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.     

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.     

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。     

Stereoselective titanium-mediated aldol reactions of (S)-2-tert-butyldimethylsilyloxy-3-pentanone

Titanium-mediated aldol reactions based on (S)-2-tert-butyldimethylsilyloxy-3-pentanone, a lactate-derived chiral ketone, provide the corresponding 2,4-syn-4,5-syn adducts in high yields and diastereomeric ratios with a wide array of achiral and chiral aldehydes. Furthermore, spectroscopic studies of intermediates involved in the process have permitted to propose a mechanism that accounts for the experimental results.     

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.     

Continuous flow and flow injection stripping voltammetric determination of silver(I), mercury(II), and bismuth(III) at a bulk modified graphite tube electrode

The epoxy-impregnated graphite tube electrode bulk modified with 2-mercaptobenzoxazole, employed in a wall-jet configuration, was found to be useful for the continuous flow and flow injection stripping voltammetric determinations of Ag^I, Hg^II and Bi^III. For continuous flow, detection limits for Ag^I, Hg^II and Bi^III were 1.8 × 10⁻¹⁰ M, 1.9 × 10⁻⁹ M and 9.5 × 10⁻⁹ M, respectively (10 min accumulation, S/N = 3). Precisions for 5.00 × 10⁻⁹ M Ag^I, 1.00 × 10⁻⁸ M Hg^II and 1.00 × 10⁻⁷ M Bi^III were 10.5%, 5.77 % and 7.90% (relative standard deviations, n = 6), respectively. In the case of flow injection stripping, with a 500 μL injection loop, detection limits of 0.59 ng, 2.0 ng and 120 ng were obtained for Ag^I, Hg^II and Bi^III, respectively (S/N = 3). Selected metal ions, inorganic and organic substances were investigated for interferences. The electrode was tested with a certified sample and then applied to the determinations of the metal ions in a urine and a sea-water sample.     

A NEW ONE-STEP REDUCTIVE N-ALKYLATION OF AMINO ACIDS AND THEIR ESTERS

The reductive alkylation of amine with carbonyl compounds usingsodium hydrogen telluride has been investigated in recent years.Application of this method to the synthesis of N-alkyl derivativesof biologically important amino acids and their esters is described.