Let $R$ be a 2-torsion free ring and $U$ be a square closed Lie ideal of $R$. Suppose that $alpha, beta$ are automorphisms of $R$. An additive mapping $delta: R longrightarrow R$ is said to be a Jordan left $(alpha,beta)$-derivation of $R$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin R$. In this paper it is established that if $R$ admits an additive mapping $G : Rlongrigh...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

Let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $R$.  In this paper we  study the relationship between an$R$-module $M_R$ and the  general polynomial module  $M[x]$ over theskew polynomial ring $R[x;alpha,delta]$. We introduce the notionsof skew-Armendariz modules and skew quasi-Armendariz modules whichare generalizations of $alpha$-Armendariz modules and extend thecla...

The main purpose of this article is to offer some characterizations of $delta$-double derivations on rings and algebras. To reach this goal, we prove the following theorem:Let $n > 1$ be an integer and let $mathcal{R}$ be an $n!$-torsion free ring with the identity element $1$. Suppose that there exist two additive mappings $d,delta:Rto R$ such that $$d(x^n) =Sigma^n_{j=1} x^{n-j}d(x)x^{j-1}+Si...

This paper is an attempt to prove the following result:Let $n>1$ be an integer and let $mathcal{R}$ be a $n!$-torsion-free ring with the identity element. Suppose that $d, delta, varepsilon$ are additive mappings satisfyingbegin{equation}d(x^n) = sum^{n}_{j=1}x^{n-j}d(x)x^{j-1}+sum^{n-1}_{j=1}sum^{j}_{i=1}x^{n-1-j}Big(delta(x)x^{j-i}varepsilon(x)+varepsilon(x)x^{j-i}delta(x)Big)x^{i-1}quadend{e...

Increasing anthropogenic pollution from urban centers and fossil fuel combustion can impact the carbon and nitrogen cycles in forests. To assess the impact of twentieth century anthropogenic pollution on forested system carbon and nitrogen cycles, variations in the carbon and nitrogen isotopic compositions of tree-rings were measured. Individual annual growth rings in trees from six sites acros...

AIMS Bifunctional apoptosis regulator (BAR) is an endoplasmic reticulum protein that interacts with both the extrinsic and intrinsic apoptosis pathways. We hypothesize that over-expression of BAR Delta RING prevents apoptosis and injury following ischaemia/reperfusion (I/R) and attenuates doxorubicin (DOX)-induced cardiotoxicity. METHODS AND RESULTS We generated a line of transgenic mice that...

The dimeric ring-shaped sliding clamp of E. coli DNA polymerase III (beta subunit, homolog of eukaryotic PCNA) is loaded onto DNA by the clamp loader gamma complex (homolog of eukaryotic Replication Factor C, RFC). The delta subunit of the gamma complex binds to the beta ring and opens it. The crystal structure of a beta:delta complex shows that delta, which is structurally related to the delta...

We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by Berrick-Cohen-Wong-Wu. We then prove an isomorphism theorem relating these two Delta-groups. This is the first of a pair of papers on this topic.