Abstract We give the equations of n -th symmetric product $$X^n/S_n$$ X n / S a flat affine scheme $$X=\mathrm {Spec}\,A$$ = Spec A</...

using the group inverse, an explicit solution to a symmetric singular system is described. The general explicit solution is derived when the symmetric singular system satisfies the regularity condition. Certain special properties of these singular systems are presented. Finally, a symmetric balanced realization is obtained from an equivalent standard control system. @ 2002 Elsevier Science Ltd....

In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X−A1XA1− . . .−A∗mXAm = Q and X+A1XA1+ . . .+ A∗mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

Non-Hermitian optics utilizes judicious engineering of the spatial and spectral distribution gain loss in order to tailor behavior photonic systems ways that could not be achieved by modulating only real part refractive index. In this respect, a question has never been addressed is whether uniform or can also lead nontrivial non-Hermitian effects linear systems, beyond just signal amplification...

in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

In this paper a linear Fuzzy Fredholm Integral Equation(FFIE) with arbitrary Fuzzy Function input and symmetric triangular (Fuzzy Interval) output is considered. For each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (FFIE).