A theorem of Mina evaluates the determinant of a matrix with entries D(f(x)). We note the important special case where the matrix entries are evaluated at x = 0 and give a simple proof of it, as well as some special additivity properties that hold in this case, but not in general. Some applications are given also. We then give a short proof of the general case. October 25, 1998 An old theorem o...

According to the fundamental theory of Markov chains, under a simple connectedness condition, iteration of a Markov transition matrix P , on any random initial state probability vector, will converge to a unique stationary distribution, whose probability vector corresponds to the left eigenvector associated with the dominant eigenvalue λ1 = 1. The corresponding convergence speed is governed by ...

We compute the nucleon matrix elements of QCD operators of twist 3 and 4 in the instanton vacuum. We consider the operators determining 1/Q 2 –power corrections to the Bjorken, Ellis–Jaffe and Gross–Llewellyn-Smith sum rules. The nucleon is described as a soliton of the effective chiral theory derived from instantons in the 1/N c –expansion. QCD operators involving the gluon field are systemati...

A noncommutative rational function which is regular at 0 can be expanded into a noncommutative formal power series. In fact, by the results of Kleene, Schützenberger, and Fliess, a noncommutative formal power series is rational (i.e., belongs to the smallest subring containing the noncommutative polynomials and closed under the inversion of invertible power series) if and only if the correspond...

In this paper we give a new formula for the n-th power of a 2× 2 matrix. More precisely, we prove the following: Let A = ( a b c d ) be an arbitrary 2×2 matrix, T = a+ d its trace, D = ad− bc its determinant and define yn : = bn/2c ∑ i=0 ( n− i i ) T n−2i(−D)i. Then, for n ≥ 1, A = ( yn − d yn−1 b yn−1 c yn−1 yn − a yn−1 ) . We use this formula together with an existing formula for the n-th pow...

Matrix converters have attracted an amount of interest over the past 25 years already, but they find time after time once again new utilisation. The presented paper deals with the recent concept of hybrid and power splitting traction drive systems. Special attention is paid to electric power splitting. In the investigated system a traction induction motor is employed. The matrix converter reali...

population growth, industrial pollution and high-energy consumption, cause the release of significant amounts of pollutants in the environment. power plants play an important role in the release of pollutants such as sulfur dioxide, nitrogen oxides, and carbon dioxide. if the necessary measures in the field of prevention and control do not be implemented, human health and other living creatures...

In this paper a new and efficient method for the reliable load flow solution of power network branches controlled by flexible AC transmission systems (FACTS) is presented. In the various methods proposed in past, the formulations was derived in which the Jacobian matrix is in UDU form, where U is a constant upper triangular matrix depending solely on system topology and D is a block diagonal ma...

Keywords: Google problem Power Method Stochastic matrices Global rate of convergence Gradient methods Strong convexity a b s t r a c t In this paper, we develop new methods for approximating dominant eigenvector of column-stochastic matrices. We analyze the Google matrix, and present an averaging scheme with linear rate of convergence in terms of 1-norm distance. For extending this convergence ...

The purpose of this paper is to study optimal transmit power control and capacity of a wireless multimedia network, where there is incomplete information about the link gain coefficients. Previously, Perron-Frobenius theory has been applied to the study of optimal power control under complete information about the link gain matrix and the interference matrix. This paper derives a characterizati...