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...

Many physical and combinatorial problems associated with complex networks of interacting degrees of freedom can be mapped to equivalent problems of finding the ground (or minimum cost) state of a corresponding quantum Hamiltonian H0 1,2,3,4,5,6,7,8,9. One of the approaches to finding the ground state of H0 is adiabatic quantum computation which can be formulated as follows. Consider the time de...

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...

Bose–Fermi mixtures in one dimension are studied in detail on the basis of an exact solution. Corresponding to three possible choices of the reference state in the quantum inverse scattering method, three sets of Bethe-ansatz equations are derived explicitly. The features of the ground state and low-lying excitations are investigated. The ground state phase diagram caused by the external field ...

This paper presents an algorithm for detection and resolution of air tra c con icts in a 3dimensional (3-D) airspace for two aircraft, namely ownship and intruder. A con ict is a projected incursion of the intruder aircraft within the protected zone of the ownship. A solution is a single maneuver, to be performed by the ownship, that e ectively keeps the required minimum separation without coop...

We consider singular solutions of the L 2-critical biharmonic nonlinear Schrödinger equation. We prove that the blowup rate is bounded by a quartic-root, the solution approaches a quasi–self-similar profile, and a finite amount of L 2-norm, which is no less than the critical power, concentrates into the singularity. We also prove the existence of a ground-state solution. We use asymptotic analy...

We study the occurrence of ground-state factorization in dimerized XY spin chains in a transverse field. Together with the usual ferromagnetic and antiferromagnetic regimes, a third case emerges, with no analogous in translationally invariant systems, consisting of an antiferromagnetic Neél-type ground state where pairs of spins represent the unitary cell. Then, we calculate the exact solution ...