scholarly journals Betti Curves of Rank One Symmetric Matrices

2021 ◽  
pp. 645-655
Author(s):  
Carina Curto ◽  
Joshua Paik ◽  
Igor Rivin
Keyword(s):  
Symmetric Matrices ◽  
Rank One

scholarly journals Rank-one convexity implies quasi-convexity on certain hypersurfaces

2003 ◽  
Vol 133 (6) ◽  
pp. 1263-1272 ◽  
Author(s):  
Nirmalendu Chaudhuri ◽  
Stefan Müller
Keyword(s):  
Compact Subset ◽  
Convex Functions ◽  
Young Measure ◽  
Symmetric Matrices ◽  
Rank One ◽  
Gradient Young Measure ◽  
Quasi Convexity ◽  
Compact Subsets

We show that, if f : M2×2 → R is rank-one convex on the hyperboloid is the set of 2 × 2 real symmetric matrices, then f can be approximated by quasi-convex functions on M2×2 uniformly on compact subsets of . Equivalently, every gradient Young measure supported on a compact subset of is a laminate.

scholarly journals Upper semicontinuity of the lamination hull

2018 ◽  
Vol 24 (4) ◽  
pp. 1503-1510
Author(s):  
Terence L.J. Harris
Keyword(s):  
Convex Hull ◽  
Upper Semicontinuity ◽  
Symmetric Matrices ◽  
Compact Set ◽  
Upper Semicontinuous ◽  
Rank One ◽  
Point Set

Let  K ⊆ ℝ2×2 be a compact set, let Krc be its rank-one convex hull, and let L (K) be its lamination convex hull. It is shown that the mapping K ↦ L̅(K̅) is not upper semicontinuous on the diagonal matrices in ℝ2×2, which was a problem left by Kolář. This is followed by an example of a 5-point set of 2 × 2 symmetric matrices with non-compact lamination hull. Finally, another 5-point set K is constructed, which has L (K) connected, compact and strictly smaller than Krc.

Derivation of the Wave and Scattering Operators for an Interaction of Rank One

1970 ◽  
Vol 11 (8) ◽  
pp. 2415-2424 ◽  
Author(s):  
M. Anthea Grubb ◽  
D. B. Pearson
Keyword(s):  
Rank One ◽  
Scattering Operators

scholarly journals Ramification Theory for Extensions of Degree p. II

1972 ◽  
Vol 46 ◽  
pp. 97-109
Author(s):  
Susan Williamson
Keyword(s):  
Valuation Ring ◽  
Quotient Field ◽  
Root Of Unity ◽  
Ramification Index ◽  
Ramification Theory ◽  
Rank One ◽  
The Absolute

Let k denote the quotient field of a complete discrete rank one valuation ring R of unequal characteristic and let p denote the characteristic of R̅; assume that R contains a primitive pth root of unity, so that the absolute ramification index e of R is a multiple of p — 1, and each Gallois extension K ⊃ k of degree p may be obtained by the adjunction of a pth root.

REMARKS ON THE KIELANOWSKI PARAMETRIZATION OF THE KOBAYASHI-MASKAWA MATRIX

1996 ◽  
Vol 11 (31) ◽  
pp. 2531-2537 ◽  
Author(s):  
TATSUO KOBAYASHI ◽  
ZHI-ZHONG XING
Keyword(s):  
Symmetric Matrices

We study the Kielanowski parametrization of the Kobayashi-Maskawa (KM) matrix V. A new two-angle parametrization is investigated explicitly and compared with the Kielanowski ansatz. Both of them are symmetric matrices and lead to |V13/V23|=0.129. Necessary corrections to the off-diagonal symmetry of V are also discussed.

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