This is a tutorial on some aspects of toric varieties related to their potential use in geometric modeling. We discuss projective toric varieties and their ideals, as well as real toric varieties. In particular, we explain the relation between linear precision and a particular linear projection we call the algebraic moment map.

A study was completed of more than 170,000 records of pediatric venous blood levels and supporting demographic information collected in New York City during 1970-1976. The geometric mean (GM) blood lead level shows a consistent cyclical variation superimposed on an overall decreasing trend with time for all ages and ethnic groups studied. The GM blood lead levels for blacks are significantly gr...

We introduce a concept of Simplicity which in a sense corresponds to the reverse direction to the concept of Complexity. Many problems of Asymptotic Geometric Analysis rotate around this notion. We also describe the concept of Concentration and suggest a new direction of possible applications of the Concentration Phenomenon.

The present article applies the method of Geometric Analysis to the study H-type groups satisfying the J condition and finishes the series of works describing the Heisenberg group and the quaternion H-type group. The latter class of H-type groups satisfying the J condition is related to the octonions. The relations between the group structure and the boundary of the corresponding Siegel upper h...

Given a weighted graph G = (V,E) and a real number t ≥ 1, a t-spanner of G is a spanning subgraph G′ with the property that for every edge xy in G, there exists a path between x and y in G′ whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.

Article history: Received 13 October 2010 Received in revised form 18 March 2012 Accepted 19 March 2012 Available online xxxx