Let P be a set of n points in the plane. The geometric minimum-diameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a monoor a dipolar MDST, i.e. a MDST with one or two nodes of degree greater 1, respectively. The more difficult dipolar case can so far only be solved in slightly subcubic time. This pap...

We study the empirical process supf∈F |N−1 ∑N i=1 f (Xi) − Ef2|, where F is a class of mean-zero functions on a probability space (Ω, μ) and (Xi)i=1 are selected independently according to μ. We present a sharp bound on this supremum that depends on the ψ1 diameter of the class F (rather than on the ψ2 one) and on the complexity parameter γ2(F, ψ2). In addition, we present optimal bounds on the...

The second geometric-arithmetic index GA2(G) of a graph G was introduced recently by Fath-Tabar et al. [2] and is defined to be ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] , where e = uv is one edge in G, and nu(e,G) denotes the number of vertices in G lying closer to u than to v. In this paper, we characterize the tree with the minimum GA2 index among the set of trees with given order and...

Let S be a set of n points in IRd and let t > 1 be a real number. A t-spanner for S is a directed graph having the points of S as its vertices, such that for any pair p and q of points there is a path from p to q of length at most t times the Euclidean distance between p and q. Such a path is called a t-spanner path. The spanner diameter of such a spanner is de ned as the smallest integer D suc...

In this paper we consider bi-criteria geometric optimization problems, in particular, the minimum diameter minimum cost spanning tree problem and the minimum radius minimum cost spanning tree problem for a set of points in the plane. The former problem is to construct a minimum diameter spanning tree among all possible minimum cost spanning trees, while the latter is to construct a minimum radi...

Geometric imperfections such as radial imperfection, diamond shape, and local dimples could affect the buckling mode and load carrying capacity of axially compressed steel tubular columns. This paper experimentally investigates the effect of radial imperfection on the load carrying capacity of tubular columns. Test samples include 100 specimens with different values for diameter, length, thickn...

To establish comprehensive criteria for detecting restenosis and remodeling, inter- and intraobserver reproducibility of quantitative arteriography in the analysis of 20 lesions immediately after and 6 months after percutaneous transluminal coronary angioplasty (PTCA) were assessed. Geometric single-plane (minimum, maximum, mean diameter and percent diameter stenosis), biplane (absolute and rel...

this paper presents a three-dimensional numerical investigation carried out in turbulent forced convection in a tube with helical ribs. enhancement of heat transfer using helically corrugated tubes has beenstudied experimentally by many researchers but there exist a few published numerical analyses results. the paper also introduces the results of heat transfer and friction factor data for inco...

We augment a tree T with a shortcut pq to minimize the largest distance between any two points along the resulting augmented tree T + pq. We study this problem in a continuous and geometric setting where T is a geometric tree in the Euclidean plane, where a shortcut is a line segment connecting any two points along the edges of T , and we consider all points on T + pq (i.e., vertices and points...