In this paper, we propose the least-squares method for computing the positive solution of a m × n fully fuzzy linear system (FFLS) of equations, where m > n, based on Kaffman’s arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of the non...

substrates' concentration profile was studied in a porous matrix containing immobilized amyloglucosidase for glucose production. this analysis was performed by using an analytical method called least square method, and the results were compared with numerical solution. effects of effective diffusivity, michael's constant, maximum reaction rate and initial substrate concentration were studied on...

We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solv...

We discuss the exponential stability in mean square of mild solution for neutral stochastic partial functional differential equations with impulses. By applying impulsive Gronwall-Bellman inequality, the stochastic analytic techniques, the fractional power of operator, and semigroup theory, we obtain some completely new sufficient conditions ensuring the exponential stability in mean square of ...

The *congruence class of a least square solution for the following matrix equations AX = B, AXA = D, AXB = D and (AX XB) = (E F) is presented. Also, we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). Crown Copyrigh...

We provide necessary and sufficient conditions for the generalized ⋆Sylvester matrix equation, AXB+CX ⋆ D = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A,B,C,D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the ex...

We provide necessary and sufficient conditions for the generalized ?Sylvester matrix equation, AXB +CX ? D = E, to have exactly one solution for any right-hand side E. These conditions are given for arbitrary coefficient matrices A,B,C,D (either square or rectangular) and generalize existing results for the same equation with square coefficients. We also review the known results regarding the e...