The colorful Carathéodory theorem asserts that if X1, X2, . . . , Xd+1 are sets in R, each containing the origin 0 in its convex hull, then exists a set S ⊆ X1 ∪ · · · ∪ Xd+1 with |S ∩ Xi| = 1 for all i = 1, 2, . . . , d + 1 and 0 ∈ conv(S) (we call conv(S) a colorful covering simplex). Deza, Huang, Stephen and Terlaky proved that if the Xi are in general position with respect to 0 (consequentl...

the manifest of value of colors in nazik al-malaika s poemsali piranishal *khadije hashemi**from the early times, colors have played an important role in developing poeticimages, and colorful images are the realistic and sensory aspects among poets. poetshave used colorful words to explore and explain the relationship between poeticimages and sometimes they have used colorful words to express t...

ports are the most important economic, political and military bottlenecks. this puts shoreline structures (port) in the class of important structures and they have a crucial role in the countries’ life. pile and deck wharf and their access bridges and offshore deck (jetties), are one of the parts which are supplier of coupling between the land and the waterfront. correct and exact estimation of...

Pathfinding by nerve growth cones depends on attractive and repulsive turning in response to a variety of guidance cues. Here we present direct evidence to demonstrate an essential and instructive role for microtubules (MTs) in growth cone steering. First, both growth cone attraction and repulsion induced by diffusible cues in culture can be completely blocked by low concentrations of drugs tha...

There are several topological results ensuring in any properly colored graph the existence of a colorful complete bipartite subgraph, whose order is bounded from below by some topological invariants of some topological spaces associated to the graph. Meunier [Electron. J. Combin., 2014] presented the first colorful type result for uniform hypergraphs. In this paper, we give some new generalizat...

We prove that for any finite point set P in the plane, a triangle T , and a positive integer k, there exists a coloring of P with k colors such that any homothetic copy of T containing at least 144k8 points of P contains at least one of each color. This is the first polynomial bound for range spaces induced by homothetic polygons. The only previously known bound for this problem applies to the ...

Over the last few years, the problem of voltage stability has received a lot of attraction from the power system community. This type of stability is now a major concern for utilities in both planning and operating conditions. Both static and dynamic aspects of the problem have been discussed and investigated by the researchers. The present paper concentrates on a Voltage Stability Analysis fun...