A generalization of the random geometric graph (RGG) model is proposed by considering a set of points uniformly and independently distributed on a rectangle of unit area instead of on a unit square [0,1](2). The topological properties of the random rectangular graphs (RRGs) generated by this model are then studied as a function of the rectangle sides lengths a and b=1/a, and the radius r used t...

Abstract We establish central limit theorems for natural volumes of random inscribed polytopes in projective Riemannian or Finsler geometries. In addition, normal approximation dual and the mean width polyhedral sets are obtained. deduce these results by proving a general theorem weighted volume convex hull points chosen from boundary smooth body according to positive continuous density Euclide...

We provide a polynomial-time algorithm to partition an orthogonal polygon of n vertices into isothetic rectangles so that the shortest rectangle side is maximized over all rectangles. Thus no rectangle is “thin”; all rectangles are “fat.”

We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [16] p.225 that the for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous real map from X attains minimum. • Every continuous real map from X attains maximum. Finally, for a co...

Lin and Chang gave a generating function of convex polyominoes with an m+1 by n + 1 minimal bounding rectangle. Gessel showed that their result implies that the number of such polyominoes is m+ n+mn m+ n ( 2m+ 2n 2m ) − 2mn m+ n ( m+ n m )2 . We show that this result can be derived from some binomial coefficients identities related to the generating function of Jacobi polynomials. Some (binomia...