We present a study of the transportation polytopes appearing in product rule elementary multi-symmetric functions introduced by F. Vaccarino.

Ayn Rand was a Russian-born American philosopher, novelist, and playwright, whose interpretation of ethical egoism is one of the most important interpretations of this theory.  Rand is a proponent of intellectual egoism, and rationalism is a fundamental element in her ethical theory. This article attempts to review, analyze, and criticize her interpretation of ethical egoism.   Additionally, an...

In tolerancing analysis, geometrical or contact specifications can be represented by polytopes. Due to the degrees of invariance of surfaces and that of freedom of joints, these operand polytopes are originally unbounded in most of the cases (i.e. polyhedra). Homri et al. proposed the introduction of virtual boundaries (called cap half-spaces) over the unbounded displacements of each polyhedron...

In this section, we present the classic quick sort algorithm and compute the expected running time of the algorithm. We assume that the elements of the set are all distinct. Below is the randomized quick sort algorithm. Algorithm RandQuickSort(S) Choose a pivot element xi u.a.r from S = {x1, x2, · · · , xn} Split the set S into two subsets S1 = {xj |xj < xi} and S2 = {xj |xj > xi} by comparing ...

For general polytopes, it has turned out that with respect to many questions it su ces to consider only the simple polytopes, i.e., d-dimensional polytopes where every vertex is contained in only d facets. In this paper, we show that the situation is very di erent within the class of 0/1-polytopes, since every simple 0/1-polytope is the (cartesian) product of some 0/1-simplices (which proves a ...