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## Structural Crystallography of Inorganic Oxysalts

*Sergey V. Krivovichev*

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199213207
- eISBN:
- 9780191707117
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213207.001.1
- Subject:
- Physics, Crystallography: Physics

This book deals with the structural crystallography of inorganic oxysalts in general. A special emphasis is placed upon structural topology and the methods of its description. The latter include ... More

## Basic concepts

*Sergry V. Krivovichev*

### in Structural Crystallography of Inorganic Oxysalts

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199213207
- eISBN:
- 9780191707117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213207.003.0001
- Subject:
- Physics, Crystallography: Physics

This chapter introduces basic concepts in structural chemistry relevant to the description and interpretation of structures of inorganic oxysalts. It starts from the structural classification of ... More

## The non-manifold part

*Friedhelm Waldhausen, Bjørn Jahren, and John Rognes*

### in Spaces of PL Manifolds and Categories of Simple Maps (AM-186)

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691157757
- eISBN:
- 9781400846528
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691157757.003.0004
- Subject:
- Mathematics, Geometry / Topology

Abstract and Keywords to be supplied.

## Linear Programming

*S. N. Afriat*

### in Logic of Choice and Economic Theory

- Published in print:
- 1987
- Published Online:
- November 2003
- ISBN:
- 9780198284611
- eISBN:
- 9780191595844
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198284616.003.0026
- Subject:
- Economics and Finance, Microeconomics

This is the third of five chapters on optimal programming (the typical mathematics of economics) and related issues as related to choice making. It discusses linear programming, which might appear to ... More

## Alternative approaches to structure description

*Sergry V. Krivovichev*

### in Structural Crystallography of Inorganic Oxysalts

- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780199213207
- eISBN:
- 9780191707117
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213207.003.0005
- Subject:
- Physics, Crystallography: Physics

This chapter is devoted to alternative approaches to description of complex structures of inorganic oxysalts. These include, first, treatment in terms of anion-centered polyhedra (either tetrahedra ... More

## Interstellar Overdrive

*Nicholas Mee*

### in Celestial Tapestry: The Warp and Weft of Art and Mathematics

- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851950
- eISBN:
- 9780191886690
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851950.003.0007
- Subject:
- Physics, History of Physics

Kepler sought patterns and symmetry in the laws of nature. In 1611 he wrote a booklet, De Niva Sexangular (The Six-Cornered Snowflake), in which he attempted to explain the structure of familiar ... More

## The Golden Number

*Nicholas Mee*

### in Celestial Tapestry: The Warp and Weft of Art and Mathematics

- Published in print:
- 2020
- Published Online:
- September 2020
- ISBN:
- 9780198851950
- eISBN:
- 9780191886690
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198851950.003.0014
- Subject:
- Physics, History of Physics

The golden number or divine proportion was defined by Euclid. It is sometimes claimed that it was used in classical architecture, but it is not mentioned by Vitruvius, so this seems unlikely. The ... More

## Areas, Angles, and Polyhedra

*Glen Van Brummelen*

### in Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175997
- eISBN:
- 9781400844807
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175997.003.0007
- Subject:
- Mathematics, History of Mathematics

This chapter explains how to find the area of an angle or polyhedron. It begins with a discussion of how to determine the area of a spherical triangle or polygon. The formula for the area of a ... More

## Crystallographic description of crystal structures

*Walter Steurer and Julia Dshemuchadse*

### in Intermetallics: Structures, Properties, and Statistics

- Published in print:
- 2016
- Published Online:
- September 2016
- ISBN:
- 9780198714552
- eISBN:
- 9780191782848
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198714552.003.0003
- Subject:
- Physics, Crystallography: Physics

Crystal structures, be they periodic or aperiodic, can be described in many different ways: as lattices, tilings, or coverings decorated by atoms or clusters on one hand, or as packings of structural ... More

## Lattices and Crystal Structures

*J. B. Ketterson*

### in The Physics of Solids

- Published in print:
- 2016
- Published Online:
- December 2016
- ISBN:
- 9780198742906
- eISBN:
- 9780191821523
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198742906.003.0008
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter begins with a definition of space lattice. For most pure materials, the lowest energy state at low temperatures is a crystalline solid, where the atoms or molecules making up the ... More

