Abstract An n × n matrix D is a Euclidean distance matrix (EDM) if there exist p, . . . , pn in some Euclidean space such that dij = ||pi − pj ||2 for all i, j = 1, . . . , n. Let D be an EDM and let Eij be the n×n symmetric matrix with 1’s in the ijth and jith entries and 0’s elsewhere. We say that [lij , uij ] is the yielding interval of entry dij if it holds that D+ tE ij is an EDM if and on...

Location quotient (LQ) is a widely used model to evaluate the spatial aggregation of water consumption. The conventional view that all domains LQ values in different water-using departments are [0, +∞). larger is, higher degree consumption concentration is. With structure evaluation Northwest China as an illustration, this study shows following: (i) has distortion phenomenon. agricultural Xinji...

We give several sufficient conditions on an infinite integer matrix (dij) for the set R = { ∑ ij∈α, i>j dij : α ⊂ N, |α| < ∞ } to be a density intersective set, including the cases dnj = j n(1 + O(1/n1+ )) and 0 < dnj = o ( √

Let G be the chemical graph of a molecule. The matrix D = [dij ] is called the detour matrix of G, if dij is the length of longest path between atoms i and j. The sum of all entries above the main diagonal of D is called the detour index of G. In this paper, a new algorithm for computing the detour index of molecular graphs is presented. We apply our algorithm on copper and silver nanoclusters ...

This first algorithm is quite simple. (Though this was probably known earlier, its proof can be found in Prof. Indyk’s 1999 paper “Sublinear Time Algorithms for Metric Space Problems”.) Let Dij denote the distance between a pair of points i and j, over m total points. The entries of Dij must satisfy the triangle inequality; additionally the matrix is symmetric. Note that the matrix size (i.e., ...

Values dj: are a measure of 'distance' between individuals i and j. Conditions are given for points Pi to exist where the distances A (Pi, Pj) = dij. The method finds an approximate configuration Qi, in a few dimensions, such that A(Qi,Qj) ≈ dij. Principal components, canonical variates, and factor analysis appear as special cases. [The SCI indicates that this paper has been cited over 215 time...

An O(n log3 n) algorithm for the continuous p-center problem on a tree is presented. Following a sequence of previous algorithms, ours is the first one whose time bound in uniform in p and less than quadratic in n. We also present an O(n log2 n log log n) algorithm for a weighted discrete p-center problem. 1. Introduction. The p-center problems are defined on a weighted undirected graph G = (V,...

Impinging jets are characterized by an acoustic feedback resonance capable of generating intense tones. This investigation examines changes in single impinging jet (SIJ) dynamics when another is added alongside to form a dual (DIJ) arrangement interest vertical takeoff and landing applications. The emphasis on the hydrodynamic coupling region between jets, which affects aircraft surface loading...

The hypermetric cone HY Pn is the set of vectors (dij)1≤i<j≤n satisfying the inequalities