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.     

Experimental study of photocatalytic oxidation of formaldehyde and its by-products

Formaldehyde is one of the most harmful pollutants that endanger occupants' health and the way of its effective removal has become a focus in the field of air quality. This paper studies the static photocatalytic removal of formaldehyde experimentally and finds out that carbon monoxide, which is more harmful to occupants' health than the formaldehyde itself, is one of the by-products in the process of photocatalytic oxidation of formaldehyde. The increase of carbon monoxide concentration should be taken into consideration in the photocatalytic application. The photocatalyst surface at room temperature can weakly adsorb CO and CO₂, which can deactivate the photocatalysts.     

离子缔合富集明极溶出伏安法测定痕量碘——Ⅰ.以丁基罗丹明B为离子缔合剂

本文提出在0.1mol/LH_2SO_4,7.5×10~(-4)mol/LBr~-和6×10~(-5)mol/L丁基罗丹明B(R~+)的底液中,在+1.0V下,I~-离子于玻璃电极上被氧化生成I_2BrR离子缔合物,藉以阴极溶出伏安法测定碘、I~-离子浓度在1～50ppb范围内与峰电流呈线性关系。用于食盐中痕碘的测定。     

Unprecedented double C-C bond cleavage of a cyclopentadienyl ligand

Double C-C bond cleavage of a cyclopentadienyl ligand proceeded to titanacyclopentadienes when 2 equiv of nitriles were added and the resulting two-carbon unit and three-carbon unit were converted into a benzene derivative and a pyridine derivative, respectively, in one-pot.     

An unusual mixed-valence Cu(I)-Cu(II) 3-D framework

The reaction of Cu(CH(3)CN)(4)ClO(4) with 2-pyridylacrylic acid (2-HPYA) affords an unusual mixed-valence Cu(I)-Cu(II) 3-D framework ([Cu(II)(2-PYA)(2)](3).[Cu(I)(2-PYA)](2).(H2O)(2))n (1) with a novel topology which features Cu(II) dimeric units (or paddle-wheel unit). The almost perpendicular coordinating direction between the N atom of pyridyl and the O atom of carboxylate groups may be responsible for the formation of such a novel network.