This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

This paper aims at combining variable ordering structures with set relations in set optimization, which have been defined using the constant ordering cone before. Since the purpose is to connect these two important approaches in set optimization, we do not restrict our considerations to one certain relation. Conversely, we provide the reader with many new variable set relations generalizing the...

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. In recent publications it was started to develop a comprehensive theory for these vector optimization problems. Thereby also notions of proper efficiency were generalized to variable ordering structu...

Recently Kazama and Yokoi (arXiv:0801.1561 [hep-th]) have used a phase-space method to study the Virasoro algebra of type IIB superstring theory in the maximally supersymmetric R-R plane wave background in a semi-light-cone gauge. Two types of normal ordering have been considered, namely “phase space normal ordering” (PNO) and “massless normal ordering” (MNO). The second one, which is the right...

In the paper [11], we introduced a partial ordering, called the reflection ordering, on the elements of G(m, p, n) and described such an ordering on the groups G(m, 1, n), m > 1. In the present paper, we describe the reflection ordering on the group G(m, m, n). As a by-product, we obtain a formula for the enumeration of a certain subset in the symmetric group Sn, which is of independent combina...

In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...

Abstract In vector optimization, it is of increasing interest to study problems where the image space (a real linear space) preordered by a not necessarily solid (and pointed) convex cone. It well-known that there are many examples ordering cone has an empty (topological/algebraic) interior, for instance in optimal control, approximation theory, duality theory. Our aim consider Pareto-type solu...

background and aims. the single-cone technique has gained some popularity in some european countries. the aim of the present study was to compare the push-out bond strength of gutta-percha to root canal dentin with the single-cone and cold lateral compaction canal obturation techniques. materials and methods. the root canals of 58 human mandibular premolars were prepared using modified crown-do...

PURPOSE To assess the effect of preoperative topographic cone location on 1-year outcomes of corneal collagen cross-linking (CXL). METHODS In this prospective, randomized, controlled clinical trial, 99 eyes (66 keratoconus, 33 ectasia) from 76 patients underwent CXL. Cone location was defined by the coordinates of preoperative maximum keratometry (maximum K) using the anterior sagittal curvat...