We consider the binomial random set model [n]p where each element in {1,…,n} is chosen independently with probability p:=p(n). show that for essentially all regimes of p and very general conditions a matrix A column vector b, count specific integer solutions to system linear equations Ax=b entries x follows (conveniently rescaled) normal limiting distribution. This applies among others number e...

In this paper, some characterizations of partial isometries, normal elements and strongly $EP$ are given by the construction elements. At same time, isometry characterized existence solutions equations in rings a set, also general form equations.

Recently, the gradient based iterative algorithms have been widely exploited for finding the (leastsquares) solutions of the different kinds of the (coupled) linear matrix equations. Nevertheless, so far, the convergence of the propounded gradient based algorithms has been studied under the circumstance that the mentioned (coupled) linear matrix equations have a unique (least-squares) solution....

A computationally efficient method is proposed for computing the simplest normal forms of vector fields. A simple, explicit recursive formula is obtained for general differential equations. The most important feature of the approach is to obtain the “simplest” formula which reduces the computation demand to minimum. At each order of the normal form computation, the formula generates a set of al...

for solving large sparse non-hermitian positive definite linear equations, bai et al. proposed the hermitian and skew-hermitian splitting methods (hss). they recently generalized this technique to the normal and skew-hermitian splitting methods (nss). in this paper, we present an accelerated normal and skew-hermitian splitting methods (anss) which involve two parameters for the nss iteration. w...