Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

The specificity of DNA-dependent RNA polymerase for target promotes is largely due to the replaceable sigma subunit that it carries. Multiple sigma proteins, each conferring a unique promoter preference on RNA polymerase, are likely to be present in all bacteria; however, their abundance and diversity have been best characterized in Bacillus subtilis, the bacterium in which multiple sigma facto...

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...

in the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{e}$$ isgiven where $sigma$ is an involution of the normed space $e$ and$k$ is a fixed positive integer. furthermore we investigate thehyers-ulam-rassias stability of the functional equation. thehyers-ulam stability on unbounded domains is also studied.applic...

let $gamma$ be a normal subgroup of the full automorphism group $aut(g)$ of a group $g$‎, ‎and assume that $inn(g)leq gamma$‎. ‎an endomorphism $sigma$ of $g$ is said to be {it $gamma$-central} if $sigma$ induces the the identity on the factor group $g/c_g(gamma)$‎. ‎clearly‎, ‎if $gamma=inn(g)$‎, ‎then a $gamma$-central endomorphism is a {it central} endomorphism‎. ‎in this article the conditi...

Gene expression in members of the family Bacillaceae becomes compartmentalized after the distinctive, asymmetrically located sporulation division. It involves complete compartmentalization of the activities of sporulation-specific sigma factors, sigma(F) in the prespore and then sigma(E) in the mother cell, and then later, following engulfment, sigma(G) in the prespore and then sigma(K) in the ...

Memory consolidation is stabilized and even enhanced by sleep (and particularly by 12-15 Hz sleep spindles in NREM stage 2 sleep) in healthy children but it is unclear what happens to these processes when sleep is disturbed by obstructive sleep disordered breathing. This cross-sectional study investigates differences in declarative memory consolidation among children with primary snoring (PS) a...

We study quasi-matter bounce cosmology in light of Planck cosmic microwave background (CMB) angular anisotropy measurements along with the BICEP2/Keck Array data. propose a new primordial scalar power spectrum by considering linear approximation equation state $w\cong w_0+\kappa(\eta-\eta_0)$ for field contracting phase universe. Using this spectrum, we constrain zeroth-order $w_0= -\,0.00340\p...

The Bacillus subtilis gene pgsA, which codes for the phosphatidylglycerophosphate synthase that catalyzes the committed step for the synthesis of phosphatidylglycerol (PG), is essential since Pspac-pgsA cells require IPTG for growth. Removal of the inducer caused a dramatic decrease of PG content in the membranes of cells and retarded growth. At 60 min and 120 min after removal, it was reduced ...