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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


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