Mechanism transition of self-pumped phase conjugation in KTa1 −xNbxO3:Fe crystals

Mechanism transitions of Self-Pumped Phase Conjugation (SPPC) with wavelength and doping concentration are observed in KTN:Fe (KTa_{1 –x} Nb _x O₃:Fe with _x = 0.48) crystals. The SPPC mechanism in KTN: Fe (0.4 wt. %) crystal transforms from Stimulated Photorefractive Backscattering and Four-Wave Mixing (SPB-FWM) to cat (or total internal reflection) as the wavelength increases from 514.5 nm to 620 nm. SPPC at 514.5 nm is formed with the cat mechanism in a 0.2 wt. % doped KTN:Fe crystal, while with the SPB-FWM mechanism in a 0.4 wt. % doped one. These mechanism transitions are discussed with respect to the dependence of the backscattering gain coefficient of the crystals on wavelength and doping concentration.     

Sensitivity analysis of the greatest eigenvalue of a symmetric matrix via the ɛ-subdifferential of the associated convex quadratic form

LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR ^m , and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper.     

A quadratically convergent O(\sqrt n L)-iteration algorithm for linear programming

Recently, Ye, Tapia and Zhang (1991) demonstrated that Mizuno—Todd—Ye's predictor—corrector interior-point algorithm for linear programming maintains the O( L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of a demonstration of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.Supported in part by NSF Grant DDM-8922636 and NSF Coop. Agr. No. CCR-8809615, the Iowa Business School Summer Grant, and the Interdisciplinary Research Grant of the University of Iowa Center for Advanced Studies.Supported in part by NSF Coop. Agr. No. CCR-8809615, AFOSR 89-0363, DOE DEFG05-86ER25017 and ARO 9DAAL03-90-G-0093.Supported in part by NSF Grant DMS-9102761 and DOE Grant DE-FG05-91ER25100.     

Modular synthesis of chiral homo- and heterotrisoxazolines. Improving the enantioselectivity in the asymmetric Michael addition of indole to benzylidene malonate

A simple approach to a diverse set of chiral trisoxazolines is described. Deprotonation of bisoxazolines 2, followed by treatment of 2-chloromethyloxazolines 3, affords chiral trisoxazolines, including chiral homo- and hetero-trisoxazolines in good to high yields. These trisoxazolines are successfully applied in the asymmetric reaction of indole with benzylidene malonate, and ee's up to 93% were obtained.