN:
9780191596117
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774036.003.0011
Subject:
Economics and Finance, Econometrics

This chapter begins with a look at convolutions and the distribution of sums of random variables. It briefly surveys complex number theory before defining the characteristic function and studying its ... More


Fourier transforms and convolutions

Dennis Sherwood and Jon Cooper

in Crystals, X-rays and Proteins: Comprehensive Protein Crystallography

Published in print:
2010
Published Online:
January 2011
ISBN:
9780199559046
eISBN:
9780191595028
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199559046.003.0005
Subject:
Physics, Crystallography: Physics

This chapter revisits the essential mathematics of integral calculus and introduces the important concept of the Fourier transform, the properties of which are elegantly demonstrated by sketching the ... More


Patterson syntheses for structure determination

William Clegg

in Crystal Structure Analysis: Principles and Practice

Published in print:
2009
Published Online:
September 2009
ISBN:
9780199219469
eISBN:
9780191722516
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199219469.003.0009
Subject:
Physics, Crystallography: Physics

The Patterson synthesis is a reverse Fourier transform in which the amplitudes are replaced by their squares and the phases are omitted. Peaks in a Patterson map represent vectors between pairs of ... More


Transformation, convolution, and correlation

Bernhard Blümich

in NMR Imaging of Materials

Published in print:
2003
Published Online:
January 2010
ISBN:
9780198526766
eISBN:
9780191709524
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198526766.003.0004
Subject:
Physics, Condensed Matter Physics / Materials

Transformation, convolution, and correlation are used over and over again in nuclear magnetic resonance (NMR) spectroscopy and imaging in different contexts and sometimes with different meanings. The ... More


. Biological Cognition–Syntax

C. Eliasmith, T. Stewart, D. Rasmussen, and Chris Eliasmith

in How to Build a Brain: A Neural Architecture for Biological Cognition

Published in print:
2013
Published Online:
January 2014
ISBN:
9780199794546
eISBN:
9780199345236
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199794546.003.0004
Subject:
Neuroscience, Behavioral Neuroscience, Techniques

A method for using semantic pointers to encode syntactic relations in a spiking network is introduced in chapter 4. The method allows binding of different semantic pointers by combining them in a ... More


Amplitude And Phase In Map And Image Enhancement

Joseph E. Robinson

in Computers in Geology - 25 Years of Progress

Published in print:
1994
Published Online:
November 2020
ISBN:
9780195085938
eISBN:
9780197560525
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195085938.003.0022
Subject:
Computer Science, Software Engineering

Many geographic information systems (GIS) and computer mapping packages for graphic display provide data enhancement routines that utilize spatial filtering and may ... More


Crystals

Jenny Pickworth Glusker and Kenneth N. Trueblood

in Title Pages

Published in print:
2010
Published Online:
November 2020
ISBN:
9780199576340
eISBN:
9780191917905
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199576340.003.0010
Subject:
Chemistry, Crystallography: Chemistry

The elegance and beauty of crystals have always been a source of delight.What is a crystal? A crystal is defined as a solid that contains a very high ... More


The ventral visual system

Edmund T. Rolls

in Brain Computations: What and How

Published in print:
2020
Published Online:
February 2021
ISBN:
9780198871101
eISBN:
9780191914157
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198871101.003.0002
Subject:
Neuroscience, Behavioral Neuroscience, Neuroendocrine and Autonomic

The brain processes involved in visual object recognition are described. Evidence is presented that what is computed are sparse distributed representations of objects that are invariant with respect ... More


Smoothness of Spectral Multipliers and Convolution Kernels in Nilpotent Gelfand Pairs

Fulvio Ricci

Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, and Stephen Wainger (eds)

in Advances in Analysis: The Legacy of Elias M. Stein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.003.0017
Subject:
Mathematics, Numerical Analysis

This chapter turns to a special class of Gelfland pairs, here called “nilpotent Gelfland pairs” for simplicity's sake and denoted by (N, K). It considers implications derived from, in principle, ... More


Multi-parameter Singular Integrals I: Examples

Brian Street

in Multi-parameter Singular Integrals. (AM-189)

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691162515
eISBN:
9781400852758
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691162515.003.0004
Subject:
Mathematics, Analysis

This chapter discusses a few special cases where a theory of multi-parameter singular integral operators has already been developed. These include the product theory of singular integrals, ... More


Introduction

Georges Matheron

Vera Pawlowsky-Glahn and Jean Serra (eds)

in Matheron's Theory of Regionalised Variables

Published in print:
2019
Published Online:
June 2019
ISBN:
9780198835660
eISBN:
9780191873249
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198835660.003.0001
Subject:
Mathematics, Applied Mathematics

This brief introductory chapter begins by providing some notation. This is followed by a reminder on the convolution (moving average) operation, which is presented here as a regularisation procedure. ... More


Lp Spaces

Fon-Che Liu

in Real Analysis

Published in print:
2016
Published Online:
January 2017
ISBN:
9780198790426
eISBN:
9780191831676
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198790426.003.0006
Subject:
Mathematics, Analysis

LP spaces are the most interesting examples of Banach spaces and play a salient role in modern analysis. In this chapter, basic features of LP spaces are studied; in particular, their dual spaces are ... More


Scientific programming with Python

Thomas P. Trappenberg

in Fundamentals of Machine Learning

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198828044
eISBN:
9780191883873
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198828044.003.0002
Subject:
Neuroscience, Behavioral Neuroscience

This chapter offers a brief introduction to scientific programming with Python with an emphasis on some mathematical operations that will form the basis of many algorithms. This will specifically ... More


Imaging

B. D. Guenther

in Modern Optics Simplified

Published in print:
2019
Published Online:
January 2020
ISBN:
9780198842859
eISBN:
9780191878770
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198842859.003.0011
Subject:
Physics, Atomic, Laser, and Optical Physics

Treating an imaging system as a linear system and use llinear system properties to d iscuss both coherent and incoherent imaging. Use a one dimensional pin hole camera to study the theory of ... More


Maximal Function; Bounding Averages and Pointwise Convergence

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 2: Contemporary Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733157
eISBN:
9780191797729
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733157.003.0013
Subject:
Mathematics, Analysis

This chapter introduces the Hardy-Littlewood maximal functions and establishes its bounded properties in various Lebesgue and Marcinkiewicz type spaces. The chapter also presents many applications to ... More


Abel-Poisson and Fejér Means of Fourier Series

Ali Taheri

in Function Spaces and Partial Differential Equations: Volume 1 - Classical Analysis

Published in print:
2015
Published Online:
September 2015
ISBN:
9780198733133
eISBN:
9780191797712
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198733133.003.0003
Subject:
Mathematics, Analysis

This chapter presents a thorough discussion of Fourier analysis on the circle and various summability methods, including Cesaro-Fejer and Abel-Poisson. The chapter also introduces the Banach algebra ... More


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