Based on concepts of relative algebraic interior and relative topological interior of sets,some conditions assuring Ari+B(A+B)ri in a linear space and conditions assuring riA+Bri(A+B) in a linear topological space are given respectively,according to Tanaka and Kuroiwa' s conclusions. Therefore,Tanaka and Kuroiwa' s conclusions about interior are generalized to the situation of relative interior.
Some new properties of explicitly quasiconcave functions are presented. These newproperties are expressed in terms of the properties of arid relationships between the levelset, the upper level set, the relative interior, and the relative boundary of the upper levelset.
During the analysis,SWOT is used to get the real situation of Longkou port. With SWOT analysis method,this thesis lists the internal advantages and disadvantages,the external opportunities and competition to Longkou port,all of which are essential to establish feasible development strategy.
The produce mechanism of this kind of medi-organization is rectify the falsity in play chess of enterprise accountant information property rights. Its mostly function is make up the failure of market enterprise information display. Accordingly it has the action of implement and enlarge the social cooperate leavings.
The lightweight aggregate interlocks with the cement paste boundary,and the depth of the interfacial transition zone is about 20—30 μm. The ratio of silica to calcium and the micro hardness of lightweight aggregates are higher than that in cement matrix.
The relative interior of the base polyhedron and the core
In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty.
An interior point of a triangle is calledCP-point if its orthogonal projection on the line containing each side lies in the relative interior of that side.
We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions.
Our result depended on a constraint qualification involving the notion ofquasi relative interior.
Partially finite convex programming, Part I: Quasi relative interiors and duality theory
We show that the GIT-classes are the relative interiors of rational polyhedral convex cones, which form a fan in the G-ample cone.
They exploit the key facts that the transition probabilities of queueing networks are shift invariant on the relative interiors of faces and the cost functions of interest are linear in the state.
A systematic procedure for choosing different quadratic functions on the relative interiors of faces to serve as surrogates of the differential costs in an inequality relaxation of the average cost function leads to linear program bounds.
In this paper we discuss the properties of strongly decomposable operators and prove that strong decomposition of T implies strong decomposition of T~* if every set spectrum F of T~* equal to Fo.
In this papers the definition of Benson-proper efficient points is generalized. A characterization of the relative interior of a convex cone is given. Without the pointedness assumption, the equivalence between Hartley-proper efficient points and the generalized Bensonproper efficient points is proved by the characterization of relative interiors of convex cones. Several results of scalarization of efficient points and proper efficient points are derived.
Some new characterizations of explicitly convex and strictly convex functionsare presented. These new characterizations are expressed in terms of the properties of andrelationships between the graph I the eplgraph, the relative interior, the relative boundary Iand the extreme points of the epigraph.