We study the problem of computing the diameter of a  set of $n$ points in $d$-dimensional Euclidean space for a fixed dimension $d$, and propose a new $(1+varepsilon)$-approximation algorithm with $O(n+ 1/varepsilon^{d-1})$ time and $O(n)$ space, where $0 < varepsilonleqslant 1$. We also show that the proposed algorithm can be modified to a $(1+O(varepsilon))$-approximation algorithm with $O(n+...

Let Γ denote a D-bounded distance-regular graph, where D ≥ 3 is the diameter of Γ. For 0 ≤ s ≤ D − 3 and a weak-geodetically closed subgraph ∆ of Γ with diameter s, define a graph G(∆) whose vertex set is the collection of all weak-geodetically closed subgraphs of diameter s+2 containing ∆, and vertex Ω is adjacent to vertex Ω′ in G if and only if Ω∩Ω′ as a subgraph of Γ has diameter s+1. We sh...

Congenital heart disease with increased blood flow commonly leads to the development of increased pulmonary vascular reactivity and pulmonary arterial hypertension by mechanisms that remain unclear. We hypothesized a shear stress paradigm of hemodynamic reactivity and network remodeling via the persistence and/or exacerbation of a fetal diameter bifurcation phenotype [parent diameter d(0) and d...

The aim of our study is to analyze the impact of insertion holes in the middle of obstacles on the flow around a surface-mounted cube, In order to do this; we studied four configurations of obstacles in a channel with a Reynods number based on obstacle height ReH = 40000. The hexahedral structured meshes were used to solve the fluid dynamics equations .The finite volume method are employed to s...

Fault tolerance and transmission delay of networks are important concepts in network design. The notions are strongly related to connectivity and diameter of a graph, and have been studied by many authors. Wide diameter of a graph combines studying connectivity with the diameter of a graph. Diameter with width k of a graph G is defined as the minimum integer d for which there exist at least k i...

In 1933 Karol Borsuk asked whether every compact subset of R can be decomposed into d + 1 subsets of strictly smaller diameter. The 0/1Borsuk conjecture asks a similar question using subsets of the vertices of a ddimensional cube. Although counterexamples to both conjectures are known, we show in this article that the 0/1-Borsuk conjecture is true when d is much larger than the diameter of the ...

The aim of the present study was to evaluate the effect of a hydro-alcoholic extract of Vitex agnus-castus (VAC) fruit on blood urea nitrogen (BUN), creatinine (Cr) and, kidney histology of a female mouse model of D-galactose induced aging. In this experimental study, 72 NMRI mice were divided into 6 groups: control, VAC, D-galactose, D-galactose+VAC, aging, and aging+VAC. D-galactose was injec...

The diameter of a tree is the largest number of edges on any path between two vertices in it. Given a weighted, connected, undirected graph G and a bound D ≥ 2, the bounded-diameter minimum spanning tree problem seeks a spanning tree on G of minimum weight whose diameter does not exceed D. An evolutionary algorithm for this NP-hard problem encodes candidate trees as permutations of their vertic...

The influence of embryos on growth of the uterus was determined by comparing uterine length, weight and diameter between gravid and nongravid horns within unilaterally pregnant gilts. Eighty-two prepubertal gilts were ovariectomized unilaterally at 5 mo of age, and the ipsilateral uterine horn was ligated near the junction of the uterine horns. Gilts were mated and were assigned randomly for ex...