The invarianee ofC-numerical rangeC-numericai radius, and their dual problems

1991 ◽  
Vol 30 (1-2) ◽  
pp. 117-128 ◽  
Author(s):  
Wai Yip Man
Keyword(s):  
Dual Problems

Some Dual Problems of Geometric Probability in the Plane

1993 ◽  
Vol 2 (1) ◽  
pp. 11-23 ◽  
Author(s):  
John Gates
Keyword(s):  
Combinatorial Geometry ◽  
Chord Length ◽  
Geometric Probability ◽  
Dual Problems ◽  
Sylvester’S Problem

A definition is adopted for convexity of a set of directed lines in the plane. Following this, the duals of a number of standard problems of geometric probability are formulated. Problems considered in detail are the duals of Sylvester's problem, chord length distributions and Ambartzumian's combinatorial geometry. The paper suggests some questions for further work.

The Dual Problems of Peace and National Security

PS ◽  
1984 ◽  
Vol 17 (1) ◽  
pp. 18
Author(s):  
Robert G. Gilpin
Keyword(s):  
National Security ◽  
Dual Problems

Flux Evaluation in Primal and Dual Boundary-Coupled Problems

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
E. H. van Brummelen ◽  
K. G. van der Zee ◽  
V. V. Garg ◽  
S. Prudhomme
Keyword(s):  
Finite Element ◽  
Free Boundary Problems ◽  
Fluid Structure Interaction ◽  
Coupled Problems ◽  
Fluid Structure ◽  
Dual Problems ◽  
Structure Interaction ◽  
Finite Element Approximations ◽  
Primal And Dual Problems ◽  
Primal And Dual

A crucial aspect in boundary-coupled problems, such as fluid-structure interaction, pertains to the evaluation of fluxes. In boundary-coupled problems, the flux evaluation appears implicitly in the formulation and consequently, improper flux evaluation can lead to instability. Finite-element approximations of primal and dual problems corresponding to improper formulations can therefore be nonconvergent or display suboptimal convergence rates. In this paper, we consider the main aspects of flux evaluation in finite-element approximations of boundary-coupled problems. Based on a model problem, we consider various formulations and illustrate the implications for corresponding primal and dual problems. In addition, we discuss the extension to free-boundary problems, fluid-structure interaction, and electro-osmosis applications.

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