The technique of relaxed power series expansion provides an efficient way to solve equations of the form F =Φ(F ), where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence 0,Φ(0),Φ(Φ(0)), . With respect to other techniques, such as Newton’s method, two major advantages are its generality and the fact that it takes advantage of possible...

Orthogonal systems in L2(ℝ), once implemented spectral methods, enjoy a number of important advantages if their differentiation matrix is skew-symmetric and highly structured. Such systems, where the skew-symmetric, tridiagonal, irreducible, have been recently fully characterised. In this paper we go step further, imposing extra requirement fast computation: specifically, that first N coefficie...

Aim: the aim of this study was to compare cusp deflection, infraction and fracture in teeth filled with three temporary filling materials. Materials & method: Forty five extracted human premolar teeth were chosen. After root canal therapy and mesio-occluso-distal cavity preparation, samples were randomly divided into three groups , each contained 15 teeth and filled with three temporary filling...

A novel integrated optimization method is proposed to combine both generation and transmission line expansion problem considering bus voltage limit. Most of the existing researches on the combined generation and transmission expansion planning cannot consider bus voltages and reactive power flow limits because they are mostly based on the DC power flow model. In this paper the AC power flow mod...

We derive a new deterministic algorithm for the computation of a sparse Legendre expansion f of degree N with M N nonzero terms from only 2M function resp. derivative values f (1), j = 0, . . . , 2M − 1 of this expansion. For this purpose we apply a special annihilating filter method that allows us to separate the computation of the indices of the active Legendre basis polynomials and the evalu...

aim: the aim of this study was to compare cusp deflection, infraction and fracture in teeth filled with three temporary filling materials. materials & method: forty five extracted human premolar teeth were chosen. after root canal therapy and mesio-occluso-distal cavity preparation, samples were randomly divided into three groups , each contained 15 teeth and filled with three temporary filling...

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...