‎generalizing the notion of character amenability for banach‎ ‎algebras‎, ‎we study the concept of $varphi$-connes amenability of‎ ‎a dual banach algebra $mathcal{a}$ with predual $mathcal{a}_*$‎, ‎where $varphi$ is a homomorphism from $mathcal{a}$ onto $bbb c$‎ ‎that lies in $mathcal{a}_*$‎. ‎several characterizations of‎ ‎$varphi$-connes amenability are given‎. ‎we also prove that the‎ ‎follo...

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.

Glucose oxidation to CO(2) in man at the fasted, steady state has been investigated in normal, hypothyroid, patients by monitoring the specific activity of plasma glucose and expired CO(2) after intravenous injection of glucose-1-(14)C, glucose-6-(14)C, and sodium bicarbonate-(24)C in tracer amounts. Making certain stoichiometric assumptions about the oxidation of the C-1 and C-6 carbons of glu...

A Hankel operator $\mathbf{H}_\varphi$ on the Hardy space $H^2$ of unit circle with analytic symbol $\varphi$ has minimal norm if $\|\mathbf{H}_\varphi\|=\|\varphi \|_2$ and maximal $\|\mathbf{H}_\varphi\| = \|\varphi\|_\infty$. The both only $|\varphi|$ is constant almost everywhere or, equivalently, a multiple an inner function. We show that norm-attaining norm, then norm. If continuous but n...

The paper deals with the problem of convergence branched continued fractions two branches branching which are used to approximate ratios Horn's hypergeometric function $H_3(a,b;c;{\bf z})$. case real parameters $c\geq a\geq 0,$ b\geq $c\neq and complex variable ${\bf z}=(z_1,z_2)$ is considered. First, it proved fraction for z}\in G_{\bf h}$, where $G_{\bf h}$ two-dimensional disk. Using this r...

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...

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_...

We investigate scattering amplitudes of the reversible $\ensuremath{\theta}$-exact Seiberg-Witten map-based noncommutative (NC) quantum electrodynamics and show explicitly SW map invariance for all types tree-level NCQED two-by-two processes, including M\o{}ller, Bhabha, Compton, pair annihilation, production, light-by-light (LbyL: $\ensuremath{\gamma}\ensuremath{\gamma}\ensuremath{\rightarrow}...

Abstract Let u be an analytic function in the unit disk $\mathbb{D}$ D and φ self-map of . We give characterizations symbols for which multiplication operator $M_{u}$ M u weighted composition $M_{u,\varphi }$ , φ</mml...