The onset of transformation optics has opened avenues for designing of a plenitude of applications related to propagation of electromagnetic waves in anisotropic media. In this paper, an algorithm is proposed using a coordinate transformation and a piecewise function for the purpose of designing a three dimensional cloak having an arbitrary geometry which could be convex or non-convex in nature...

Let P = fx j Ax bg, where A is an m n matrix. We assume that P contains a ball of radius one centered at the origin, and is contained in a ball of radius R centered at the origin. We consider the problem of approximating the maximum volume ellipsoid inscribed in P. Such ellipsoids have a number of interesting applications, including the inscribed ellipsoid method for convex optimization. We red...

In previous work, one of us calculated the Solvation force of hard ellipsoid fluid with hard Gaussian overlap potential using hard needle wall interaction and non-linear equation proposed by Grimson- Rickyazen. In present work, using density functional theory and extended restricted orientation model, the solvation force of hard ellipsoid fluid in presence of more realistic rod- sphere and rod-...

5 Algorithms 8 5.1 Fourier-Motzkin Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 The Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Seidel’s Randomized Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.4 The Ellipsoid Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 5.5 Using the Ellipsoid...

We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified nilpotent Lie groups. They satisfy a set of remarkable structure relations that are used to integrate the adjoint equations.

The integer partition polytope Pn is the convex hull of all integer partitions of n. We provide a novel extended formulation of Pn, and use it to show that the extremality, adjacency, and separation problems over Pn can be solved by linear programming without the ellipsoid method. © 2014 Elsevier B.V. All rights reserved.