The current situation of world’s environmental issues, indicates that not only the man-made environmental damages have not been diminished, but also has given rise to more acute issues such as water and soil pollution, biodiversity loss, ozone depletion, greenhouse phenomena, etc. One of the most prominent effects of urban development on environmental problems caused by solid waste generated in...

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

I. MAIN CONTENT In [1], the structural invariant subspaces V1 and V2, defined by (17) and (18) respectively, are used in (19), that is the analytic nonrecursive expression of the set of the admissible solutions of the discrete-time singular Hamiltonian system (10) over the time interval 0≤ k≤ kf − 1. In this note it will be shown that the dimension of the subspace V2 may be lower than n, where ...

Abstract A basic framework for exploiting sparsity via positive semidefinite matrix completion is presented for an optimization problem with linear and nonlinear matrix inequalities. The sparsity, characterized with a chordal graph structure, can be detected in the variable matrix or in a linear or nonlinear matrix-inequality constraint of the problem. We classify the sparsity in two types, the...

In the linear system Ax = b the points x are sometimes constrained to lie in a given subspace S of column space of A. Drazin inverse for any singular or nonsingular matrix, exist and is unique. In this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of Drazin inverse in solving such systems is investigated. Constrained linear system arise ...

The textit{QIF}  (Quadrant Interlocking Factorization) method of Evans and Hatzopoulos solves linear equation systems using textit{WZ}  factorization. The  WZ factorization can be faster than the textit{LU} factorization  because,  it performs the simultaneous evaluation of two columns or two rows. Here, we present a  method for computing the real and integer textit{WZ} and  textit{ZW} factoriz...