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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


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


Sign Variation of Vectors and TN Linear Transformations

Shaun M. Fallat and Charles R. Johnson

in Totally Nonnegative Matrices

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691121574
eISBN:
9781400839018
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691121574.003.0005
Subject:
Mathematics, Applied Mathematics

This chapter develops an array of results about TP/TN matrices and sign variation diminution, along with appropriate converses. If the entries of a vector represent a sampling of consecutive function ... More


Introduction to the WKB(J) Approximation: All Things Airy

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0007
Subject:
Mathematics, Applied Mathematics

This chapter deals with the WKB(J) approximation, commonly used in applied mathematics and mathematical physics to find approximate solutions of linear ordinary differential equations (of any order ... More


The WKB(J) Approximation Revisited

John A. Adam

in Rays, Waves, and Scattering: Topics in Classical Mathematical Physics

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691148373
eISBN:
9781400885404
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691148373.003.0022
Subject:
Mathematics, Applied Mathematics

This chapter reexamines the WKB(J) approximation and applies it to some simple one-dimensional potentials, with a focus on the case of a triangular barrier. It first considers the connection formulas ... More


Small-Volume Expansions of the Displacement Fields

Habib Ammari, Elie Bretin, Josselin Garnier, Hyeonbae Kang, Hyundae Lee, and Abdul Wahab

in Mathematical Methods in Elasticity Imaging

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691165318
eISBN:
9781400866625
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691165318.003.0004
Subject:
Mathematics, Applied Mathematics

This chapter deals with small-volume expansions of the displacement fields. It first introduces the notion of elastic moment tensor, a geometric quantity associated with a small-volume inclusion, ... 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


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