On relative commuting probability of finite rings

In this paper we study the probability that the commutator of a randomly chosen pair of elements, one from a subring of a finite ring and other from the ring itself equals to a given element of the ring

E1E1 PNC transition amplitudes of the hyperfine components for 2S1/2^2S_{1/2} −- 2D3/2^2D_{3/2} transitions of 137^{137}Ba+^{+} and 87^{87}Sr+^{+}

In this paper, we have calculated parity nonconserving electric dipole transition amplitudes of the hyperfine components for the transitions between the ground and first excited states of $^{137}$Ba$^{+}$ and $^{87}$Sr$^{+}$ using sum-over-states technique. The results are presented to extract the constants associated with the nuclear spin dependent amplitudes from experimental measurements. The wavefunctions to calculate the most dominant part of the sums are constructed using highly correlated coupled-cluster theory based on the Dirac-Coulomb-Gaunt Hamiltonian

On generalized commuting probability of finite rings

Let $R$ be a finite ring and $r \in R$. The aim of this paper is to study the probability that the commutator of a randomly chosen pair of elements of $R$ equals $r$

Finite groups whose commuting graphs are integral

A finite non-abelian group $G$ is called commuting integral if the commuting graph of $G$ is integral. In this paper, we show that a finite group is commuting integral if its central factor is isomorphic to ${\mathbb{Z}}_p \times {\mathbb{Z}}_p$ or $D_{2m}$, where $p$ is any prime integer and $D_{2m}$ is the dihedral group of order $2m$

Spectrum and genus of commuting graphs of some classes of finite rings

The commuting graph of a non-commutative ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two vertices $x, y$ are adjacent if and only if $xy = yx$. In this paper, we compute the spectrum and genus of commuting graphs of some classes of finite rings

Various energies of some super integral groups

In this paper, we obtain energy, Laplacian energy and signless Laplacian energy of the commuting graphs of some families of finite non-abelian groups.Comment: arXiv admin note: text overlap with arXiv:1608.0276

On Laplacian energy of non-commuting graphs of finite groups

In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups.Comment: arXiv admin note: substantial text overlap with arXiv:1705.01275; text overlap with arXiv:1705.0013

Spectrum of commuting graphs of some classes of finite groups

In this paper, we initiate the study of spectrum of the commuting graphs of finite non-abelian groups. We first compute the spectrum of this graph for several classes of finite groups, in particular AC-groups. We show that the commuting graphs of finite non-abelian AC-groups are integral. We also show that the commuting graph of a finite non-abelian group $G$ is integral if $G$ is not isomorphic to the symmetric group of degree $4$ and the commuting graph of $G$ is planar. Further it is shown that the commuting graph of $G$ is integral if the commuting graph of $G$ is toroidal

Relativistic coupled cluster calculations on hyperfine structures and electromagnetic transition amplitudes of In III

Hyperfine constants and anomalies of ground as well as few low lying excited states of $^{113,115,117}$In III are studied with highly correlated relativistic coupled-cluster theory. The ground state hyperfine splitting of $^{115}$In III is estimated to be 106.8 GHz. A shift of almost 1.9 GHz of the above frequency has been calculated due to modified nuclear dipole moment. This splitting result shows its applicability as communication band and frequency standards at $10^{-11}$ sec. Correlations study of hyperfine constants indicates a few distinct features of many-body effects in the wave-functions in and near the nuclear region of this ion. Astrophysically important forbidden transition amplitudes are estimated for the first time in the literature to our knowledge. The calculated oscillator strengths of few allowed transitions are compared with recent experimental and theoretical results wherever available.Comment: 11 pages, 4 figure

Precise calculations of astrophysically important allowed and forbidden transitions of Xe VIII

The present work reports transition line parameters for Xe VIII, which are potentially important for astrophysics in view of recent observations of multiply ionized xenon in hot white dwarfs. The relativistic coupled-cluster method is employed here to calculate the E1, E2, and M1 transition line parameters with high accuracy. The E1 oscillator strengths and probabilities of E2 and M1 transitions are determined using theoretical amplitudes and experimental energy values. The calculated branching ratios and the lifetimes are supplemented to the transition parameters. Accurate presentation of these calculated data is crucial for density estimation in several stellar and inter-stellar media.Comment: 14 pages, 1 figur