An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexit...

The matrix of evolutionary distances is a model-based statistic, derived from molecular sequences, summarizing the pairwise phylogenetic relationships between a collection of species. Phylogenetic tree reconstruction methods relying on this matrix are relatively fast and thus widely used in molecular systematics. However, because of their intrinsic reliance on summary statistics, distance-matri...

This study investigates optimal parameter setting in abrasive waterjet machining (AWJM) on aluminium alloy AA 6351, using taguchi based Grey Relational Analysis (GRA) is been reported. The water pressure, traverse speed and stand-off-distance were chosen as the process parameters in this study. An L 9 orthogonal matrix array is used for the experimental plan. The performance characteristics whi...

model order reduction is known as the problem of minimizing the -norm of the difference between the transfer function of the original system and the reduced one. in many papers, linear matrix inequality (lmi) approach is utilized to address the minimization problem. this paper deals with defining an extra matrix inequality constraint to guarantee that the minimum phase characteristic of the sys...

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented ...

We show that the traveling salesman problem with a symmetric relaxed Monge matrix as distance matrix is pyramidally solvable and can thus be solved by dynamic programming. Furthermore, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix becomes a relaxed Monge matrix.

We show that the traveling salesman problem with a symmetric relaxed Monge matrix as distance matrix is pyramidally solvable and can thus be solved by dynamic programming. Furthermore, we present a polynomial time algorithm that decides whether there exists a renumbering of the cities such that the resulting distance matrix becomes a relaxed Monge matrix.