the linear system of equations ax = b where a = [aij ] in cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. in this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as drazin inverse andpseudo-inverse are investigated.

In this paper we study the dynamic bifurcation of the SwiftHohenberg equation on a periodic cell Ω = [−L,L]. It is shown that the equations bifurcates from the trivial solution to an attractor Aλ when the control parameter λ crosses the critical value. In the odd periodic case, Aλ is homeomorphic to S 1 and consists of eight singular points and their connecting orbits. In the periodic case, Aλ ...

In this paper, we establish a model reduction technique for periodic discrete-time descriptor systems exploiting the generalized inverses of the periodic singular matrix pairs associated with the systems. We compute the generalized inverses of periodic singular matrix pairs to implement a structure preserving iterative method for the solution of the periodic projected Lyapunov equations that ar...

The main result is a computation of the Nahm transform of a SU(2)-instanton over R× T , called spatially-periodic instanton. It is a singular monopole over T , a solution to the Bogomolny equation, whose rank is computed and behavior at the singular points is described.

In this paper, optimal control for stochastic linear singular periodic neuro Takagi–Sugeno (T–S) fuzzy system with singular cost is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation (MRDE) is computed by solving differential algebraic equation (DAE) using a novel and nontraditional ACP approach. ACP solution is equiv...

and Applied Analysis 3

We calculate the effective conductivity of a two-phase composite with a periodic array of inhomogeneities. The shape of the inhomogeneities is assumed to be a periodic E-inclusion. The effective conductivity is expressed in terms of the volume fraction of the inhomogeneities and a matrix, which characterizes the shape of the periodic E-inclusion. This solution is rigorous, closed-form, and appl...

The paper deals with the singular differential equation x 00 + g(x) = p(t), g having a weak singularity at 0 and 2π-periodic function p. For any positive integers m n, coexistence of 2mπ-periodic bouncing solutions n impacts classical periodic solution is proven.