On the convergence of the exponential multiplier method for convex programming

In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy proximal term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.Research supported by the National Science Foundation under Grant DDM-8903385, and the Army Research Office under Grant DAAL03-86-K-0171.     

Double photoionisation spectra of small molecules and a new empirical rule for double ionisation energies

Complete double photoelectron spectra are presented for 18 small molecules where the location of charges in the cations and dications is relatively clearly defined. The data demonstrate the importance of a coulombic repulsion contribution to the double ionisation energies. Examination of data for a wide range of molecules leads to a new empirical rule to calculate double ionisation energies from the molecules’ single ionisation energies and maximum dimensions. Where single and double ionisation energies are known the rule allows the deduction of plausible intercharge distances.     

Application of an intensified diode array system to diagnosis of matrix effects and the rapid sequential determination of thiamine and riboflavin with fluorescence detection

The unique capabilities of a multiple wavelength spectrofluorometer based on an intensified diode array detector are used for diagnosis of matrix effects and for rapid sequential determination of two analytes. This system is used to investigate problems due to background fluorescence, blank reactions, and scattering for the determination of thiamine in cereal and urine samples by a fluorometric kinetic procedure. A novel determination of thiamine and riboflavin in vitamin pills is based on monitoring the native fluorescence of riboflavin over one wavelength region, and the rate of formation of fluorescent thiochrome from thiamine over another wavelength region, after a computer-controlled change in the pH of the reaction mixture.     

Automated,continuous, and dynamic speciation of urinary arsenic in the bladder of living organisms using microdialysis sampling coupled on-line with high performance liquid chromatography and hydride generation atomic absorption spectrometry

An on-line and fully automated method was developed for the continuous and dynamic in vivo monitoring of four arsenic species [arsenite (AsIII), arsenate (AsV), monomethylarsonic acid (MMA) and dimethylarsinic acid (DMA)] in urine of living organisms. In this method a microdialysis sampling technique was employed to couple on-line with high performance liquid chromatography (HPLC) and hydride generation atomic absorption spectrometry (HGAAS). Dialysates perfused through implanted microdialysis probes were collected with a sample loop of an on-line injector for direct and automated injection into HPLC system hyphenated with HGAAS. The saline (0.9% NaCl) solution was perfused at the rate of 1 microl min(-1) through the microdialysis probe and the dialysate was loaded into 50 microl of sample loop. The separation conditions were optimally selected to be in phosphate buffer solution at a pH 5.2 with a flow rate of 1.2 ml min(-1). The effluent from the HPLC was first mixed on-line at the exit of the column with HCl (1 M) solution and then mixed with a NaBH4 (0.2% m/v) solution. Based on the optimal conditions obtained, linear ranges of 2.5-50 ng ml(-1) for AsIII and 6.75-100 ng ml(-1) for the other three arsenic species were obtained. Detection limits of 1.00, 2.18, 1.03 and 2.17 ng ml(-1) were obtained for AsIII, DMA, MMA and AsV, respectively. Typical precision values of 3.4% (AsIII), 5.4% (DMA), 3.6% (MMA) and 7.5% (AsV) were obtained, respectively, at a 25 ng ml(-1) level. Recoveries close to 100%, relative to an aqueous standard, were observed for each species. The average in vivo recoveries of AsIII, DMA, MMA and AsV in rat bladder urine were 56+/-5%, 60+/-9%, 49+/-3% and 55+/-7%, respectively. The use of an on-line microdialysis-HPLC-HGAAS system permitted the determination of four urinary arsenic species in the bladder of an anesthetized rat with a temporal resolution of 50 min sampling.     

Trifluoromethanesulfonyl azide: an efficient reagent for the preparation of α-cyano-α-diazo carbonyls and an α-sulfonyl-α-diazo carbonyl

The reaction scope of trifluoromethanesulfonyl azide in diazo transfer reactions was extended to include the preparation of α-cyano-α-diazo-carbonyls, phenyl sulfonyl diazoacetophenone and diethyl diazomalonate in high yields. The effect of the bases used in the diazo transfer reactions were found to have a dramatic influence on the success of the reaction with pyridine being the base of choice.     

Ruthenium-catalyzed [2+2] cycloadditions between C1-substituted 7-oxanorbornadienes and alkynes

Ruthenium-catalyzed [2+2] cycloadditions between C1-substituted 7-oxanorbornadienes and alkynes were investigated. Most of the cycloadditions occurred smoothly at 65 °C, giving the cyclobutene cycloadducts in moderate to good yields. The C1 substituent showed strong effect on the regioselectivity (up to 110:1) of the cycloadditions.     

Vacuum ultraviolet spark emission spectra of fluorine and some polyatomic fluorides in noble gases

Spark emission spectra in the vacuum ultraviolet are reported for several polyatomic fluorides in He + Ar mixtures, and for pure fluorine. These results are discussed in terms of the potential of a given fluorine compound for ArF formation. The 158 nm emission in fluorine is tentatively assigned to the ³Π_g → ³Π_u.