this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer...

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

Let // be the integral of f(x) over an A^-dimensional hypercube and Q(m>f be the approximation to //obtained by subdividing the hypercube into m equal subhypercubes and applying the same quadrature rule Q to each. In order to extrapolate efficiently for // on the basis of several different approximations Q ' /, it is necessary to know the form of the error functional Q\m'f If as an expansion in...

In the past few years, Bogoya, Böttcher, Grudsky, and Maximenko obtained for the eigenvalues of a Toeplitz matrix Tn(f), under suitable assumptions on the generating function f , the precise asymptotic expansion as the matrix size n goes to infinity. On the basis of several numerical experiments, it was conjectured by Serra-Capizzano that a completely analogous expansion also holds for the eige...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

in this paper, at first we have formulated the lowest order constrained variational method for the relativistic case of an interacting fermion system at finite temperature. then we have used this formalism to calculate some thermodynamic properties of liquid in the relativistic regime. the results show that the difference between total energies of relativistic and non-relativistic cases of liqu...