We present a robust Farkas lemma, which provides a new generalization of the celebrated Farkas lemma for linear inequality systems to uncertain conical linear systems. We also characterize the robust Farkas lemma in terms of a generalized characteristic cone. As an application of the robust Farkas lemma we establish a characterization of uncertainty-immunized solutions of conical linear program...

An algorithm based on the Monte Carlo method is described that permits the precise calculation of radiant emission characteristics of nonisothermal blackbody cavities for use as standard sources in radiometry, photometry, and radiation thermometry. The algorithm is realized for convex axisymmetric specular-diffuse cavities formed by three conical surfaces. The numerical experiments provide esti...

The recording characteristics of the monopolar needle in three dimensions have not been well established. A simple spherical recording territory is commonly assumed with the very tip proposed to have a greater spatial recording sensitivity by some authors. We demonstrate by enlarged physical modeling in a homogeneous volume conductor that the recorded amplitude diminishes more gradually radiall...

This work is devoted to the study of how spin texture excitations are affected by the presence of a static nonmagnetic impurity whenever they lie on a conical support. We realize a number of novelties as compared to the flat plane case. Indeed, by virtue of the conical shape, the interaction potential between a soliton and an impurity appears to become stronger as long as the cone is tighten. A...

Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal dielectric constants 1 < 0, 0 < 2 = 3. In this general case the two sheets of the index surface intersect, forming conical singularities. We derive the ray des...

We study conical square function estimates for Banach-valued functions, and introduce a vector-valued analogue of the Coifman–Meyer–Stein tent spaces. Following recent work of Auscher–MIntosh–Russ, the tent spaces in turn are used to construct a scale of vector-valued Hardy spaces associated with a given bisectorial operator A with certain off-diagonal bounds, such that A always has a bounded H...