The effects of using both directions and directional subdividing on adaptive gridembedding on the computational time and the number of grid points required for the same accuracy are considered. Directional subdividing is used from the beginning of the adaptation procedure without any restriction. To avoid the complication of unstructured grid, the semi-structured grid was used. It is used to so...

Given a spatial expression, or its computational semantic form, how is the expression’s spatial semantics to be allocated lexically, i.e., among entries in the lexicon? In interlingua-based machine translation (MT) research, lexical allocation is the problem of allocating or subdividing a linguistic expression’s full interlingual (IL) structure into the substructures that are lexical IL forms, ...

Given two simplicial complexes C1 and C2 embedded in Euclidean space IR, C1 subdivides C2 if (i) C1 and C2 have the same underlying space, and (ii) every simplex in C1 is contained in a simplex in C2. In this paper we present a method to compute a set of weighted points whose alpha complex subdivides a given simplicial complex. Following this, we also show a simple method to approximate a given...

Let S be a convex polytope. The set of all valid inequalities carries the structure of a convex polytope S, called the polar (polytope) of S. The facial structure of the polar provides information for each of its points: two points a and b are in the same face of S if and only if the faces of S obtained by intersecting it with the hyperplanes given respectively by a and b coincide. Suppose now ...