Third order differential subordination and superordination results for analytic functions involving the Srivastava-Attiya operator

In this article, by making use of the linear operator introduced and studied by Srivastava and Attiya \cite{srivastava1}, suitable classes of admissible functions are investigated and the dual properties of the third-order differential subordinations are presented. As a consequence, various sandwich-type theorems are established for a class of univalent analytic functions involving the celebrated Srivastava-Attiya transform. Relevant connections of the new results are pointed out.Comment: 16. arXiv admin note: substantial text overlap with arXiv:1809.0651

Particle Production at CBM in a Thermal Model Approach

The Compressed Baryonic Matter (CBM) experiment planned at Facility for Antiproton and Ion Research (FAIR) will provide a major scientific effort for exploring the properties of strongly interacting matter in the high baryon density regime. One of the important goal behind such experiment is to precisely determine the equation of state (EOS) for the strongly interacting matter at extreme baryon density. In this paper, we have used a thermal model EOS incorporating excluded volume description for the hot and dense hadron gas (HG). We then predict different particle ratios and the total multiplicity of various hadrons in the CBM energy range i.e. from $10$ A GeV to $40$ A GeV lab energies, which corresponds to $4.43$ A GeV and $8.71$ A GeV center-of-mass energies. Our main emphasis is to estimate the strange particles enhancement as well as increase in the net baryon density in CBM experiment. We have also compared our results with the results obtained from various other theoretical approaches existing in the literature such as hadron string dynamics (HSD) model and ultra-relativistic quantum molecular dynamics (UrQMD) etc.Comment: 16 pages, 8 figure

Shell model description of Ge isotopes

A shell model study of the low energy region of the spectra in Ge isotopes for $38\leq N\leq 50$ is presented, analyzing the excitation energies, quadrupole moments, $B(E2)$ values and occupation numbers. The theoretical results have been compared with the available experimental data. The shell model calculations have been performed employing three different effective interactions and valence spaces.We have used two effective shell model interactions, JUN45 and jj44b, for the valence space $f_{5/2} \, p \,g_{9/2}$ without truncation. To include the proton subshell $f_{7/2}$ in valence space we have employed the $fpg$ effective interaction due to Sorlin {\it et al.}, with $^{48}$Ca as a core and a truncation in the number of excited particles.Comment: 10 pages, 10 figures, Proc. of the XXXV Nuclear Physics Symposium, January 3-6 2012, Cocoyoc, Morelos, Mexico. IOP Journal of Physics: Conference Series (in press

Spectroscopic Observations and Modelling of Impulsive Alfv\'en Waves Along a Polar Coronal Jet

Using the Hinode/EIS 2$"$ spectroscopic observations, we study the intensity, velocity, and FWHM variations of the strongest Fe XII 195.12 \AA\ line along the jet to find the signature of Alfv\'en waves. We simulate numerically the impulsively generated Alfv\'en waves within the vertical Harris current-sheet, forming the jet plasma flows, and mimicking their observational signatures. Using the FLASH code and the atmospheric model with embedded weakly expanding magnetic field configuration within a vertical Harris current-sheet, we solve the two and half-dimensional (2.5-D) ideal magnetohydrodynamic (MHD) equations to study the evolution of Alfv\'en waves and vertical flows forming the plasma jet. At a height of $\sim 5~\mathrm{Mm}$ from the base of the jet, the red-shifted velocity component of Fe XII 195.12 \AA\ line attains its maximum ($5~\mathrm{km\,s}^{-1}$) which converts into a blue-shifted one between the altitude of $5-10~\mathrm{Mm}$. The spectral intensity continously increases up to $10~\mathrm{Mm}$, while FWHM still exhibits the low values with almost constant trend. This indicates that the reconnection point within the jet's magnetic field topology lies in the corona $5-10~\mathrm{Mm}$ from its footpoint anchored in the Sun's surface. Beyond this height, FWHM shows a growing trend. This may be the signature of Alfv\'en waves that impulsively evolve due to reconnection and propagate along the jet. From our numerical data, we evaluate space- and time- averaged Alfv\'en waves velocity amplitudes at different heights in the jet's current-sheet, which contribute to the non-thermal motions and spectral line broadening. The synthetic width of Fe XII $195.12~\mathrm{\AA}$ line exhibits similar trend of increment as in the observational data, possibly proving the existence of impulsively generated (by reconnection) Alfv\'en waves which propagate along the jet