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## Category Theory

*Steve Awodey*

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568612
- eISBN:
- 9780191717567
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568612.001.0001
- Subject:
- Mathematics, Algebra

This book is a text and reference book on Category Theory, a branch of abstract algebra. The book contains clear definitions of the essential concepts, which are illuminated with numerous accessible ... More

## Procrustes Problems

*John C Gower and Garmt B Dijksterhuis*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.001.0001
- Subject:
- Mathematics, Probability / Statistics

Procrustean methods are used to transform one set of data to represent another set of data as closely as possible. This book unifies several strands in the literature and contains new algorithms. It ... More

## An Introduction to Model-Based Survey Sampling with Applications

*Ray Chambers and Robert Clark*

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.001.0001
- Subject:
- Mathematics, Probability / Statistics

This book is an introduction to the model-based approach to survey sampling. It consists of three parts, with Part I focusing on estimation of population totals. Chapters 1 and 2 introduce survey ... More

## GROUP ORBITALLY CONSTRAINED APPROXIMATION

*Moody T. Chu and Gene H. Golub*

### in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0009
- Subject:
- Mathematics, Applied Mathematics

Group actions together with properly formulated objective functions can offer a channel to tackle various classical or new and challenging problems rising from applied linear algebra. This chapter ... More

## CONCRETE GROUP THEORY

*A. A. Ivanov*

### in The Fourth Janko Group

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198527596
- eISBN:
- 9780191713163
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198527596.003.0001
- Subject:
- Mathematics, Pure Mathematics

This chapter discusses concrete group theory. Topics covered include symplectic and orthogonal GF(2)-forms, transvections and Siegel transformations, Witt's theorem, and the space of forms.

## FUNCTORS AND NATURALITY

*Steve Awodey*

### in Category Theory

- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780198568612
- eISBN:
- 9780191717567
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568612.003.0007
- Subject:
- Mathematics, Algebra

This chapter develops a general theory for functors. Topics discussed include category of categories, representable structure, stone duality, naturality, examples of natural transformations, ... More

## Weighting, scaling, and missing values

*J. C. Gower and G. B. Dijksterhuis*

### in Procrustes Problems

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0008
- Subject:
- Mathematics, Probability / Statistics

This chapter introduces the different forms of weighting. One form of weighting is when the rows of X1 are weighted. It is also possible to weight the columns. In these cases the ... More

## Mirror Symmetry of Fourier—Mukai Transformation for Elliptic Calabi—Yau Manifolds

*Naichung Conan Leung and Shing‐Tung Yau*

### in The Many Facets of Geometry: A Tribute to Nigel Hitchin

- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199534920
- eISBN:
- 9780191716010
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199534920.003.0015
- Subject:
- Mathematics, Geometry / Topology

Mirror symmetry conjecture says that for any Calabi–Yau (CY) manifold M near the large complex/symplectic structure limit, there is another CY manifold X, called the mirror manifold, such that the ... More

## Global Existence Theorems: Asymptotically Euclidean Data

*Yvonne Choquet-Bruhat*

### in General Relativity and the Einstein Equations

- Published in print:
- 2008
- Published Online:
- May 2009
- ISBN:
- 9780199230723
- eISBN:
- 9780191710872
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199230723.003.0015
- Subject:
- Mathematics, Applied Mathematics

This chapter shows how the Penrose transform can be used to prove global existence of solutions of various semilinear field equations. It outlines the foundation points of Friedrich's conformal ... More

## Using Transformations in Sample Survey Inference

*Raymond L. Chambers and Robert G. Clark*

### in An Introduction to Model-Based Survey Sampling with Applications

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780198566625
- eISBN:
- 9780191738449
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566625.003.0017
- Subject:
- Mathematics, Probability / Statistics

Using transformations in sample survey inference is the final chapter of this book and describes the extension of the empirical best prediction approach to the situation where the population values ... More

## Enterprise Transformation

*William B. Rouse*

### in Computing Possible Futures

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780198846420
- eISBN:
- 9780191881589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198846420.003.0009
- Subject:
- Mathematics, Logic / Computer Science / Mathematical Philosophy

This chapter focuses on the topic of enterprise transformation. Successful adoption of the model-based approaches presented in this book can be helped or hindered by the nature of the enterprise ... More

## Material symmetry

*David J. Steigmann*

### in Finite Elasticity Theory

- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198567783
- eISBN:
- 9780191746536
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198567783.003.0004
- Subject:
- Mathematics, Applied Mathematics

This chapter invokes the notion of local symmetry transformations to derive restrictions on constitutive response for specific material classes. This is used to derive formulas for stress in ... More

## Other sparsity-oriented issues

*I. S. Duff, A. M. Erisman, and J. K. Reid*

### in Direct Methods for Sparse Matrices

- Published in print:
- 2017
- Published Online:
- April 2017
- ISBN:
- 9780198508380
- eISBN:
- 9780191746420
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198508380.003.0015
- Subject:
- Mathematics, Numerical Analysis

We consider solving a problem that is closely related to one that we have previously solved or whose parts have previously been solved. We study backward error analysis for sparse problems, obtaining ... More

## Descriptive statistics

*Andrew Gelman and Deborah Nolan*

### in Teaching Statistics: A Bag of Tricks

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198785699
- eISBN:
- 9780191827518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198785699.003.0003
- Subject:
- Mathematics, Educational Mathematics

Descriptive statistics is the typical starting point for a statistics course, and it can be tricky to teach because the material is more difficult than it first appears. The activities in this ... More

## Linear regression and correlation

*Andrew Gelman and Deborah Nolan*

### in Teaching Statistics: A Bag of Tricks

- Published in print:
- 2017
- Published Online:
- September 2017
- ISBN:
- 9780198785699
- eISBN:
- 9780191827518
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198785699.003.0005
- Subject:
- Mathematics, Educational Mathematics

This chapter addresses the descriptive treatment of linear regression with a single predictor: straight-line fitting, interpretation of the regression line and standard deviation, the confusing ... More

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