Abstract. In this paper, we construct a binary linear code connected with the Kloosterman sum for GL(2, q). Here q is a power of two. Then we obtain a recursive formula generating the power moments 2-dimensional Kloosterman sum, equivalently that generating the even power moments of Kloosterman sum in terms of the frequencies of weights in the code. This is done via Pless power moment identity ...

let $g$ be a molecular graph with vertex set $v(g)$, $d_g(u, v)$ the topological distance between vertices $u$ and $v$ in $g$. the hosoya polynomial $h(g, x)$ of $g$ is a polynomial $sumlimits_{{u, v}subseteq v(g)}x^{d_g(u, v)}$ in variable $x$. in this paper, we obtain an explicit analytical expression for the expected value of the hosoya polynomial of a random benzenoid chain with $n$ hexagon...

For a wide class of integer-valued random walks, we obtain exact expressions for the distribution first excess over level and corresponding renewal function as well trajectory supremum if it is finite. We discuss possibilities obtaining explicit pre-stationary stationary distributions walk with switchings at strip boundaries. The research based on factorization representations double moment gen...

We study a process of generating random positive integer weight sequences $$\{ W_n \}$$ where the gaps between weights X_n = - W_{n-1} are i.i.d. integer-valued variables. The main result paper is that if gap distribution has moment function with large enough radius convergence, then sequence almost surely asymptotically m-complete for every $$m\ge 2$$ , i.e. multiple greatest common divisor (g...

A new lifetime distribution with two parameters, known as the sine half-logistic inverse Rayleigh distribution, is proposed and studied an extension of model. The model a extension. In application section, we show that more flexible than distributions. statistical properties are calculated, including quantile function, moments, moment generating incomplete moment, Lorenz Bonferroni curves. Entr...

In this paper, we propose a two-component mixture of Akash model (TC-MAM). The behavior TC-MAM distribution has been presented graphically. Moment-based measures, including skewness, index dispersion, kurtosis, and coefficient variation, have determined hazard rate functions are probability generating function, Mills ratio, characteristic cumulants, mean time to failure, factorial moment functi...