On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50The principle eigenvalue and the maximum principle for second-order elliptic equations is studied. New necessary and sufficient conditions for symmetric and nonsymmetric operators are obtained. Applications for the estimation of the first eigenvalue are given

Stimulated Raman adiabatic passage into continuum

We propose a technique which produces nearly complete ionization of the population of a discrete state coupled to a continuum by a two-photon transition via a lossy intermediate state whose lifetime is much shorter than the interaction duration. We show that using counterintuitively ordered pulses, as in stimulated Raman adiabatic passage (STIRAP), wherein the pulse coupling the intermediate state to the continuum precedes and partly overlaps the pulse coupling the initial and intermediate states, greatly increases the ionization signal and strongly reduces the population loss due to spontaneous emission through the lossy state. For strong spontaneous emission from that state, however, the ionization is never complete because the dark state required for STIRAP does not exist. We demonstrate that this drawback can be eliminated almost completely by creating a laser-induced continuum structure (LICS) by embedding a third discrete state into the continuum with a third control laser. This LICS introduces some coherence into the continuum, which enables a STIRAP-like population transfer into the continuum. A highly accurate analytic description is developed and numerical results are presented for Gaussian pulse shapes

Broadband sum frequency generation via chirped quasi-phase-matching

An efficient broadband sum frequency generation (SFG) technique using the two collinear optical parametric processes \omega 3=\omega 1+\omega 2 and \omega 4=\omega 1+\omega 3 is proposed. The technique uses chirped quasi-phase-matched gratings, which, in the undepleted pump approximation, make SFG analogous to adiabatic population transfer in three-state systems with crossing energies in quantum physics. If the local modulation period %for aperiodically poled quasi-phase-matching first makes the phase match occur for \omega 3 and then for \omega 4 SFG processes then the energy is converted adiabatically to the \omega 4 field. Efficient SFG of the \omega 4 field is also possible by the opposite direction of the local modulation sweep; then transient SFG of the \omega 3 field is strongly reduced. Most of these features remain valid in the nonlinear regime of depleted pump

Extension of the Morris-Shore transformation to multilevel ladders

We describe situations in which chains of N degenerate quantum energy levels, coupled by time-dependent external fields, can be replaced by independent sets of chains of length N, N-1,...,2 and sets of uncoupled single states. The transformation is a generalization of the two-level Morris-Shore transformation [J.R. Morris and B.W. Shore, Phys. Rev. A 27, 906 (1983)]. We illustrate the procedure with examples of three-level chains

Is it better at home with my family? The effects of people and place on children's eating behavior.

The people and places children eat with can influence food consumption. This study investigates the people and places Swiss school-aged children ate with over a 7-day period and analyses the effects of eating at home with family on food consumption. Children completed a 7-day food diary documenting the foods they consumed, the people with whom they ate, and the place where they ate. Analyses were conducted for all meals and included 9911 meal occasions. Most meals (80.5%) were consumed at home with family. Generalized estimating equations were used to model the effects of the home-family dyad on the child's chance of consuming a certain food while controlling for age, gender and BMI of the child, education, nationality and BMI of the parent. Compared to eating in other dyads (e.g. school-peers or restaurant-family), eating in the home-family dyad was associated with higher consumption of vegetables (+66% and +142% at weekday lunch and dinner and +180% and +67% at weekend lunch and dinner), lower consumption of sweets (-45% and -49% at weekday lunch and dinner; -43% and -49% at weekend lunch and dinner), and fewer soft drinks (-37% and -61% at weekday lunch and dinner; -66% and -78% at weekend lunch and dinner). This study shows the positive influence of eating at home with the family on food consumption in a sample of Swiss children. Interventions and policies that encourage children and parents to eat together at home could serve as effective prevention against a poor diet

<i>CHANDRA</i> OBSERVATIONS OF OUTFLOWS FROM PSR J1509–5850

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