In this paper, we consider a flexible skew-generalized normal distribution. This distribution is denoted by $FSGN(/lambda _1, /lambda _2 /theta)$. It contains the normal, skew-normal (Azzalini, 1985), skew generalized normal (Arellano-Valle et al., 2004) and skew flexible-normal (Gomez et al., 2011) distributions as special cases. Some important properties of this distribution are establi...

For a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-Armendariz ring, that is a generalization of both $pi$-Armendariz rings, and $(alpha,delta)$-compatible skew Armendariz rings. We first observe the basic properties of skew $pi$-Armendariz rings, and extend the class of skew $pi$-Armendariz rings through various ring extensions. We nex...

In this paper, we discuss a generalization of Balakrishnan skew-normal distribution with two parameters that contains the skew-normal, the Balakrishnan skew-normal and the two-parameter generalized skew-normal distributions as special cases. Furthermore, we establish some useful properties and two extensions of this distribution. 

for a finite field $mathbb{f}_q$, the bivariate skew polynomial ring $mathbb{f}_q[x,y;rho,theta]$ has been used to study codes cite{xh}. in this paper, we give some characterizations of the ring $r[x,y;rho,theta]$, where $r$ is a commutative ring. we investigate 2-d skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $r[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ a...

The Generalised Randić index R−α(T ) of a tree T is the sum over the edges uv of T of (d(u)d(v))−α where d(x) is the degree of the vertex x in T . For all α > 0, we find the minimal constant βc = βc(α) such that for all trees on at least 3 vertices R−α(T ) ≤ βc(n + 1) where n = |V (T )| is the number of vertices of T . For example, when α = 1, βc = 15 56 . This bound is sharp up to the additive...

The general Randić index Rα(G) is the sum of the weights (dG(u)dG(v)) over all edges uv of a (molecular) graph G, where α is a real number and dG(u) is the degree of the vertex u of G. In this paper, for any real number α ≤ −1, the minimum general Randić index Rα(T ) among all the conjugated trees (trees with a Kekulé structure) is determined and the corresponding extremal conjugated trees are ...