About positive invariance and asymptotic stability

In this note we consider the differential equation , t0 with initial conditionx(0)G, whereG is a closed pointed convex cone. Our results pertain to positive invariance and asymptotic stability. A result by Stern, [3], will be improved. Subtangentiality will also be discussed as this notion is important in deriving results about positive invariance.     

Synthesis and Diels-Alder Reactions of a New Kind of Chiral Dienophiles: Cyclic Vinyl-p-tolylsulfilimines

A new kind of chiral dienophiles, cyclic vinyl-p-tolylsulfilimines (2a and 2b), were obtained from the corresponding (Z)-sulfinylacrylonitriles with HBF(4) and methanol. The asymmetric Diels-Alder reaction of optically pure 2a with cyclopentadiene under mild thermal or catalyzed conditions afforded only the endo-4a adduct with complete endo and pi-facial selectivities. The ability of the sulfilimine moiety to enhance the dienophilic reactivity of the double bond is similar to that of the sulfinyl group.     

Another application of Guignard's generalized Kuhn-Tucker conditions

Necessary conditions are given for a real-valued function to have a minimum, subject to a generalized inequality constraint. Under the appropriate hypotheses, the problem is demonstrated to be a special case of the type of problem to which Guignard's Kuhn-Tucker theorem can be applied.The author would like to thank the referee for his valuable suggestions.     

Curriculum-based course timetabling with SAT and MaxSAT

This paper describes our work on applying novel techniques based on propositional satisfiability (SAT) solvers and optimizers to the Curriculum-based Course Timetabling problem. Out of 32 standard benchmark instances derived from the Second International Timetabling Competition held in 2007, our techniques yield the best known solutions for 21 of them (19 of them being optimal), improving the previously best known solutions for 9. In addition, we obtain 18 new lower bounds for this benchmark set by applying a new full (Weighted) Partial MaxSAT approach of the Curriculum-based Course Timetabling problem.     

High-efficiency mid-infrared ZnGeP2 optical parametric oscillator directly pumped by a lamp-pumped, Q-switched CrTmHo:YAG laser

We report a singly resonant optical parametric oscillator (SRO) based on a ZnGeP(2) crystal directly pumped by a lamp-pumped Q-switched CrTmHo:YAG laser. The IR was tunable from 4.7 to 7.8 microm via crystal angle tuning. A maximum optical to optical efficiency of 56% was obtained from the pump (2.09 microm) to total IR at a pump energy of 6.5 mJ. The corresponding idler energy was 1.45 mJ. The SRO was measured to have a slope efficiency of 64% and a threshold of 1 mJ. The spatial beam quality of the idler, characterized by the M(2) parameter, was 1.38 when the SRO was pumped at 2.5 times threshold. These results show that ZnGeP(2) optical parametric oscillators directly pumped by a CrTmHo:YAG laser can be operated efficiently, while maintaining good IR beam quality.     

O(4) Expansion of the Ladder Bethe-Salpeter Equation

The Bethe-Salpeter amplitude is expanded on a hyperspherical basis thereby reducing the original four-dimensional integral equation into an infinite set of coupled one-dimensional ones. It is shown that this representation offers a highly accurate method to determine numerically the bound state solutions. For generic cases only a few hyperspherical waves are needed to achieve convergence, both for the ground state as well as for radially or orbitally excited states. The wave function is reconstructed for several cases and in particular it is shown that it becomes independent of the relative time in the nonrelativistic regime. Received July 18, 1996; accepted in final form October 2, 1996