The minimization of annual operating costs in radial distribution networks with the optimal selection and siting fixed-step capacitor banks is addressed this research by means a two-stage optimization approach. first stage proposes an approximated mixed-integer quadratic model to select nodes where must be installed. In second stage, recursive power flow method employed make exhaustive evaluati...

Sinc-Galerkin method based upon double exponential transformation for solving Troesch's problem was given in this study. Properties of the Sinc-Galerkin approach were utilized to reduce the solution of nonlinear two-point boundary value problem to same nonlinear algebraic equations, also, the matrix form of the nonlinear algebraic equations was obtained.The error bound of the method was found. ...

We present algebraic laws for a language similar to a subset of sequential Java that includes inheritance, recursive classes, dynamic binding, access control, type tests and casts, assignment, but no sharing. These laws are proved sound with respect to a weakest precondition semantics. We also show that they are complete in the sense that they are sufficient to reduce an arbitrary program to a ...

An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these notions as a very simple algebraic system, called a configuration machine. If an abstract machine is defined as a configuration machine consisting of primitive...

In this paper, a new type of bivariate basis on a triangle is presented, which is constructed by extending the univariate NTP basis proposed by Delgado and Peña. Some algebraic properties and its recursive formulae are given. Then a new type of surfaces that is called triangular DP surface is defined, and its recursive evaluation algorithm is obtained. Also, in the case of low degree, its subdi...

We describe a parameterized decision procedure that extends the decision procedure for functional recursive algebraic data types (trees) with the ability to specify and reason about abstractions of data structures. The abstract values are specified using recursive abstraction functions that map trees into other data types that have decidable theories. Our result yields a decidable logic which c...

Let L be a recursive algebraic extension of Q. Assume that, given α ∈ L, we can compute the roots in L of its minimal polynomial over Q and we can determine which roots are Aut(L)-conjugate to α. We prove there exists a pair of polynomials that characterizes the Aut(L)-conjugates of α, and that these polynomials can be effectively computed. Assume furthermore that L can be embedded in R, or in ...

In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine factorization techniques of both implicit and explicit type, recursive combinatorial algorithms, multilevel mechanisms and overlapping strategies to maximize...

We give a uniform algebraic framework for computing hybrid spectral transforms in an eecient manner. Based on properties of the Kronecker product, we derive a set of recursive equations, which leads naturally to an algorithm for computing such transforms eeciently. As a result, many applications of transforms like the Walsh transform and the Reed-Muller transform, which were previously impossib...

We consider the problem of establishing a relationship between two interpretations of base type terms of a λc-calculus extended with algebraic operations. We show that the given relationship holds if it satisfies a set of natural conditions. We apply this result to 1) comparing two monadic semantics related by a strong monad morphism, and 2) comparing two monadic semantics of fresh name creatio...