Let $mathcal {N}_G$ denote the set of all proper‎ ‎normal subgroups of a group $G$ and $A$ be an element of $mathcal‎ ‎{N}_G$‎. ‎We use the notation $ncc(A)$ to denote the number of‎ ‎distinct $G$-conjugacy classes contained in $A$ and also $mathcal‎ ‎{K}_G$ for the set ${ncc(A) | Ain mathcal {N}_G}$‎. ‎Let $X$ be‎ ‎a non-empty set of positive integers‎. ‎A group $G$ is said to be‎ ‎$X$-d...

In this paper we study the almost universal convergence of weighted sums for sequence {x ,n } of negatively dependent (ND) uniformly bounded random variables, where a, k21 is an may of nonnegative real numbers such that 0(k ) for every ?> 0 and E|x | F | =0 , F = ?(X ,…, X ) for every n>l.

Let $R$ be a unitary ring with an endomorphism $σ$ and $F∪{0}$ be the free monoid generated by $U={u_1,…,u_t}$ with $0$ added, and $M$ be a factor of $F$ setting certain monomial in $U$ to $0$, enough so that, for some natural number $n$, $M^n=0$. In this paper, we give a sufficient condition for a ring $R$ such that the skew monoid ring $R*M$ is quasi-Armendariz (By Hirano a ring $R$ is called...

The use of sterile males to control a cage population of a laboratory strain of Anopheles quadrimaculatus was not successful, even though 80 to 90% of the females laid sterile egg clutches. At the ratio of sterile males to normal males being used, complete sterility should have been quickly achieved. Subsequent studies of the survival and sexual vigor of these sterile males indicated that only ...

We present two complementary NuSTAR x-ray searches for keV-scale dark matter decaying to mono-energetic photons in the Milky Way halo. In first, we utilize known intensity pattern of unfocused stray light across detector planes -- dominant source from diffuse sources separate astrophysical emission internal instrument backgrounds using ${\sim}$7-Ms/detector deep blank-sky exposures. second, an ...