in this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the hermitian matrix expression $$‎ ‎f(x,y)=c_{4}-b_{4}y-(b_{4}y)^{*}-a_{4}xa_{4}^{*},$$ where $c_{4}$ is‎ ‎hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$x$ and $y$ satisfy‎ ‎the following consistent system of matrix equations $a_{3}y=c_{3}‎, ‎a_{1}x=c_{1},xb_{1}=d_{1},a_{2}xa_{2}^{*}=c_{2},x=x^{*}.$ as‎ ‎consequences‎, ‎we g...

Based on the Randic suggestion of the resolution of a structure into shape, size, and function an index representing structure-catabolic fate relationships of amino acids is constructed. The index obtained by multiplying three factors; (nb2 + nr), nc and M; representing shape, size and function respectively, where nb2 = number of double bonds, nr = number of rings, nc = number of carbon atoms, ...

introduction: cleaner productions in textile industry is achieved by reducing water and chemicals’ consumption, saving energy, reducing production of air pollution and solid wastes, reducing toxicity and noise pollution through many solutions. the purpose of the present research was to apply strengths, weaknesses, opportunities, threats (swot) and quality systems planning matrix (qspm) techniqu...

the star-mesh transformation allows the reduction of nodes in an electrical circuit. the gauss elimination method allows the reduction of unknowns in a system of linear equations . triangular decomposition can be used to find the inverse of a matrix. in this paper the coherence between these methods are discussed. it is shown that the gauss elimination method gives the same formula for star-mes...

A completely general method of analysis for three-dimensional raked piles under harmonic excitation is discussed. The piles have been represented by a three-dimensional frame structure and the soil has been represented by a boundary element discretization scheme. A computer program has been written which carries out this analysis and produces a group stiffness matrix that can be included as a f...

abstract. topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. graph theory is a delightful playground for the exploration of proof techniques in discrete mathematics and its results have applications in many areas of sciences. a graph is a ...

This paper considers the problem of estimating a high dimensional inverse covariance matrix that can be well approximated by “sparse” matrices. Taking advantage of the connection between multivariate linear regression and entries of the inverse covariance matrix, we propose an estimating procedure that can effectively exploit such “sparsity”. The proposed method can be computed using linear pro...

I argue that we should reject the sparse view that there are or could be only a small number of rather distinct senses. When one appreciates this then one can see that there is no need to choose between the standard criteria that have been proposed as ways of individuating the senses—representation, phenomenal character, proximal stimulus and sense organ—or any other criteria that one may deem ...