In this paper, we first present a new important property for Bouligand tangent cone (contingent cone) of a star-shaped set. We then establish optimality conditions for Pareto minima and proper ideal efficiencies in nonsmooth vector optimization problems by means of Bouligand tangent cone of image set, where the objective is generalized cone convex set-valued map, in general real normed spaces.

The first part of this paper is devoted to establish new rigidity results for proper holomorphic maps from the complex unit ball to higher rank bounded symmetric domains. The rigidity properties have been extensively studied in the past decades for proper holomorphic maps F : Ω1 → Ω2, between bounded symmetric domains Ω1,Ω2. The pioneer works are due to Poincaré [P] and later to Alexander [Al] ...

We provide a proof of Nagata’s compactification theorem: any separated map of finite type between quasi-compact and quasi-separated schemes (e.g., noetherian schemes) factors as an open immersion followed by a proper morphism. This is a detailed exposition of private notes of Deligne that translate Nagata’s method into modern terms, and includes some applications of general interest in the theo...

Popular statistical software packages do not have the proper procedures for determining the number of components in factor and principal components analyses. Parallel analysis and Velicer's minimum average partial (MAP) test are validated procedures, recommended widely by statisticians. However, many researchers continue to use alternative, simpler, but flawed procedures, such as the eigenvalue...

1. INTRODUCTION. Suppose that Alice wants to color a planar map using four colors in a proper way, that is, so that any two adjacent regions get different colors. Despite the fact that she knows for certain that it is eventually possible, she may fail in her first attempts. Indeed, there are usually many proper partial colorings not extend-able to proper colorings of the whole map. Thus, if she...

forest classification on the basis of satellite images is a promising technique both for primary map production and for map updating and forest monitoring. for accurate for-est classification into three classes, using mapping by canopy cover density “high spatial resolution satellite images have to be used in order to obtain the required spatial detail” [schneider, 1999]. at the same time, the ...

In this paper we consider the Jacobian conjecture for a map f of complex affine spaces of dimension n. It is well-known that if f is proper then the conjecture will hold. Using topological arguments, specifically Smith theory, we show that the conjecture holds if and only if f is proper onto its image.

A recently proposed swarm intelligence technique for Fuzzy Cognitive Map learning is described. The technique employs the Particle Swarm Optimization algorithm to minimize a proper objective function, whose global minimizers correspond to suboptimal weight matrices of the Fuzzy Cognitive Map. New instances of an industrial test problem are studied, justifying the usefulness of the technique as ...