In this paper, we generalize the definitions of approximately inner $C_0$-groups and their ground states to the two- parameter case and study necessary and sufficient conditions for a state to be ground state. Also we prove that any approximately inner two- parameter $C_0$--group must have at least one ground state. Finally some applications are given.

‎This paper is devoted to get a ground state solution for a class of nonlinear elliptic equations with fast increasing weight‎. ‎We apply the variational methods to prove the existence of ground state solution‎.

in this research, structural and electronic properties of zncdn-1ten clusters (n=1-10) have been studied by formalism of density functional theory and using the projector augmented wave within local density approximation. the structural properties (such as bond length/angle and coordination number), electronic and optical properties (such as binding energy, kohn-sham spectrum and partial charge...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

the ultraviolet-visible (uv) spectra of toluene, ortho-bromo and para-bromo toluene in different solvents have been studied. the electric dipole moments and polarizabilities in the molecular excited electronic states were determined. it was found that the electric dipole moments for the excited states (µ*) and the ground states (µ) of these compounds are equal, and the change in dipole moment i...

time-dependent schrödinger equation for a 1-d model of hydrogen molecular ion h2+ in intenselaser field linearly polarized along the molecular axis is solved. ionization rates are calculated for differentinitial states. the evolution of electronic wavefunction at fixed inter-nuclear separations are simulated andanalyzed. the results obtained for the ground state of this 1-d model of h2+ show ap...

In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and mag...