Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

We find restrictions on the mass and mixing angle of the dark matter sterile neutrinos using X-ray observations of Coma and Virgo galaxy clusters.

a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

Results: Four hundred and ninety-three consecutive patients presenting for minor skin excisions were randomly allocated to the two treatment groups: non-sterile clean boxed gloves (n = 250) or sterile gloves (n = 243). Four hundred and seventy-eight patients contributed data for analysis (241 non-sterile, 237 sterile gloves). The incidence of infection in the nonsterile gloves group (8.7%; 95% ...

‎Suppose $n$ is a fixed positive integer‎. ‎We introduce the relative n-th non-commuting graph $Gamma^{n} _{H,G}$‎, ‎associated to the non-abelian subgroup $H$ of group $G$‎. ‎The vertex set is $Gsetminus C^n_{H,G}$ in which $C^n_{H,G} = {xin G‎ : ‎[x,y^{n}]=1 mbox{~and~} [x^{n},y]=1mbox{~for~all~} yin H}$‎. ‎Moreover‎, ‎${x,y}$ is an edge if $x$ or $y$ belong to $H$ and $xy^{n}eq y^{n}x$ or $x...

PURPOSE To investigate the telescope use and driving patterns of bioptic drivers with age-related macular degeneration (AMD). METHODS A questionnaire addressing telescope use and driving patterns was administered by telephone interview to three groups of bioptic drivers: AMD (n = 31; median 76 years); non-AMD first licensed with a bioptic (n = 38; 53 years); and non-AMD first licensed without...