Several new results on the multicritical behavior of rectangular matrix models are presented. We calculate the free energy in the saddle point approximation, and show that at the triple-scaling point, the result is the same as that derived from the recursion formulae. In the triple-scaling limit, we obtain the string equation and a flow equation for arbitrary multicritical points. Parametric so...

Ahstruct-A “coordinate recurrence” method for solving sparse systems of linear equations over finite fields is described. The algorithms discussed all require O( n,( w + nl) logkn,) field operations, where nI is the maximum dimension of the coefficient matrix, w is approximately the number of field operations required to apply the matrix to a test vector, and the value of k depends on the algor...

The classes of P-, P 0-, R 0-, semimonotone, strictly semimonotone, column suucient, and nondegenerate matrices play important roles in studying solution properties of equations and complementarity problems and conver-gence/complexity analysis of methods for solving these problems. It is known that the problem of deciding whether a square matrix with integer/rational entries is a P-(or nondegen...

Some connections between linear minimum mean square error estimators, maximum output SNR filters and the least square solutions are presented. The notes have been prepared to be distributed with EE 503 (METU, Electrical Engin.) lecture notes. 1 Linear Minimum Mean Square Error Estimators The following signal model is assumed: r = Hs + v (1) Here r is a N × 1 column vector denoting the observati...

Fuzzy liner systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of inconsistent fuzzy matrix equation. Also some numerical examples are considered.  

in this paper operational matrix of bernstein polynomials (bps) is used to solve bratu equation. this nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. by using operational matrix of fractional integration...