The double electron E1 transition energies, probabilities, and oscillator strengths between the $2s2p^{n}$ $1s^{2}2p^{n-1}$($1\!\leq\!n\leq\!6$) configurations of Xe$^{q+}$($47\!\leq\!q\leq\!52$) ions with different spectator electrons have been calculated based on multi-configuration Dirac-Hartree-Fock method. A reasonable correlation model is constructed aid active space finite mass nuclear, ...

inthis paper, the main aim is to introduce the class $mathcal{u}_p(lambda,alpha,beta,k_0)$ of $p$-harmonic mappings togetherwith its subclasses $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p$ and $mathcal{u}_p(lambda,alpha,beta,k_0)capmathcal {t}_p^0$, andinvestigate the properties of the mappings in these classes. first,we give a sufficient condition for mappings to be in $mathcal{u}_p(l...

Abstract A subset R of the vertex set a graph $\Gamma $ is said to be $(\kappa ,\tau )$ -regular if induces $\kappa subgraph and every outside adjacent exactly $\tau vertices in . In particular, some Cayley on finite group G , then called Let H nontrivial normal subgroup pair integers satisfying $0\leq \kappa \leq |H|-1$ $1\leq \tau |H|$ $\gcd (2,|H|-1)\mid It proved that (i) even, ; (ii) odd, ...

We present a new variant of the secretary problem. Let $A$ be totally ordered set $n$ \emph{applicants}. Given $P\subseteq A$ and $x\in A$, let $rr(P,x)=\vert\{z\in P \mid z\leq x\}\vert\mbox{ }$ \emph{relative rank of} $x$ \emph{with regard to} $P$, $rr_n(x)=rr(A,x)$. $x_1,x_2,\dots,x_n\in random sequence distinct applicants. The aim is to select $1<j\leq n$ such that $rr_n(x_{j-1})-rr_n(x_j)\...

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

in this work, byemploying the leggett-williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

let $a = (a_{i,j})_{1 leq i,j leq n}$ be an $n times n$ matrixwhere $n geq 2$. let $dt(a)$, its second immanant be the immanant corresponding to the partition $lambda_2 = 2,1^{n-2}$. let $g$ be a connected graph with blocks $b_1, b_2, ldots b_p$ and with$q$-exponential distance matrix $ed_g$. we given an explicitformula for $dt(ed_g)$ which shows that $dt(ed_g)$ is independent of the manner in ...

The settling velocity of porous particles in linear stratification is affected by the diffusive exchange between interstitial and ambient water. extent to which buoyancy mass adaptation alters depends on ratio viscous time scales. We conducted schlieren experiments lattice Boltzmann simulations for highly (95 %) but impermeable spheres stratification. For a parameter range that resembles marine...