The purpose of this paper is to provide a modified open mapping theorem, which also applies to maps which are not open, but whose intersection with a convex cone is relatively open. We give a constructive proof, which for the special maps considered here may be seen as an alternative to the indirect proof of Frankowska’s more general open mapping principle. Open mapping theorems are of utmost i...

Introduction: Nowadays radiotherapy plays an important role in cancer treatment. Different radiotherapy techniques improvement emphasizes on using of the precise ، appropriate and useful algorithms. one of these techniques are wedged which is used in radiotherapy to compensate missing tissues and create a uniform dose distribution in tissues. The Siemens Artiste linear accelera...

Given A ∈ Ωn, the n-dimensional spectral unit ball, we show that B is a ”generalized” tangent vector at A to an entire curve in Ωn if and only if B is in the tangent cone CA to the isospectral variety at A. If B 6∈ CA, then the Kobayashi–Royden pseudometric is positive at (A;B). In the case of Ω3, the zero set of this metric is completely described.

To honor Yves Bouligand, champion of new ideas, complexity and living systems, I give a brief overview of our recent discovery of a biaxial Bouligand arceau in achiral tetrahedratic banana liquid crystals. To cite this article: P. Elizabeth Cladis, C. R. Chimie 11 (2008). 2008 Published by Elsevier Masson SAS on behalf of Académie des sciences.

Let (M, g) be a compact Riemannian manifold of dimension n ≥ 3, and let Γ be a nonempty closed subset of M . The negative case of the Singular Yamabe Problem concerns the existence and behavior of a complete metric ĝ on M\Γ that has constant negative scalar curvature and is pointwise conformally related to the smooth metric g. Previous results have shown that when Γ is a smooth submanifold of d...

Let M be an n-dimensional riemannian manifold. A natural problem in geometry is that of finding k-dimensional submanifolds N ⊂ M with the property that for any bounded open set U in M , the k-volume of N ∩ U is less than or equal to the volume of any other submanifold in M with boundary equal to ∂(N ∩ U). The submanifolds of M with the property above are called area-minimizing. Notice that when...

We give an explicit combinatorial description of the multiplicity as well as the Hilbert function of the tangent cone at any point on a Schubert variety in the symplectic Grassmannian.

In this paper, we define a class of linear conic programming (which we call matrix cone programming or MCP) involving the epigraphs of five commonly used matrix norms and the well studied symmetric cone. MCP has recently found many important applications, for example, in nuclear norm relaxations of affine rank minimization problems. In order to make the defined MCP tractable and meaningful, we ...