Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

On continuous selection problems for multivalued mappings with the local intersection property in hyperconvex metric spaces

In the paper we present two continuous selection theorems in hyperconvex metric spaces and apply these to study xed point and coincidence point problems as well as variational inequality problems in hyperconvex metric spaces.

Using the flexibility index to compare batch and continuous activated sludge processes

This paper considers the question of which is better: the batch or the continuous activated sludge processes? It is an important question because dissension still exists in the wastewater industry as to the relative merits of each of the processes. A review of perceived differences in the processes from the point of view of two related disciplines, process engineering and biotechnology, is presented together with the results of previous comparative studies. These reviews highlight possible areas where more understanding is required. This is provided in the paper by application of the flexibility index to two case studies. The flexibility index is a useful process design tool that measures the ability of the process to cope with long term changes in operation.

Stokes-operator-squeezed continuous-variable polarization states

We investigate nonclassical Stokes-operator variances in continuous-wave polarization-squeezed laser light generated from one and two optical parametric amplifiers. A general expression of how Stokes-operator variances decompose into two-mode quadrature operator variances is given. Stokes parameter variance spectra for four different polarization-squeezed states have been measured and compared with a coherent state. Our measurement results are visualized by three-dimensional Stokes-operator noise volumes mapped on the quantum Poincare sphere. We quantitatively compare the channel capacity of the different continuous-variable polarization states for communication protocols. It is shown that squeezed polarization states provide 33% higher channel capacities than the optimum coherent beam protocol.

Experimental investigation of criteria for continuous variable entanglement

We generate a pair of entangled beams from the interference of two amplitude squeezed beams. The entanglement is quantified in terms of EPR paradox and inseparability criteria, with both results clearly beating the standard quantum limit. We experimentally analyze the effect of decoherence on each criterion and demonstrate qualitative differences. We also characterize the number of required and excess photons present in the entangled beams and provide contour plots of the efficacy of quantum information protocols in terms of these variables.

Experimental investigation of continuous-variable quantum teleportation

We report the experimental demonstration of quantum teleportation of the quadrature amplitudes of a light field. Our experiment was stably locked for long periods, and was analyzed in terms of fidelity F and with signal transfer T-q=T++T- and noise correlation V-q=Vinparallel to out+Vinparallel to out-. We observed an optimum fidelity of 0.64+/-0.02, T-q=1.06+/-0.02, and V-q=0.96+/-0.10. We discuss the significance of both T-q>1 and V-q

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump pump, Stokes signal, and Raman coherence idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

Continuous variable polarization entanglement, experiment and analysis

We generate and characterize continuous variable polarization entanglement between two optical beams. We first produce quadrature entanglement, and by performing local operations we transform it into a polarization basis. We extend two entanglement criteria, the inseparability criteria proposed by Duan et al (2000 Phys. Rev. Lett. 84 2722) and the Einstein–Podolsky–Rosen (EPR) paradox criteria proposed by Reid and Drummond (1988 Phys. Rev. Lett. 60 2731), to Stokes operators; and use them to characterize the entanglement. Our results for the EPR paradox criteria are visualized in terms of uncertainty balls on the Poincaré sphere. We demonstrate theoretically that using two quadrature entangled pairs it is possible to entangle three orthogonal Stokes operators between a pair of beams, although with a bound √3 times more stringent than for the quadrature entanglement.