scholarly journals Regularity for Shape Optimizers: The Nondegenerate Case

2018 ◽  
Vol 71 (8) ◽  
pp. 1535-1596 ◽  
Author(s):  
Dennis Kriventsov ◽  
Fanghua Lin
Keyword(s):  
Nondegenerate Case

EQUIVALENT L-SHAPES OF DOUBLE-LOOP NETWORKS FOR THE DEGENERATE CASE

2000 ◽  
Vol 01 (01) ◽  
pp. 47-60 ◽  
Author(s):  
CHIUYUAN CHEN ◽  
F. K. HWANG
Keyword(s):  
Local Area Networks ◽  
Local Area ◽  
Degenerate Case ◽  
Algebraic Operation ◽  
Double Loop ◽  
Nondegenerate Case ◽  
Distance Properties ◽  
Double Loop Networks ◽  
Geometric Operation

Double-loop networks have been widely studied as architecture for local area networks. The L-shape is an important tool for studying the distance properties of double-loop networks. Two L-shapes are equivalent if the numbers of nodes k steps away from the origin are the same for every k. Hwang and Xu first studied equivalent L-shapes through a geometric operation called a 3-rectangle transformation. Rödseth gave an algebraic operation, which was found by Huang, Hwang and Liu to correspond to the 3-rectangle transformation. Recently, Chen and Hwang obtained all equivalent transformations for the nondegenerate case. In this paper, we do the same for the degenerate case.

scholarly journals Laplace Approximations for Large Deviations of Nonreversible Markov Processes. The Nondegenerate Case

1995 ◽  
Vol 23 (1) ◽  
pp. 236-267 ◽  
Author(s):  
Erwin Bolthausen ◽  
Jean-Dominique Deuschel ◽  
Yozo Tamura
Keyword(s):  
Large Deviations ◽  
Markov Processes ◽  
Nondegenerate Case

scholarly journals On LA-Courant Algebroids and Poisson Lie 2-Algebroids

2020 ◽  
Vol 23 (3) ◽  
Author(s):  
M. Jotz Lean
Keyword(s):  
Lie Algebroids ◽  
General Context ◽  
Matched Pairs ◽  
Courant Algebroids ◽  
Dirac Structures ◽  
Courant Algebroid ◽  
The Core ◽  
Precise Sense ◽  
Nondegenerate Case ◽  
New Construction

Abstract This paper reformulates Li-Bland’s definition for LA-Courant algebroids, or Poisson Lie 2-algebroids, in terms of split Lie 2-algebroids and self-dual 2-representations. This definition generalises in a precise sense the characterisation of (decomposed) double Lie algebroids via matched pairs of 2-representations. We use the known geometric examples of LA-Courant algebroids in order to provide new examples of Poisson Lie 2-algebroids, and we explain in this general context Roytenberg’s equivalence of Courant algebroids with symplectic Lie 2-algebroids. We study further the core of an LA-Courant algebroid and we prove that it carries an induced degenerate Courant algebroid structure. In the nondegenerate case, this gives a new construction of a Courant algebroid from the corresponding symplectic Lie 2-algebroid. Finally we completely characterise VB-Dirac and LA-Dirac structures via simpler objects, that we compare to Li-Bland’s pseudo-Dirac structures.

scholarly journals A modified barrier function method with improved rate of convergence for degenerate problems

1980 ◽  
Vol 21 (3) ◽  
pp. 305-329 ◽  
Author(s):  
Krisorn Jittorntrum ◽  
M. R. Osborne
Keyword(s):  
Rate Of Convergence ◽  
Barrier Function ◽  
Function Method ◽  
Degenerate Problems ◽  
Scaling Properties ◽  
Classical Algorithm ◽  
Nondegenerate Case ◽  
Accelerate Convergence

AbstractIn a previous paper the authors have shown that the classical barrier function has anO(r) rate of convergence unless the problem is degenerate when it reducesO(r½). In this paper a modified barrier function algorithm is suggested which does not suffer from this problem. It turns out to have superior scaling properties which make it preferable to the classical algorithm, even in the nondegenerate case, if extrapolation is to be used to accelerate convergence.

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