A generalized Dantzig—Wolfe decomposition principle for a class of nonconvex programming problems

Since Dantzig—Wolfe's pioneering contribution, the decomposition approach using a pricing mechanism has been developed for a wide class of mathematical programs. For convex programs a linear space of Lagrangean multipliers is enough to define price functions. For general mathematical programs the price functions could be defined by using a subclass of nondecreasing functions. However the space of nondecreasing functions is no longer finite dimensional. In this paper we consider a specific nonconvex optimization problem min {f(x):h _j (x)g(x),j=1, ,m, xX}, wheref(·),h _j (·) andg(·) are finite convex functions andX is a closed convex set. We generalize optimal price functions for this problem in such a way that the parameters of generalized price functions are defined in a finite dimensional space. Combining convex duality and a nonconvex duality we can develop a decomposition method to find a globally optimal solution.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.     

Identification of Shiga toxins in Shiga toxin-producing Escherichia coli using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry

We developed a rapid and reliable identification method for Shiga toxins in Shiga toxin-producing Escherichia coli (STEC) using immunoprecipitation and high-performance liquid chromatography-electrospray ionization mass spectrometry (HPLC-ESI-MS). Polyclonal antisera specific for Shiga toxin 1 (Stx1) and Shiga toxin 2 (Stx2) were raised in rabbits so as to be used for the immunoprecipitation. The immunoprecipitaion was carried out by mixing sample solutions with 50 microl each of the antisera to Stx1 and Stx2 followed by allowing the mixed solutions to stand for 30 min. The quantity required to obtain the immunoprecipitate was more than 0.5 microg of Shiga toxins. HPLC-ESI-MS analysis of the resulting immunoprecipitates provided accurate molecular weight information on Shiga toxins, leading to direct evidence for the presence of these toxins. It requires at most two days to perform our procedure from toxin extraction to measurement of HPLC-ESI-MS whereas the previous method using isolation procedures required about two weeks to complete. The usefulness of the present method has been demonstrated by identifying Stx1, Stx2 and a variant of Stx2 (Stx2e) in the immunoprecipitates prepared from STEC strains.     

Photoinduced electron-transfer systems consisting of electron-donating pyrenes or anthracenes and benzimidazolines for reductive transformation of carbonyl compounds

Photoinduced electron-transfer reactions of several ketone substrates were studied to evaluate the utilities of 1,6-bis(dimethylamino)pyrene (BDMAP), 1,6-dimethoxypyrene (DMP), 9,10-bis(dimethylamino)anthracene (BDMAA), and 9,10-dimethoxyanthracene (DMA) as electron-donating sensitizers cooperating with 2-aryl-1,3-dimethylbenzimidazolines. BDMAP and DMP generally led higher conversion of ketones and better yield of reduction products compared to BDMAA and DMA.     

Improvement of an integral approximation scheme based on semiorthogonalized orbitals

In a previous paper, a scheme of integral approximation was proposed, in which a large number of two-electron integrals containing a certain kind of orbital pairs, i.e., weakly related pairs, can be neglected. A new criterion for partitioning orbital pairs into two groups, i.e., strongly and weakly related pairs, is introduced in order to allow for neglect of more integrals without sacrificing the accuracy of a computation. Test calculations on the BH₃? C₂H₄ complex show that by the use of the new version, results of roughly the same accuracy as was obtained by the old version is obtained by retaining 80% of the integrals used in the old version. This kind of saving is more significant for larger molecules. For example, in a calculation on Cu-porphine with 203 CGTO 'S , the revised version will require about 2.0 × 10⁶ integrals, while the original version will require about 4.5 × 10⁶. And these two approximate calculations are expected to give the results of roughly the same accuracy.     

Radiation-induced heterogeneous polymerization of acrylamide in acetone and acetone–water mixtures

The effects of temperature, dose rate, and monomer concentration on the heterogeneous polymerization of acrylamide in acetone–water mixtures have been studied. Heterogeneous polymerization takes place in mixtures containing less than 60 vol-% water. The polymerization is steady in acetone and nonsteady in acetone an nonsteady in mixtures containing 10–50 vol-% water. The average rate of polymerization is highest in mixtures with about 20 vol-% water. Polymer molecular weight increases with the increasing water content in range 0–10 vol-% and does not change in the range of 30–70 vol-% water. For the polymerization in acetone and an acetone–water 60/40 mixture the activation energies are 2.3 and ?1.8 kcal/mole, the dose rate exponents of rate are 0.78 and 0.52, and the monomer concentration exponents of rate are 0.5 and 1.6, respectively. The polymer molecular weight increases with decreasing dose rate, decreasing temperature, and increasing monomer concentration. These results are discussed in connection with the mechanism of heterogeneous polymerization and the solvent effect.     

Coprecipitation with metal hydroxides for the determination of beryllium in seawater by graphite furnace atomic absorption spectrometry

Coprecipitation first with magnesium hydroxide, next with tin(IV) hydroxide is developed for the determination of traces of beryllium in sea-water. To a 200-ml sample is added a sodium hydroxide solution to form magnesium hydroxide at pH 11.5, on which beryllium is quantitatively coprecipitated. The precipitate is separated by centrifugation and dissolved in 2 ml of 12 mol/l hydrochloric acid. The resulting solution (ca. 10 ml) is mixed with 2 mg of tin (IV) carrier and the pH is adjusted to 5.0 to collect the beryllium on tin (IV) hydroxide, leaving magnesium ions in the solution. The tin (IV) hydroxide is centrifuged, dissolved in 0.1 ml of 5 mol/l hydrobromic acid, and then diluted to 1 ml with water. Magnesium is so added as to be 500 g/ml for increasing the sensitivity about four times, and the beryllium in the solution is determined by graphite furnace atomic absorption spectrometry. The experiments with synthetic seawater samples showed that pg — g amounts of beryllium can be coprecipitated on the metal hydroxides and beryllium at the low ng/1 level can be determined with reasonable precision (RSD < 10%). The detection limit of the proposed method is 0.5 ng/l of beryllium in seawater.     

Aminyl radical cyclization by means of anodic oxidation. Stereoselective synthesis of cis-1-methyl-2,5-disubstituted pyrrolidines

Neutral aminyl radicals generated by anodic oxidation of lithium alkenylamides 2 undergo a stereoselective cyclization to give $\text{cis}$-1-methyl-2,5-disubstituted pyrrolidines 4. Their $\text{cis}$ stereochemistry was confirmed by a comparison with $\text{trans}$-1,2-dimethyl-5-phenylpyrrolidine, the structure of which was established by X-ray crystallographic analysis of its quarternary ammonium bromide 6.