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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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