We introduce the Exel-Pardo $$*$$ -algebra $${\textrm{EP}}_R(G,\Lambda )$$ associated to a self-similar k-graph $$(G,\Lambda ,\varphi . also prove $${\mathbb {Z}}^k$$ -graded and Cuntz–Krieger uniqueness theorems for such algebras investigate their ideal structure. In particular, we modify graded theorem 1-graphs then apply it present as Steinberg algebra study

Murthy, K. S., J. R. Grider, J. F. Kuemmerle, and G. M. Makhlouf. Sustained muscle contraction induced by agonists, growth factors, and Ca mediated by distinct PKC isozymes. Am J Physiol Gastrointest Liver Physiol 279: G201–G210, 2000.—The role of protein kinase C (PKC) in sustained contraction was examined in intestinal circular and longitudinal muscle cells. Initial contraction induced by ago...

The asymptotic behaviour of the sequence with general term $P_n=(varphi(1)+varphi(2)+cdots+varphi(n))/(1+2+cdots+n)$, is studied which appears in the studying of coprime integers, and an explicit bound for the difference $P_n-6/pi^2$ is found.

let $r$ be a commutative ring with identity‎. ‎we use‎ ‎$varphi (r)$ to denote the comaximal ideal graph‎. ‎the vertices‎ ‎of $varphi (r)$ are proper ideals of r which are not contained‎ ‎in the jacobson radical of $r$‎, ‎and two vertices $i$ and $j$ are‎ ‎adjacent if and only if $i‎ + ‎j = r$‎. ‎in this paper we show some‎ ‎properties of this graph together with planarity of line graph‎ ‎assoc...

Relative energies of the ground state isomers of 1,4-diphenyl-1,3-butadiene (DPB) are determined from the temperature dependence of equilibrium isomer compositions obtained with the use of diphenyl diselenide as catalyst. Temperature and concentration effects on photostationary states and isomerization quantum yields with biacetyl or fluorenone as triplet sensitizers with or without the presenc...

In this paper, based on the classical Yano’s formula, we first establish an optimal integral inequality for compact Lagrangian submanifolds in complex space forms, which involves Ricci curvature direction \(J\mathbf {H}\) and norm of covariant differentiation second fundamental form h, where J is almost structure \(\mathbf mean vector field. Second analogously, Legendrian Sasakian forms with \(...

Endothelin is a potent vasoconstrictor peptide which has recently been localized in the gastrointestinal tract. We have investigated the transmembrane signaling properties of endothelin in isolated smooth muscle cells of the rabbit rectosigmoid. Endothelin induced a dose dependent contraction of smooth muscle cells in a range of 10(-10) to 10(-6)M. In normal buffer, contraction peaked at 30 sec...

let $varphi(z)=z^m, z in mathbb{u}$, for some positive integer $m$, and $c_varphi$ be the composition operator on the bergman space $mathcal{a}^2$ induced by $varphi$. in this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $c^*_varphi c_varphi, c_varphi c^*_varphi$ as well as self-commutator and anti-self-commutators of $c_...

In this paper, we introduce the (G-$psi$) contraction in a metric space by using a graph. Let $F,T$ be two multivalued mappings on $X.$ Among other things, we obtain a common fixed point of the mappings $F,T$ in the metric space $X$ endowed with a graph $G.$