The point cloud is the basis for 3D object surface reconstruction. An incomplete significantly reduces accuracy of downstream work such as reconstruction and recognition. Therefore, point-cloud repair indispensable work. However, original shape difficult to restore due uncertainty position new filling point. Considering advantages convex set in dealing with problems, we propose a method via tha...

The corner polyhedron is described by minimal valid inequalities from maximal lattice-free convex sets. For the Relaxed Corner Polyhedron (RCP) with two free integer variables and any number of non-negative continuous variables, it is known that such facet defining inequalities arise from maximal lattice-free splits, triangles and quadrilaterals. We improve on the tightest known upper bound for...

in this paper, we investigate the concept of topological stationary for locally compact semigroups. in [4], t. mitchell proved that a semigroup s is right stationary if and only if m(s) has a left invariant mean. in this case, the set of values ?(f) where ? runs over all left invariant means on m(s) coincides with the set of constants in the weak* closed convex hull of right translates of f. th...

In this paper, we introduce soft sets over 2 where 2 is the power set of the universe U , propose some operations on soft sets over 2 and investigate some types of soft sets over 2 such as keeping intersection and keeping union. We obtain lattice and topological structures of soft sets over 2 . We consider soft rough approximations and soft rough sets, and obtain structures of soft rough sets. ...

Let S ⊆ Zn satisfy the property that conv(S) ∩ Zn = S. Then a convex set K is called an S-free convex set if int(K) ∩ S = ∅. A maximal S-free convex set is an S-free convex set that is not properly contained in any S-free convex set. We show that maximal S-free convex sets are polyhedra. This result generalizes a result of Basu et al. [6] for the case where S is the set of integer points in a r...

in this paper we study the concept of latin-majorizati-on. geometrically this concept is different from other kinds of majorization in some aspects. since the set of all $x$s latin-majorized by a fixed $y$ is not convex, but, consists of :union: of finitely many convex sets. next, we hint to linear preservers of latin-majorization on $ mathbb{r}^{n}$ and ${m_{n,m}}$.

The aim of this paper is to give sufficient conditions for a quasiconvex setvalued mapping to be convex. In particular, we recover several known characterizations of convex real-valued functions, given in terms of quasiconvexity and Jensen-type convexity by K. Nikodem [1], F.A. Behringer [2], and X.M. Yang, K.L. Teo and X.Q. Yang [3].

The goal of this article is to present a survey of the recent theory of plurisubharmonic functions of quaternionic variables, and its applications to theory of valuations on convex sets and HKT-geometry (HyperKähler with Torsion). The exposition follows the articles [4], [5], [7] by the author and [8] by M. Verbitsky and the author.

Assume Xn is a random sample of n uniform, independent points from a triangle T . The longest convex chain, Y , of Xn is defined naturally (see the next paragraph). The length |Y | of Y is a random variable, denoted by Ln. In this paper we determine the order of magnitude of the expectation of Ln. We show further that Ln is highly concentrated around its mean, and that the longest convex chains...