Cosine theorems on simplexes in $E_n$

Counting Simplexes in R

A finite set of vectors S ⊆ R is called a simplex iff S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in some H ⊆ R , which we denote by simp(H). This investigation is particularly interesting for H spanning R and containing no collinear vectors. Our mai...

Counting Simplexes in R3

A nite set of vectors S R n is called a simplex ii S is linearly dependent but all its proper subsets are independent. This concept arises in particular from stoichiometry. We are interested in this paper in the number of simplexes contained in

Delaunay simplexes in physics

Delaunay simplexes are very helpful instrument for analysis of computer models of atomic, molecular and granular systems. This paper illustrates their application to the current physical problems. The first one is the structure of non-crystalline packing of spheres. Recently it got the advance thanks to application of the Delaunay simplexes with quantitative measures of simplex shape. The secon...

Perturbation Theorems for Convoluted C-semigroups and Cosine Functions

Sparsity on Statistical Simplexes and Diversity in Social Ranking

We study sparsity on a statistical simplex consisting of all categorical distributions. This is different from the case in < because such a simplex is a Riemannian manifold, a curved space. A learner with sparse constraints would be likely to fall into its low-dimensional boundaries. We present a novel analysis on the statistical simplex as a manifold with boundary. We investigate the learning ...