## Combinatorics: Ancient and Modern

*Robin Wilson and John J. Watkins (eds)*

- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199656592
- eISBN:
- 9780191748059
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199656592.001.0001
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics, History of Mathematics

The history of mathematics is a well-studied and vibrant area of research, with books and scholarly articles published on various aspects of the subject. Yet, the history of combinatorics seems to ... More

## Introducing Graphs

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0001
- Subject:
- Mathematics, Applied Mathematics

This chapter provides an introduction to graphs, a mathematical structure for visualizing, analyzing, and generalizing a situation or problem. It first consider four problems that have a distinct ... More

## Drawing Graphs

*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

### in The Fascinating World of Graph Theory

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0010
- Subject:
- Mathematics, Applied Mathematics

This chapter considers the concept of planar graph and its underlying theory. It begins with a discussion of the Three Houses and Three Utilities Problem and how it can be represented by a graph. It ... More

##
Problems of Harmonic Analysis Related to Finite-Type Hypersurfaces in ^{R}3, and Newton Polyhedra *Detlef Müller*

*Charles Fefferman, Alexandru D. Ionescu, D. H. Phong, Stephen Wainger, 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/9780691159416.003.0013
- Subject:
- Mathematics, Numerical Analysis

This chapter presents three sets of problems and explains how these questions can be answered in an (almost) complete way in terms of Newton polyhedra associated to the given surface S (here, a ... More

## Wright-Fisher Geometry

*Charles L. Epstein and Rafe1 Mazzeo*

### in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

- Published in print:
- 2013
- Published Online:
- October 2017
- ISBN:
- 9780691157122
- eISBN:
- 9781400846108
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691157122.003.0002
- Subject:
- Mathematics, Probability / Statistics

This chapter introduces the geometric preliminaries needed to analyze generalized Kimura diffusions, with particular emphasis on Wright–Fisher geometry. It begins with a discussion of the natural ... More

## Introduction

*Isroil A. Ikromov, Detlef Müller, Isroil A. Ikromov, and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0001
- Subject:
- Mathematics, Geometry / Topology

This chapter discusses the Fourier restriction. The Fourier restriction problem presents one important instance of a wide circle of related problems, such as the boundedness properties of Bochner ... More

## Reduction to Restriction Estimates near the Principal Root Jet

*Isroil A. Ikromov and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0003
- Subject:
- Mathematics, Geometry / Topology

This chapter shows that one may reduce the desired Fourier restriction estimate to a piece Ssubscript Greek small letter psi of the surface S lying above a small, “horn-shaped” neighborhood ... More

## Proofs of Propositions 1.7 and 1.17

*Isroil A. Ikromov and Detlef Müller*

### in Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

- Published in print:
- 2016
- Published Online:
- October 2017
- ISBN:
- 9780691170541
- eISBN:
- 9781400881246
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691170541.003.0009
- Subject:
- Mathematics, Geometry / Topology

This chapter showcases the remaining proofs of two results from the first chapter. It turns to the first of these results, based on a proposition made Chapter 1, on the characterization of linearly ... More

## Crystals and crystal structures

*Christopher Hammond*

### in The Basics of Crystallography and Diffraction

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198738671
- eISBN:
- 9780191801938
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198738671.003.0001
- Subject:
- Physics, Crystallography: Physics, Condensed Matter Physics / Materials

This first chapter considers the nature of the crystalline state by constructing crystal structures. It then moves on to look at interstitial, covalent and ionic structures, stacking faults, and ... More

## Bravais lattices and crystal systems

*Christopher Hammond*

### in The Basics of Crystallography and Diffraction

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780198738671
- eISBN:
- 9780191801938
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198738671.003.0003
- Subject:
- Physics, Crystallography: Physics, Condensed Matter Physics / Materials

Chapter 3 describes the fourteen Bravais (space) lattices. It looks at centro and non-centrosymmetric (enantiomorphous and non-enantiomorphous) point groups and geometrical relations between the ... More

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