in this paper some upper and lower bounds for the greatest eigenvalues of the pi and vertex pimatrices of a graph g are obtained. those graphs for which these bounds are best possible arecharacterized.

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

this paper describes an optimal design for multivariable pi controller with a high gain structure for an irregular system by genetic algorithm. pi controllers with a high gain structure leads to the asymptotic decomposition of the fast and slow modes in the closed loop system that have unique characteristics. the slow modes are asymptotically uncontrollable and unobservable; therefore, they hav...

We compared the two-dimensional patterns of nuclear proteins obtained from normal quiescent T lymphocytes with those from normal proliferating T lymphocytes and three lymphoblastoid cell lines (CEM, Namalwa, and Molt-4). We identified sets of nuclear proteins which are specific for normal quiescent or normal proliferating T lymphocytes, or shared by the three lymphoblastoid cell lines and absen...

In recent years, motivated by computational purposes, the singular value and spectral features of symmetrization Toeplitz matrices generated a Lebesgue integrable function have been studied. Indeed, under assumptions that $f$ belongs to $L^1([-\pi,\pi])$ it has real Fourier coefficients, distribution matrix-sequence $\{Y_nT_n[f]\}_n$ identified, where $n$ is matrix size, $Y_n$ anti-identity mat...