the corona product $gcirc h$ of two graphs $g$ and $h$ isobtained by taking one copy of $g$ and $|v(g)|$ copies of $h$;and by joining each vertex of the $i$-th copy of $h$ to the$i$-th vertex of $g$, where $1 leq i leq |v(g)|$. in thispaper, exact formulas for the eccentric distance sum and the edgerevised szeged indices of the corona product of graphs arepresented. we also study the conditions...

In this paper we investigate the stability of one-sided perturbation to g-frame expansions. We show that if $Lambda$ is a g-frame of a Hilbert space $mathcal{H}$, $Lambda_{i}^{a}=Lambda_{i}+Theta_{i}$ where $Theta_{i} in mathcal{L}(mathcal{H},mathcal{H}_{i})$, and $widetilde{f}=sum_{i in J}Lambda_{i}^{star}widetilde{Lambda}_{i}^{a}f$, $widehat{f}=sum_{i in J}(Lambda_{i}^{a})^{star}widetilde{Lam...

Abstract We prove that analogues of the Hardy–Littlewood generalised twin prime conjecture for almost primes hold on average. Our main theorem establishes an asymptotic formula number integers $n=p_1p_2 \leq X$ such $n+h$ is a product exactly two which holds all $|h|\leq H$ with $\log^{19+\varepsilon}X\leq H\leq X^{1-\varepsilon}$ , under restriction size one factors n and . Additionally, we co...

The Kerr black holes possess a photon region with prograde and retrograde orbits radii, respectively, $M\leq r_p^-\leq 3M$ $3M\leq r_p^+\leq 4M$, thereby always cast closed ring or shadow silhouette for $a\leq M$. For $a>M$, it is no-horizon spacetime (naked singularity) wherein spiral into the central singularity, produce an arc-like dark spot at center. We compare holes' structure those produ...

let $p(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. in this paper, some algebraic and geometrical properties of the $k$-numerical range of $p(lambda)$ are investigated. in particular, the relationship between the $k$-numerical range of $p(lambda)$ and the $k$-numerical range of its companion linearization is stated. moreover, the $k$-numerical ...

in this work, by employing the krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prim...