In this paper, we show that a matrix A in Mn(C) that has n coneigenvectors, where coneigenvaluesassociated with them are distinct, is condiagonalizable. And also show that if allconeigenvalues of conjugate-normal matrix A be real, then it is symmetric.  

The discrete-time periodic Lyapunov equation has several important applications in the analysis and design of linear periodic control systems. Specific applications considered in the paper are the solution of stateand output-feedback optimal periodic control problems, the stabilization by periodic state feedback and the square-root balancing of discrete-time periodic systems. Efficient numerica...

This paper generalizes results of Lempert and Szöke on the structure of the singular set of a solution of the homogeneous Monge-Ampère equation on a Stein manifold. Their a priori assumption that the singular set has maximum dimension is shown to be a consequence of regularity of the solution. In addition, their requirement that the square of the solution be smooth everywhere is replaced by a s...

The acidity constants (pKa) of thirty four (34) ;-substituted carboxylic acids in aqueous solution havebeen calculated using conductor-like polarizable continuum (C-PCM) solvation model. The gasphaseenergies at the Density Functional Theory (DFT-MPW1PW91) and solvation energies atHartree Fock (HF) are combined to estimate the pKa values which are very close to the experimentalvalues where, and ...

The GMRES method is one of the most popular iterative schemes for the solution of large linear systems of equations with a square nonsingular matrix. GMRES-type methods also have been applied to the solution of linear discrete ill-posed problems. Computational experience indicates that for the latter problems variants of the standard GMRES method, that require the solution to live in the range ...

We propose an extension of Walsh’s classical martingale measure stochastic integral that makes it possible to integrate a general class of Schwartz distributions, which contains the fundamental solution of the wave equation, even in dimensions greater than 3. This leads to a square-integrable random-field solution to the non-linear stochastic wave equation in any dimension, in the case of a dri...

We investigate cosmological dynamics of multiple tachyon fields with inverse square potentials. A phase-space analysis of the spatially flat FRW models shows that there exists a unique power-law cosmological scaling solution. We study the stability of the solution and find that the solution is a global attractor and a successful inflationary solution which is driven by multiple tachyon fields a...

Suppose that L is a latin square of order m and P ⊆ L is a partial latin square. If L is the only latin square of order m which contains P , and no proper subset of P has this property, then P is a critical set of L. The critical set spectrum problem is to determine, for a given m, the set of integers t for which there exists a latin square of order m with a critical set of size t. We outline a...