We obtained the region of convergence and the summation formula for some modified generalized hypergeometric series (1.2). We also investigated rationality of the sums of the power series (1.3). As a result the series (1.4) cannot be the same rational number in all Zp. 1991 Mathematics Subject Classification: 40A30,40D99

Let f(z) be a function, meromorphic in \z\ < 1 , whose power series around the origin has integral coefficients. In [5], Salem shows that if there exists a nonzero polynomial p(z) such that p(z)f(z) is in H, or else if there exists a complex number a, such that l/(f(z)—a) is bounded, when |JS| is close to 1, then f(z) is rational. In [2], Chamfy extends Salem's results by showing that if there ...

The interline power flow controller (IPFC) is a concept of the FACTS controller for series compensation which can inject a voltage with controllable magnitude and phase angle among multi lines. This paper proposes a novel IPFC-Based Damping Neuro-control scheme using PSO for damping oscil‌la‌t‌i‌o‌ns in a power system to improve power system stability. The add‌i‌tion of a supplementary controll...

In this paper, we describe an algorithm for the “uniformization” of a multivariate power series. Let K[[T]] be the field of “grid-based power series” over a sufficiently large non archimedean “monomial group” (or value group) T, such as T = {t1 α1 tnα: α1, , αn ∈ R} with the lexicographical ordering on α1, , αn. We interpret power series f ∈K[[x1, , xn]] as functions K[[T]]→K[[T]]. On certain “...

k = 0 sponding analytic functions. Since a goal of Computer Algebra is to work with formal objects and preserve such symbolic information, it should be possible to automate conversion between these forms in Computer Algebra Systems (CASs). However, only MACSYMA provides a rather limited procedure powerser• to calculate FPS from analytic expressions in certain special cases. We present an algori...

23] C.L. Monma and A.J. Morton. Computational experimental with a dual aane variant of Karmarkar's method for linear programming. extension of Karmarkar type algorithm to a class of convex separable programming problems with global linear rate of convergence. Techni-28] J. Renegar. A polynomial-time algorithm based on Newton's method for linear programming. Implementing an interior point method...

We consider Fréchet algebras which are subalgebras of the algebra F = C [[X]] of formal power series in one variable and of Fn = C [[X1, . . . , Xn]] of formal power series in n variables where n ∈ N. In each case, these algebras are taken with the topology of coordinatewise convergence. We begin with some basic definitions about Fréchet algebras, (F )-algebras, and other topological algebras, ...

If A is a set of nonnegative integers containing 0, then there is a unique nonempty set B of nonnegative integers such that every positive integer can be written in the form a + b, where a ∈ A and b ∈ B, in an even number of ways. We compute the natural density of B for several specific sets A, including the Prouhet-Thue-Morse sequence, {0} ∪ {2 : n ∈ N}, and random sets, and we also study the ...