## 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