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An inverse problem in crystallography (1985)

Rubinstein, R. ; Fitzgerald, J. E.

College Park, Md. : American Institute of Physics (AIP)

Journal of Mathematical Physics 26 (1985), S. 2717-2720

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ISSN: 1089-7658

Source: AIP Digital Archive

Topics: Mathematics , Physics

Notes: Coordinate-independent formulations are derived for the conditions satisfied by the elastic modulus tensor of materials with trigonal, hexagonal, and cubic symmetry. Analogous results for two-dimensional modulus tensors are also derived.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.526741

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Optimal coverage of convex regions (1986)

Rubinstein, R. Y. ; Samorodnitsky, G.

Springer

Journal of optimization theory and applications 51 (1986), S. 321-343

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ISSN: 1573-2878

Keywords: Coverage problems ; convex hulls ; Monte Carlo optimization ; nonconvex programming

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract The problem of the coverage of convex regions with polygons and quadratic configurations of minimal volume is considered. The regions are presented as inequality constraints of a linear or nonlinear programming problem. It is shown that the problem of the optimal coverage with an arbitrary polygon can be reduced to a convex one of coverage with a multidimensional rectangle. If, however, rotation of the coordinate system is allowed, an additional nonconvex problem must be solved. It is also shown that, to find the minimal covering hypersphere or hyperellipsoid, one has to solve two convex programming problems. Algorithms and examples illustrating the feasibility of the proposed methods are presented.