We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show that this condition is also sufficient when the module is a ring with some additional properties. To prove this result we show an effective Weierstrass Division Theorem and an effective solution to the Ideal Membership P...

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

In this paper, we introduce a new class of bivariate distributions by compounding the bivariate generalized exponential and power-series distributions. This new class contains some new sub-models such as the bivariate generalized exponential distribution, the bivariate generalized exponential-poisson, -logarithmic, -binomial and -negative binomial distributions. We derive different properties o...

We develop power series approximations for a discrete-time queueing system with two parallel queues and one processor. If both queues are non-empty, a customer of queue 1 is served with probability β and a customer of queue 2 is served with probability 1 − β. If one of the queues is empty, a customer of the other queue is served with probability 1. We first describe the generating functionU(z1,...

suppose $gamma$ is a graph with $v(gamma) = { 1,2, cdots, p}$and $ mathcal{f} = {gamma_1,cdots, gamma_p} $ is a family ofgraphs such that $n_j = |v(gamma_j)|$, $1 leq j leq p$. define$lambda = gamma[gamma_1,cdots, gamma_p]$ to be a graph withvertex set $ v(lambda)=bigcup_{j=1}^pv(gamma_j)$ and edge set$e(lambda)=big(bigcup_{j=1}^pe(gamma_j)big)cupbig(bigcup_{ijine(gamma)}{uv;uin v(gamma_i),vin ...

In [HY] Hara and Yoshida defined the notion of generalized test ideals τ(a) ⊆ R for ideals a of regular local rings R and non-negative parameters c ∈ R. Since then several papers studied the dependence of these ideals on the real parameter c. Notably, in [BMS1] the authors studied the jumping coefficients originating of these generalized test ideals: these are the non-negative c ∈ R for which τ...

A new family of recursive power-series distributions involving the generalized hypergeometric function is proposed. The probability generating and moment generating functions are given; and extensions of the Poisson, geometric, negative binomial, log-series, and generalized Waring distributions are presented as examples.