In this paper we study the influence of electron screening on Bohr-Weisskopf (BW) effect in many-electron atoms. The BW gives finite-nucleus magnetization contribution to hyperfine structure. Relativistic atomic many-body calculations are performed for s and p_1/2 states several systems interest studies parity violation time-reversal-violating electric dipole moments -- Rb, Cs, Fr, Ba+, Ra+, Tl...

Let $\sigma=(\sigma_{1},\sigma_{2},\dots,\sigma_{n})\in \mathbb{S}^{n-1}$ and $d\sigma$ denote the normalised Lebesgue measure on $\mathbb{S}^{n-1},~n\geq 2$. For functions $f_1, f_2,\dots,f_n$ defined $\R$ consider multilinear operator given by $$T(f_{1},f_{2},\dots,f_{n})(x)=\int_{\mathbb{S}^{n-1}}\prod^{n}_{j=1}f_{j}(x-\sigma_j)d\sigma, ~x\in \R.$$ In this paper we obtain necessary sufficien...

Let \(G=(V,E)\) be a finite graph. We consider the existence of solutions to generalized Chern–Simons–Higgs equation $$\begin{aligned} \Delta u=-\lambda e^{g(u)}\left( e^{g(u)}-1\right) ^2+4\pi \sum \limits _{j=1}^{N}\delta _{p_j} \end{aligned}$$on G, where \(\lambda \) is positive constant; g(u) inverse function \(u=f(\upsilon )=1+\upsilon -e^{\upsilon }\) on \((-\infty , 0]\); N integer; \(p_...

Abstract It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all elements are represented by so-called power words, i.e., words of form $$p_1^{z_1} p_2^{z_2} \cdots p_k^{z_k}$$ p 1 z </mml:...

Let $$S= \{ p_1, \ldots, p_s\}$$ be a finite, non-empty set of distinct prime numbers and $$(U_{n})_{n \geq 0}$$ linear recurrence sequence integers order at least 2. For any positive integer k, $$w = (w_k, w_1)\in\mathbb{Z}^k, w_1, w_k\neq 0$$ we define $$(U_j^{(k, w)})_{j\geq 1}$$ an increasing composed the form $$|w_kU_{n_k} +\cdots + w_1U_{n_1}|$$ , $$ n_k>\cdots >n_1$$ . Under certain assu...

&lt;p style='text-indent:20px;'&gt;In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the align with triangulation. The problem written mixed form using nonconforming &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ P_1 $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt; ...

The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

Let$mathbb{C}^n$ be the space of $n$ complex variables. Let$Omega_{n,p_2,ldots,p_n}$ be a complete Reinhardt on$mathbb{C}^n$. The Minkowski functional on complete Reinhardt$Omega_{n,p_2,ldots,p_n}$ is denoted by $rho(z)$. The concept ofspirallike mapping of type $beta$ and order $alpha$ is defined.So, the concept of the strong and almost spirallike mappings o...