We obtain improved upper bounds and new lower bounds on the chromatic number as a linear function of the clique number, for the intersection graphs (and their complements) of finite families of translates and homothets of a convex body in R.

the minimal prime decomposition for semiprime ideals is defined and studied on z-ideals of c(x). the necessary and sufficient condition for existence of the minimal prime decomposition of a z-ideal / is given, when / satisfies one of the following conditions: (i) / is an intersection of maximal ideals. (ii) i is an intersection of o , s, when x is basically disconnected. (iii) i=o , when x x ha...

a new model is proposed for two-dimensional simulation of the concrete fracture in compression. the model generated by using the voronoi diagram method and with considering random shape and distribution of full graded aggregates at the mesoscopic level. the aggregates modeled by combining irregular polygons, which then is placed into the concrete with no intersection between them. by this new m...

In this paper, we survey the state of the art in collision detection between general geometric models. The set of models include polygonal objects, spline or algebraic surfaces, CSG models, and deformable bodies. We present a number of techniques and systems available for contact determination. We also describe several N-body algorithms to reduce the number of pairwise intersection tests.

sink location is considered as a basic service in geographic routing in wireless sensor networks. obtaining the location of sink node by source node using an efficient method with low complexity has always been a challenging issue in research. in this paper, a sink location algorithm based on fano plane is proposed. the research challenge is how to ensure the intersection of two slq and sla rou...

Let a topological space. An intersection graph on a topological space , which denoted by ‎ , is an undirected graph which whose vertices are open subsets of and two vertices are adjacent if the intersection of them are nonempty. In this paper, the relation between topological properties of  and graph properties of ‎  are investigated. Also some classifications and representations for the graph ...