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Algebraic and Geometric Surgery

Andrew Ranicki

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509240
eISBN:
9780191708725
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509240.001.0001
Subject:
Mathematics, Geometry / Topology

This book is an introduction to surgery theory, the standard algebraic topology classification method for manifolds of dimension greater than 4. It is aimed at those who have already been on a basic ... More


Artificial likelihoods and estimating functions

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0006
Subject:
Mathematics, Probability / Statistics

This chapter discusses the problem of root selection using artificial objective functions associated with an estimating function; the artificial likelihoods discussed in this chapter share many ... More


THE NONLINEAR RADON AND FOURIER TRANSFORMS

Leon Ehrenpreis

in The Universality of the Radon Transform

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198509783
eISBN:
9780191709166
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509783.003.0005
Subject:
Mathematics, Mathematical Physics

In order to deal with the nonlinear Radon transform, this chapter introduces a new type of Fourier transform: the nonlinear Fourier transform. This can be used to analyze various nonlinear Radon ... More


Are there discontinuities in financial prices?

Neil Shephard

in Celebrating Statistics: Papers in honour of Sir David Cox on his 80th birthday

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566540
eISBN:
9780191718038
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566540.003.0012
Subject:
Mathematics, Probability / Statistics

This chapter explores whether there are discontinuities in financial price processes using daily data on the Japanese yen and United States dollar. It opens with a brief description of the data, ... More


Methodologies for root selection

Christopher G. Small and Jinfang Wang

in Numerical Methods for Nonlinear Estimating Equations

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198506881
eISBN:
9780191709258
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198506881.003.0005
Subject:
Mathematics, Probability / Statistics

This chapter studies the specific problem of selecting a root of an estimating equation with more than one root, for instance, using methods by removing the irregularity of the estimating function or ... More


PARTIALLY DESCRIBED INVERSE EIGENVALUE PROBLEMS

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/9780198566649.003.0005
Subject:
Mathematics, Applied Mathematics

In practice, it is often the case that only partial information on eigenvalues and eigenvectors is available. In many cases, just a few eigenpairs can determine much of the desirable reconstruction. ... More


THE EVEN-DIMENSIONAL SURGERY OBSTRUCTION

Andrew Ranicki

in Algebraic and Geometric Surgery

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509240
eISBN:
9780191708725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509240.003.0011
Subject:
Mathematics, Geometry / Topology

This chapter gives the algebraic construction and geometric properties of the even-dimensional surgery obstruction groups. It includes quadratic and kernel forms.


THE ODD-DIMENSIONAL SURGERY OBSTRUCTION

Andrew Ranicki

in Algebraic and Geometric Surgery

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198509240
eISBN:
9780191708725
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198509240.003.0012
Subject:
Mathematics, Geometry / Topology

This chapter provides the algebraic construction and geometric properties of the odd-dimensional surgery obstruction groups. It includes quadratic and kernel forms.


*SOME COMMENTS ON VECTORIAL PROBLEMS

Andrea Braides

in Gamma-Convergence for Beginners

Published in print:
2002
Published Online:
September 2007
ISBN:
9780198507840
eISBN:
9780191709890
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198507840.003.0013
Subject:
Mathematics, Applied Mathematics

This chapter shows that some notions used in a one-dimensional setting can be extended to higher dimensions and vector problems if properly modified. In particular, convexity requirements for lower ... More


Theory and Econometrics

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0001
Subject:
Economics and Finance, History of Economic Thought

This chapter sets out the book's focus, namely constructing and applying competitive equilibria for a class of linear-quadratic-Gaussian dynamic economies with complete markets. Here, an economy will ... More


Quadratic Forms of Type F4

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0009
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents various results about quadratic forms of type F₄. The Moufang quadrangles of type F₄ were discovered in the course of carrying out the classification of Moufang polygons and ... More


Neural Coherence and Stochastic Resonance

André Longtin

in Stochastic Methods in Neuroscience

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199235070
eISBN:
9780191715778
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199235070.003.0004
Subject:
Mathematics, Biostatistics

This chapter concerns the influence of noise and periodic rhythms on the firing patterns of neurons in their subthreshold regime. Such a regime conceals many computations that lead to successive ... More


Finite Sample Moments

Aman Ullah

in Finite Sample Econometrics

Published in print:
2004
Published Online:
August 2004
ISBN:
9780198774471
eISBN:
9780191601347
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198774478.003.0002
Subject:
Economics and Finance, Econometrics

This chapter derives techniques for obtaining exact and approximate moments of a function of random vector/matrix. A special case of the function considered is the ratio of quadratic forms, which ... More


Quadratic Forms

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0002
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter presents a few standard definitions and results about quadratic forms and polar spaces. It begins by defining a quadratic module and a quadratic space and proceeds by discussing a ... More


Optimal Resource Allocations

Lars Peter Hansen and Thomas J. Sargent

in Recursive Models of Dynamic Linear Economies

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691042770
eISBN:
9781400848188
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691042770.003.0005
Subject:
Economics and Finance, History of Economic Thought

This chapter describes a planning problem that generates competitive equilibrium allocations and compares two methods for solving it. The first method uses state- and date-contingent Lagrange ... More


Linear Quadratic Approximations: An Introduction

Javier Díaz‐Giménez

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0002
Subject:
Economics and Finance, Macro- and Monetary Economics

This is a brief introduction to dynamic programming and the method of using linear quadratic (LQ) approximations to the return function; the method is an approximation because it computes the ... More


Optimal Fiscal Policy in a Linear Stochastic Economy

Thomas J. Sargent and François R. Velde

in Computational Methods for the Study of Dynamic Economies

Published in print:
2001
Published Online:
November 2003
ISBN:
9780199248278
eISBN:
9780191596605
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0199248273.003.0009
Subject:
Economics and Finance, Macro- and Monetary Economics

The Lucas and Stokey (1983) economy without capital is used to exhibit features of the Lucas and Stokey model of optimal taxation, and show how they compare with Barro's (1979) tax‐smoothing model. ... More


Semi-ramified Quadrangles of Type E6, E7 and E8

Bernhard M¨uhlherr, Holger P. Petersson, and Richard M. Weiss

in Descent in Buildings (AM-190)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.003.0012
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This chapter deals with the case that the building at infinity of the Bruhat-Tits building Ξ‎ is a Moufang semi-ramified quadrangle of type E⁶, E₇ and E₈. The basic proposition is that Ξ‎ is a ... More


Economic Production Functions

John McDonald and G. D. Snooks

in Domesday Economy: A New Approach to Anglo-Norman History

Published in print:
1986
Published Online:
November 2003
ISBN:
9780198285243
eISBN:
9780191596636
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/0198285248.003.0009
Subject:
Economics and Finance, Economic History

‘Economic production functions’ describes the characteristics of deterministic production functions used in the analysis of Domesday production. These include the Cobb–Douglas, Constant Elasticity of ... More


BROADENING OF SPECTRAL LINES

Takashi Fujimoto

in Plasma Spectroscopy

Published in print:
2004
Published Online:
September 2007
ISBN:
9780198530282
eISBN:
9780191713149
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198530282.003.0007
Subject:
Physics, Nuclear and Plasma Physics

The Doppler broadening, the natural broadening, and the quasi-static broadening are introduced. The last broadening is due to the Stark effect in the Holtsmark micro-field with the Debye shielding. ... More


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