PURPOSE This study was designed to assess the effect of mitochondrial DNA (mtDNA) mutation T8993C on cone structure in a family expressing neurogenic muscle weakness, ataxia, and retinitis pigmentosa (NARP) syndrome. METHODS Five family members were studied, using clinical examination, nerve conduction studies, perimetry, optical coherence tomography (OCT) measures of central retinal thicknes...

This work adresses the problem of the approximation of the normals of the offsets of general compact sets in euclidean spaces. It is proven that for general sampling conditions, it is possible to approximate the gradient vector field of the distance to general compact sets. These conditions involve the μ-reach of the compact set, a recently introduced notion of feature size. As a consequence, w...

Molecular genetic studies demonstrate that the human cone opsin gene array on the q-arm of the X-chromosome typically consists of one long-wave-sensitive (L) cone opsin gene and from one to several middle-wave-sensitive (M) cone opsin genes. Although the presence of the single L-cone opsin gene and at least one M-cone opsin gene is essential for normal red-green colour discrimination, the funct...

Given a flat, projective morphism Y → T from an equidimensional scheme to a nonsingular curve and a subscheme Z of Y , we give conditions under which specialization of the Segre class s(NZY ) of the normal cone of Z in Y implies flatness of the normal cone. We apply this result to study when the relative tangent star cone of a flat family is flat.

An example in which CRCQ holds. The left figure shows a set S(u) defined by 3 constraints. The normal cone NS(u)(x) is the cone generated by the two dashed halflines originated from the point x. The red curve indicates the neighborhood X. The normal cone NS(u)(x) has four nonempty faces, and the family {I(x′, u), x′ ∈ S(u)∩X} contains four elements {1, 3},{1},{3} and ∅, each of which correspond...

Objectives: In this paper, we have to establish a generalized common fixed point theorem in cone rectangular metric spaces. Methods: use the Banach contraction principle technique theorem. Findings: The paper presents unique for two weakly compatible self-maps satisfying expansive type mapping space without assuming normality condition of cone. Our result extends and supplements some well-known...

We study the geometric structure of Lorentzian spin manifolds, which admit imaginary Killing spinors. The discussion is based on the cone construction and a normal form classification of skew-adjoint operators in signature (2, n−2). Derived geometries include Brinkmann spaces, Lorentzian Einstein-Sasaki spaces and certain warped product structures. Exceptional cases with decomposable holonomy o...

A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown—by several authors using different techniques—that the convex hull of the intersection of an ellipsoid, E , and a split disjunction, (l−xj)(xj−u) ≤ 0 with l < u, equals the intersection of E with an additional second-order-cone...

Since the early 1970's there have been many papers devoted to tangent cones and their applications to optimization. Much of the debate over which tangent cone is \best" has centered on the properties of Clarke's tangent cone and whether other cones have these properties. In this paper it is shown that there are an innnite number of tangent cones with some of the nicest properties of Clarke's co...

In this paper we show that by renorming an ordered Banach space, every cone P can be converted to a normal cone with constant K = 1 and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.