Abstract:
In the present paper the self similar solution of strong cylindrical shock wave in magnetogasdynamics using Langrangian mass co-ordinate has been studied. Analytic solutions of governing equations in closed form are obtained. The strong cylindrical shock wave generated by sudden line source explosion in an inhomogeneous medium of infinite electrical conductivity has been studied. The influence of specific heat ratio and magnetic field strength on flow variables for various cases is assessed. The general behaviour of velocity distribution remains unaffected. However, the density and pressure profiles are significantly affected in presence magnetic field interaction.

Abstract:
In this work, we study the evolution of primordial black holes within the context of Brans-Dicke theory by considering the presence of a dark energy component with a super-negative equation of state called phantom energy as a background. Besides Hawking evaporation, here we consider two type of accretions - radiation accretion and phantom energy accretion. We found that radiation accretion increases the lifetime of primordial black holes whereas phantom accretion decreases the lifespan of primordial black holes. Investigating the competition between the radiation accretion and phantom accretion, we got that there is an instant during the matter-dominated era beyond which phantom accretion dominates radiation accretion. So the primordial black holes which are formed in the later part of radiation dominated era and in matter dominated era are evaporated at a quicker rate than the Hawking evaporation. But for presently evaporating primordial black holes, radiation accretion and Hawking evaporation terms are dominant over phantom accretion term and hence presently evaporating primordial black holes are not much affected by phantom accretion.

Abstract:
When two non-relativistic particles scatter in one dimension, they can become entangled. This entanglement process is constrained by the symmetries of the scattering system and the boundary conditions on the incoming state. Applying these constraints, three different mechanisms of entanglement can be identified: the superposition of reflected and transmitted modes, momentum correlations of the reflected mode due to inversion of the relative momentum, and momentum correlations in the transmitted and reflected modes due to dependence of the scattering amplitude on the relative momentum. We consider three standard potentials, the hard core, Dirac delta, and double Dirac delta, and show that the relative importance of these mechanisms depends on the interaction and on the properties of the incoming wave function. We find that even when the momenta distributions of the incoming articles are sharply peaked, entanglement due to the momentum correlations generated by reflection can be quite large for particles with unequal mass.

Abstract:
The main purpose of this paper is to obtain a common fixed point for a pair of set-valued mappings of Greguš type condition. Our theorem extend Diviccaro et al. (1987), Guay et al. (1982), and Negoescu (1989).

Abstract:
The effect of C-field in high density matter has been studied. We find that the negative energy and negative pressure of the C-field helps in formation of massive compact stable neutron stars of mass $\sim$ 0.5 solar mass which is in the range of 0.01 to 1.0 solar mass of recently observed dwarf stars.

Abstract:
We use a modified SU(2) chiral sigma model to study nuclear matter component and simple bag model for quark matter constituting a neutron star. We also study the phase transition of nuclear matter to quark matter with the mixed phase characterized by two conserved charges in the interior of highly dense neutron stars. Stable solutions of Tolman-Oppenheimer-Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.67$M_{\odot}$ and radius around 8.9 km.

Abstract:
We use a modified SU(2) chiral sigma model to study nuclear matter at high density using mean field approach. We also study the phase transition of nuclear matter to quark matter in the interior of highly dense neutron stars. Stable solutions of Tolman-Oppenheimer-Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.69 $M_{\odot}$, radii around 9.3 kms and a quark matter core constituting nearly 55-85 % of the star radii.

Abstract:
We study here the equation of state of symmetric nuclear matter at finite temperatures using a modified SU(2) Chiral Sigma model. The effect of temperature on effective mass, pressure, entropy and binding energy is discussed. The liquid-gas phase transition is investigated and the critical values of temperature, density and pressure are calculated.