Picosecond four-wave mixing reflectivity of GaAs at 1.06 μm

The picosecond degenerate four-wave mixing reflectivity of semi-insulating gallium arsenide at 1.06 m is calculated in this paper. The dependence of the reflectivity on the pump and signal fluences is measured. Reflectivities of more than one are possible. The Fourier components of the excited-carrier densities are calculated as a function of the pump fluence. The wavefront-correction property of this reflectivity is demonstrated with a lens group in the signal beam.     

Geometric optimization andD P -completeness

In this paper we show a number of natural geometric optimization problems in the plane to becomplete for a classD ^P . The classD ^p contains both NP and Co-NP and is contained in ₂ ^P =P ^NP. Completeness inD ^p is exhibited under many-one and positive reductions. Further anOptP(O(logn)) result is also obtained for some of these optimization problems.Work on this paper by the first author was supported in part by NSF Grant No. MIP 85-21356 and ARO Contract No. DAAG29-85-C-0018 under Cornell/MSI. Work by the second author was supported in part by NSF Grant No. DCR 86-06366 at Ohio State and ONR Grant No. N00014-k-0045 at Harvard.On leave from Ohio State University.     

Quadratically constrained minimum cross-entropy analysis

Quadratically constrained minimum cross-entropy problem has recently been studied by Zhang and Brockett through an elaborately constructed dual. In this paper, we take a geometric programming approach to analyze this problem. Unlike Zhang and Brockett, we separate the probability constraint from general quadratic constraints and use two simple geometric inequalities to derive its dual problem. Furthermore, by using the dual perturbation method, we directly prove the strong duality theorem and derive a dual-to-primal conversion formula. As a by-product, the perturbation proof gives us insights to develop a computation procedure that avoids dual non-differentiability and allows us to use a general purpose optimizer to find an-optimal solution for the quadratically constrained minimum cross-entropy analysis.     

由肉桂酸生物合成L-苯丙氨酸

本文评述了Ｌ－苯丙氮酸的各种合成路线、国内外的研究现状及工业化情况，重点讨论了由肉桂酸和氨生物合成Ｌ－苯丙氨酸的路线，提出了在国内进一步工作的建议。