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NON-PARAMETRIC IMAGE REGISTRATION

Jan Modersitzki

in Numerical Methods for Image Registration

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.003.0008
Subject:
Mathematics, Applied Mathematics

This chapter introduces non-parametric registrations. The idea behind this type of registration is to come up with an appropriate measure both for the similarity as well as for the likelihood of a ... More


Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175)

Ben Brubaker, Daniel Bump, and Solomon Friedberg

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691150659
eISBN:
9781400838998
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691150659.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, ... More


Catalan Numbers with Applications

Thomas Koshy

Published in print:
2008
Published Online:
January 2009
ISBN:
9780195334548
eISBN:
9780199868766
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780195334548.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

Fibonacci and Lucas sequences are “two shining stars in the vast array of integer sequences,” and because of their ubiquitousness, tendency to appear in quite unexpected and unrelated places, ... More


HYPERBOLIC CONSERVATION LAWS

George Em Karniadakis and Spencer J. Sherwin

in Spectral/hp Element Methods for Computational Fluid Dynamics

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198528692
eISBN:
9780191713491
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528692.003.0010
Subject:
Mathematics, Numerical Analysis

This chapter discusses compressible Euler and Navier-Stokes equations as well as general hyperbolic conservation laws. The principle issue is how effectively to use the high-order expansions of the ... More


RADON TRANSFORM AS THE INTERRELATION OF GEOMETRY AND ANALYSIS

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/9780198509783.003.0008
Subject:
Mathematics, Mathematical Physics

This chapter deals with various questions which are related to the Radon transform, for example, the analog for forms, Selberg's trace formula. It gives a sharpening of the classical Euler-Maclaurin ... More


Existence of Ball Quotients Covering Line Arrangements

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter justifies the assumption that ball quotients covering line arrangements exist. It begins with the general case on the existence of finite covers by ball quotients of weighted ... More


THE MATHEMATICAL SETTING

Jan Modersitzki

in Numerical Methods for Image Registration

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.003.0003
Subject:
Mathematics, Applied Mathematics

The basic mathematical notation is introduced, including formal definitions of images and digital images, midpoint and meshpoint grids. Local and global interpolation techniques such as ... More


ELASTIC REGISTRATION

Jan Modersitzki

in Numerical Methods for Image Registration

Published in print:
2003
Published Online:
September 2007
ISBN:
9780198528418
eISBN:
9780191713583
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198528418.003.0009
Subject:
Mathematics, Applied Mathematics

This chapter introduces elastic registration using the general framework introduced in Chapter 8. A physical motivation for this particular regularizer is given. The two images are viewed as two ... More


The Case of SL(2); the Examples of Evans and Rudnick

Nicholas M. Katz

in Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.003.0015
Subject:
Mathematics, Number Theory

This chapter treats both of these examples, as well as all the examples to come, using the Euler–Poincaré formula, cf. [Ray, Thm. 1] or [Ka-GKM, 2.3.1] or [Ka-SE, 4.6, (v) atop p. 113] or [De-ST, ... More


Topological Invariants and Differential Geometry

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0002
Subject:
Mathematics, Geometry / Topology

This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number ... More


Riemann Surfaces, Coverings, and Hypergeometric Functions

Paula Tretkoff

in Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.003.0003
Subject:
Mathematics, Geometry / Topology

This chapter deals with Riemann surfaces, coverings, and hypergeometric functions. It first considers the genus and Euler number of a Riemann surface before discussing Möbius transformations and ... More


Tic-tac-toe on Affine Planes

Maureen T. Carroll and Steven T. Dougherty

in The Mathematics of Various Entertaining Subjects: Research in Recreational Math

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164038
eISBN:
9781400881338
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164038.003.0013
Subject:
Mathematics, History of Mathematics

This chapter introduces a new game of tic-tac-toe that fits squarely within the body of work inspired by mathematician Leonhard Euler's findings on the so-called “Graeco-Latin squares” and the ... More


Partial differential equations for fluids

Bijan Mohammadi and Olivier Pironneau

in Applied Shape Optimization for Fluids

Published in print:
2009
Published Online:
February 2010
ISBN:
9780199546909
eISBN:
9780191720482
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199546909.003.0003
Subject:
Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ... More


Relativistic Fluids

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/9780199230723.003.0009
Subject:
Mathematics, Applied Mathematics

This chapter presents general properties of perfect fluids. When appropriate definitions are given, some of these properties generalize well-known properties of non-relativistic perfect fluids. ... More


The Euler-Reynolds System

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0001
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter provides a background on the Euler-Reynolds system, starting with some of the underlying philosophy behind the argument. It describes low frequency parts and ensemble averages of Euler ... More


The Main Iteration Lemma

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0010
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter properly formalizes the Main Lemma, first by discussing the frequency energy levels for the Euler-Reynolds equations. Here the bounds are all consistent with the symmetries of the Euler ... More


Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.001.0001
Subject:
Mathematics, Computational Mathematics / Optimization

Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if ... More


Graph Theory: A Look Back—The Road Ahead

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/9780691175638.003.0013
Subject:
Mathematics, Applied Mathematics

This book concludes with an epilogue, which traces the evolution of graph theory, from the conceptualization of the Königsberg Bridge Problem and its generalization by Leonhard Euler, whose solution ... More


Structure of the Book

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0002
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter provides an overview of the book's structure. Section 3 deals with the error terms which need to be controlled, whereas Part III explains some notation of the book and presents a basic ... More


Basic Technical Outline

Philip Isett

in Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0003
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter provides a more technical outline of the construction, starting with a solution to the Euler-Reynolds system and a correction v₁ = v + V, p₁ = p + P. The correction V is a divergence ... More


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