## Set Theory: Boolean-Valued Models and Independence Proofs

*John L. Bell*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568520
- eISBN:
- 9780191717581
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568520.001.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This is the third edition of a well-known graduate textbook on Boolean-valued models of set theory. The aim of the first and second editions was to provide a systematic and adequately motivated ... More

## TWENTY QUESTIONS

*Roman Kossak and James H. Schmerl*

### in The Structure of Models of Peano Arithmetic

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0012
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter gives a list of open problems the book's authors have considered most interesting. Two of the problems (7 and 9) have already been solved by Enayat. The chapter includes a website which ... More

## Macromolecular Crystallization and Crystal Perfection

*Naomi E. Chayen, John R. Helliwell, and Edward H. Snell*

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199213252
- eISBN:
- 9780191707575
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213252.001.0001
- Subject:
- Physics, Crystallography

Structural crystallography provides key information to understand the mechanism involved for biological processes. The technique requires high‐quality crystals. The book Macromolecular ... More

## Modern Perspectives in Lattice QCD: Quantum Field Theory and High Performance Computing: Lecture Notes of the Les Houches Summer School: Volume 93, August 2009

*Laurent Lellouch, Rainer Sommer, Benjamin Svetitsky, Anastassios Vladikas, and Leticia F. Cugliandolo (eds)*

- Published in print:
- 2011
- Published Online:
- January 2012
- ISBN:
- 9780199691609
- eISBN:
- 9780191731792
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691609.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The book is based on the lectures delivered at the XCIII Session of the ´Ecole de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of Ph.D. ... More

## DETERMINATION OF THE SUPERSPACE GROUP

*Sander Van Smaalen*

### in Incommensurate Crystallography

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570820
- eISBN:
- 9780191718762
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570820.003.0009
- Subject:
- Physics, Crystallography

This chapter presents the steps that are required to determine the superspace group of an aperiodic crystal from its diffraction pattern. This includes the analysis of the metric of the reciprocal ... More

## Introduction to diffraction

*Peter Main*

### 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/9780199219469.003.0001
- Subject:
- Physics, Crystallography

This introductory chapter provides information on some fundamental aspects of crystal structures and their diffraction of X-rays as a basis for the rest of the book. It describes electrons, atoms, ... More

## Binomial Coefficients Revisited

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0004
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents additional properties of binomial coefficients and several occurrences of Catalan numbers. Vandermonde's identity is explained and the lattice point and lattice-walking are also ... More

## Cross‐Talk in Movements: Reconceiving the Culture‐Network Link

*Ann Mische*

### in Social Movements and Networks: Relational Approaches to Collective Action

- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780199251780
- eISBN:
- 9780191599057
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199251789.003.0011
- Subject:
- Political Science, Comparative Politics

In dialogue with recent developments in cultural sociology, this chapter looks at the forms of discourse generated by movement activists in response to the multiple relations in which they are ... More

## PHONONS

*J. M. Ziman*

### in Electrons and Phonons: The Theory of Transport Phenomena in Solids

- Published in print:
- 2001
- Published Online:
- September 2007
- ISBN:
- 9780198507796
- eISBN:
- 9780191709937
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507796.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter discusses the basic properties of phonons. Topics covered include solid matter as a gas of excitations, the crystal lattice, dynamics of a linear lattice, dynamics of space lattices, the ... More

## Lattice Paths and Catalan Numbers

*Thomas Koshy*

### in Catalan Numbers with Applications

- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0009
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a number of occurrences of Catalan numbers in the study of lattice paths and their relationships to binary words, mountain ranges, and postfix expressions. The chapter also ... More

## AN ELEMENTARY CHARACTERIZATION OF KRULL DIMENSION

*Thierry Coquand Henri Lombardi and Marie-Françoise Roy*

### in From Sets and Types to Topology and Analysis: Towards practicable foundations for constructive mathematics

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566519
- eISBN:
- 9780191713927
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566519.003.0015
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter contributes to the new direction in constructive algebra originated by Coquand, Lombardi, and others, which aims at a partial realisation of Hilbert's programme. The idea is to prove ... More

## Crystal systematics

*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/9780199559046.003.0003
- Subject:
- Physics, Crystallography

This chapter describes the nature of the crystalline state and introduces the concepts of the motif and symmetry — an understanding of both is very important in analysing the molecular structure of ... More

## BOOLEAN AND HEYTING ALGEBRAS: THE ESSENTIALS

*John L. Bell*

### in Set Theory: Boolean-Valued Models and Independence Proofs

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568520
- eISBN:
- 9780191717581
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568520.003.0001
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter provides a brief account of the theory of Boolean and Heyting algebras, including the basic representation theorems and their connections with logic.

## SUBSTRUCTURE LATTICES

*Roman Kossak and James H. Schmerl*

### in The Structure of Models of Peano Arithmetic

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568278
- eISBN:
- 9780191718199
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568278.003.0004
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter examines substructure lattices, with emphasis on how to obtain models with specific finite lattices as substructure lattices. The finite distributive lattice case is presented in full. ... More

## Numerical Simulation Of Microflows And Nanoflows

*Narayan R. Aluru and George Em Karniadakis*

### in Micro/Nano Technology Systems for Biomedical Applications: Microfluidics, Optics, and Surface Chemistry

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199219698
- eISBN:
- 9780191594229
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199219698.003.0003
- Subject:
- Mathematics, Mathematical Biology

In this chapter we review recent advances in numerical simulation of micro and nanoflows. For coarse-grained simulation of microfuidics, we present an overview of Lattice Boltzmann, Brownian ... More

## Diffraction by a three‐dimensional lattice

*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/9780199559046.003.0008
- Subject:
- Physics, Crystallography

This chapter describes the basis of X-ray diffraction by a three-dimensional crystal and introduces the Laue equations which describe the geometric conditions for constructive interference of X-rays ... More

## Practical Quantum Mechanics: Modern Tools and Applications

*Efstratios Manousakis*

- Published in print:
- 2015
- Published Online:
- December 2015
- ISBN:
- 9780198749349
- eISBN:
- 9780191813474
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198749349.001.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics

The book contains lectures notes for a graduate two-semester course in quantum mechanics. It differs from other quantum mechanics textbooks as various parts of the book are inspired by rather recent ... More

## Other macromolecular crystal diffraction disorders

*Naomi E. Chayen, John R. Helliwell, and Edward H. Snell*

### in Macromolecular Crystallization and Crystal Perfection

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199213252
- eISBN:
- 9780191707575
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213252.003.0013
- Subject:
- Physics, Crystallography

The phenomenon of so‐called ‘order—disorder’ in crystals has few examples in the world of biological macromolecules. Thus, the crystal repetition may only approximately be covered by the unit cell. ... More

## Small and large worlds

*Sergey N. Dorogovtsev*

### in Lectures on Complex Networks

- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199548927
- eISBN:
- 9780191720574
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199548927.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses and compares the geometries of small worlds, lattices and fractals. The first measurements of the diameter of the World Wide Web are described. The Watts–Strogatz model of a ... More

## Electrons and Phonons: The Theory of Transport Phenomena in Solids

*J.M. Ziman*

- Published in print:
- 2001
- Published Online:
- September 2007
- ISBN:
- 9780198507796
- eISBN:
- 9780191709937
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507796.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This book is a study of the theory of electrical and thermal conduction in metals, semiconductors, and insulators. The basic ideas of crystal lattice dynamics, electron zone structure, and transport ... More