The following general problem is studied: Given a positive integer $$c$$ and two multiplicative functions $$f$$ $$g$$ , it required to determine for what values of $$n$$ the equality $$f(n)-g(n)=c$$ holds. It proved that, under certain constraints on solutions (in particular, constraint $$f(n)>g(n)$$ $$n>1$$ ), this equation has at most $$c^{1-\epsilon}$$ solutions. For $$n-\varphi(n)=c$$ that ...

The signaling cascades initiated by motilin receptors in gastric and intestinal smooth muscle cells were characterized. Motilin bound with high affinity (IC(50) 0.7 +/- 0.2 nM) to receptors on smooth muscle cells; the receptors were rapidly internalized via G protein-coupled receptor kinase 2 (GRK2). Motilin selectively activated G(q) and G(13), stimulated G alpha(q)-dependent phosphoinositide ...

Suppose $(X, g)$ is a compact, spin Riemannian $7$-manifold, with Dirac operator ${\mathrm{D}\mspace{-12mu}/\mspace{4mu}}^g : C^\infty (X, {\mathrm{S}\mspace{-10mu}/\mspace{2mu}}) \to {\mathrm{S}\mspace{-10mu}/\mspace{2mu}})$. Let $G$ be $\mathrm{SU}(m)$ or $\mathrm{U}(m)$, and $E X$ rank $m$ complex bundle $G$-structure. Write $\mathcal{B}_E$ for the infinite-dimensional moduli space of connec...

An electrophoretic purification of Rhodospirillum rubrum photoreceptor subunits prepared by alkaline urea-detergent disruption is described. Completely active photoreceptor subunits with less than 0.30 eq of iron (or any other transition metal) per phototrap can routinely be prepared. A new photoproduced electron paramagnetic resonance (EPR) signal has been detected in these preparations; it wa...

Let $T=\bigl(\begin{smallmatrix}A&0\U\&B\end{smallmatrix}\bigr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We prove: (1) If $U\_{A}$ ${B}U$ have finite flat dimensions, then left $T$-module $\bigl(\begin{smallmatrix}M\_1\ M\_2\end{smallmatrix}\bigr){\varphi^{M}}$ Ding projective if only $M\_1$ $M\_2/{\operatorname{im}(\varphi^{M})}$ the morphism $...

Abstract Let $\varphi $ be Euler’s function and fix an integer $k\ge 0$ . We show that for every initial value $x_1\ge 1$ , the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi (x_n)+k$ all $n\ge is eventually periodic. Similarly, values $x_1,x_2\ge $x_{n+2}=\varphi (x_{n+1})+\varphi periodic, provided k even.

The role of protein kinase C (PKC) in sustained contraction was examined in intestinal circular and longitudinal muscle cells. Initial contraction induced by agonists (CCK-8 and neuromedin C) was abolished by 1) inhibitors of Ca(2+) mobilization (neomycin and dimethyleicosadienoic acid), 2) calmidazolium, and 3) myosin light chain (MLC) kinase (MLCK) inhibitor KT-5926. In contrast, sustained co...

The contraction degeneracy of a graph G is the maximum minimum degree of G′ over all minors G′ of G. The corresponding decision problem is known to be NP -complete. In this paper, we present a dynamic programming approach for computing the contraction degeneracy of cographs.

In this paper, we find the best proximity point in G-metric spaces for G-generalized ζ-β-T contraction mappings and verify existence uniqueness of complete G metric space using idea an approximatively compact set. addition, example is provided to illustrate outcome.