It is very important to accurately identify the critical nodes of power grid for its safe and stable operation. In this paper, a method identifying based on improved entropy weight (IEWM) proposed, IEWM corrects issues with information overlap between evaluation indices inconsistency (EW) value (EV). First, considering topology operating conditions, structural factor state are established. On b...

An asymptotic expansion for the Jacobi polynomials and for the functions of the second kind is extended to the case of a weight function that is the product of the Jacobi weight function with an arbitrary positive analytic function.

Fourier orthogonal series with respect to the weight function (1 − |x|2)μ−1/2 on the unit ball in Rd are studied. Compact formulae for the sum of the product of orthonormal polynomials in several variables and for the reproducing kernel are derived and used to study the summability of the Fourier orthogonal series. The main result states that the expansion of a continuous function in the Fourie...

We employ Monte Carlo computer simulations to investigate the simultaneous controlled radical polymerization in solution and from a flat surface. The bulk polymers grow at faster rates and possess narrower molecular weight distribution than polymers initiated from flat, impenetrable surfaces. The rate of surface-initiated polymerization depends on the density of initiator sites. Our results pro...

and Applied Analysis 3 2. Preliminaries Let w α,β x 1 − x α 1 x β be a weight function in the usual sense for α, β > −1. The set of Jacobi polynomials {P α,β k x } k 0 forms a complete L 2 w α,β −1, 1 -orthogonal system, and ∥ ∥ ∥P α,β k ∥ ∥ ∥ 2 w α,β h α,β k 2 β 1Γ k α 1 Γ ( k β 1 ) ( 2k α β 1 ) Γ k 1 Γ ( k α β 1 ) . 2.1 Here, L2 w α,β −1, 1 is a weighted space defined by L2 w α,β −1, 1 {v : v...