The set of all n-by-n complex matrices is denoted by Cn×n. Let A aij ∈ Cn×n. Denote the Hermitian adjoint of matrix A by A∗. Then the singular values of A are the eigenvalues of AA∗ . It is well known that matrix singular values play a very key role in theory and practice. The location of singular values is very important in numerical analysis and many other applied fields. For more review abou...

We present efficiently verifiable sufficient conditions for the validity of specific NPhard semi-infinite systems of linear matrix inequalities (LMIs) arising from LMIs with uncertain data and demonstrate that these conditions are “tight” up to an absolute constant factor. In particular, we prove that given an n × n interval matrix Uρ = {A | |Aij − Aij | ≤ ρCij}, one can build a computable lowe...

Let A = (aij) be an n × n symmetric matrix with all positive entries and just one positive eigenvalue. Bapat proved then that the Hadamard inverse of A, given by A = ( 1 aij ) is positive semidefinite. We show that if moreover A is invertible then A is positive definite. We use this result to obtain a simple proof that with the same hypotheses on A, except that all the diagonal entries of A are...

We develop the convergence analysis for a numerical scheme proposed for approximating the solution of the elliptic problem L u = − ∂ ∂xi aij(x/ ) ∂ ∂xj u = f in Ω, u = 0 on ∂Ω, where the matrix a(y) = (aij(y)) is symmetric positive definite and periodic with period Y . The major goal is to develop a numerical scheme capturing the solution oscillations in the scale on a mesh size h > (or h >> )....

objective(s) in the present study, the differences in the relaxant effects of aqueous, ethyl acetate and n-butanol fractions of rosa damascena on tracheal smooth muscle of guinea pigs were examined. materials and methods the relaxant effects of three cumulative concentrations of each fraction (0.1, 0.2 and 0.4 g%) in comparison with saline and three cumulative concentrations of theophylline (0....

Let A = (aij)k×n be a matrix with entries in the Galois field GF (2), and let x = (x1, x2, . . . , xn) be a vector of variables assuming values in GF (2). The gate complexity of A, denoted by C(A), is the minimum number of XOR gates necessary to compute the matrix-vector product Ax. In this paper it is shown that C(Hk) = 2k+1 − 2k − 2, where Hk is the parity-check matrix of the [2k − 1, 2k − k ...

abstract             this study was conducted to investigate the effects of different levels of yeast and molasses on chemical composition and nutritional value of artiplex lentiformis silage. the levels of yeast include: zero (control), 2.5 and 5 g/kg dry matter and levels of molasses include: zero (control), 10 and 15 percent that were added to atriplex and then ensiled. the experiment arrang...

We consider hermitian dissipative mappings δ which are densely defined in unital C∗-algebras A. The identity element in A is also in the domain of δ. Completely dissipative maps δ are defined by the requirement that the induced maps, (aij) → (δ(aij)), are dissipative on the n by n complex matrices over A for all n. We establish the existence of different types of maximal extensions of completel...

A matrix A = (aij) ∈ Rn×n is said to be symmetric and antipersymmetric matrix if aij = aji = −an−j+1,n−i+1 for all 1 ≤ i, j ≤ n. Peng gave the bisymmetric solutions of the matrix equation A1X1B1+A2X2B2+. . .+AlXlBl = C, where [X1, X2, . . . , Xl] is a real matrices group. Based on this work, an adjusted iterative method is proposed to find the symmetric and antipersymmetric solutions of the abo...