We investigate 3-adic valuations of generalized harmonic numbers H n . These valuations are completely determined by the 3-adic expansion of n. Moreover, we also give 3-adic valuations of generalized alternating harmonic numbers.

The nodal admittance matrix (NAM) expansion is used to generate the voltage generalized impedance converter (VGIC) and the current generalized impedance converter (CGIC) with both A and D of the transmission matrix (T ) being negative. Simulation results are included.

An asymptotic expansion for inverse moments of positive binomial and Poisson distributions is derived. The expansion coefficients of the asymptotic series are given by the positive central moments of the distribution. Compared to previous results, a single expansion formula covers all (also non-integer) inverse moments. In addition, the approach can be generalized to other positive distributions.

Given a lazy regular graph G, we prove that the expansion of G is at least Ω( √ t) times the expansion of G. This bound is tight and can be generalized to small set expansion. We show some applications of this result. 1998 ACM Subject Classification G.2.2 Graph Theory

This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certai...

The generalized Taylor expansion including a secret auxiliary parameter h which can control and adjust the convergence region of the series is the foundation of the homotopy analysis method proposed by Liao. The secret of h can’t be understood in the frame of the homotopy analysis method. This is a serious shortcoming of Liao’s method. We solve the problem. Through a detailed study of a simple ...

The exact traveling wave solutions of the nonlinear variable coefficients Burgers-Fisher equation and the generalized Gardner equation with forced terms can be found in this article using the generalized ( ′ G )-expansion method. As a result, hyperbolic, trigonometric and rational function solutions with parameters are obtained. When these parameters are taken special values, the solitary wave ...