Let K be a field of characteristic 0, t a transcendental over K, and Γ be the absolute Galois group of K(t). Then two non-constant polynomials f, g ∈ K[X] are said to be Kronecker conjugate if an element of Γ fixes a root of f(X) − t if and only if it fixes a root of g(X) − t. If K is a number field, and f, g ∈ OK [X] where OK is the ring of integers of K, then f and g are Kronecker conjugate i...

where 1 2 1 2 , , , r r θ θ are any real numbers, and n is any positive integer. We can obtain the infinite series forms of these double integrals using Taylor series expansions and integration term by term theorem; these are the major results of this paper (i.e., Theorems 1-3). Adams et al. [1], Nyblom [2], and Oster [3] provided some techniques to solve the integral problems. Yu [4-29], Yu an...

In the present paper, The homotopy perturbation method (HPM) is applied to obtain approximate analytical solutions of the fractional non-linear Schrodinger equations. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Finally, we have illustrated the ability of the method for solving fractional non linear equation by some examples.

We show that a set of uniformly width-bounded infinite seriesparallel pomsets is ω-series-rational iff it is axiomatizable in monadic second order logic iff it is ω-recognizable. This extends recent work by Lodaya and Weil on sets of finite series-parallel pomsets in two aspects: It relates their notion of series-rationality to logical concepts, and it generalizes the equivalence of recognizabi...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...