Mosco approximation of integrands and integral functionals

It is shown that, given a lower semicontinuous convex integrandf satisfying a suitable integrability condition, there exists a sequence of Lipschitz simple integrands which Mosco converges tof and such that the sequence of conjugate integrands Mosco converges tof ^*. Moreover, this sequence can be chosen so that the sequence of associated integral functionals, respectively defined onL ¹(X) andL (X ^*), Mosco converges as well.We wish to thank Professor Erik J. Balder for interesting remarks on the first version of this work.     

Synthesis of pyridine derivatives by reactions of α,β-unsaturated nitriles with 2-oxo-cycloalkano carbothioic acid anilides

Summary The tandem Michael addition-cyclization of 2-oxo-cycloalkane carbothioic acid anilides1–3 to benzylidenemalononitrile4 yielded spiroannulated pyridines5–7. Reaction of acrylonitrile with2 and3 gave 2,2-disubstituted Michael adducts14,15, whereas with1 led to 2,2,5-tri(2-cyanoethyl)-cyclopentanone11.

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Synthese von Pyridinderivaten durch Reaktionen von ,-ungesättigten Nitrilen mit 2-Oxo-cycloalkano-thiokohlensäure-aniliden

Zusammenfassung Die Michael Tandem-Addition-Cyclisierung von 2-Oxo-cycloalkano-thiokohlensäure-aniliden1–3 mit Benzylidenmalononitril4 ergab die spiroannelierten Pyridine5–7. Reaktion von Acrylnitril mit2 und3 ergab die 2,2-disubstituierten Michael-Addukte14,15, wohingegen mit1 2,2,5-Tri(2-cyanethyl)-cyclopentanon11 erhalten wurde.

     

Composition and properties of freeze-dried products of nicotinic acid withβ-cyclodextrin and heptakis (2,6-0-dimethyl)-β-cyclodextrin

The purpose of the study was to examine the formation of inclusion compounds in the freeze-dried products obtained from aqueous solutions of nicotinic acid and -cyclodextrin (-CD), or heptakis (2,6-0-dimethyl)--cyclodextrin (DIMEB). The molar ratios used were 1:1 and 2:1. In addition two freezing temperatures (–40 and –196°C) and different secondary drying temperatures (+50 and +80°C) were used. Freeze-dried products with -CD obtained after low temperature freezing are of the same crystallographic structure as seen in a pure inclusion compound prepared by coprecipitation. Amorphous products were formed after fast freezing. The molar ratios of included nicotinic acid in the freeze-dried products vary — dependent on the preparation conditions — between 0.75:1 and 1:1. A factorial design proves that the included drug amount can be increased by enhancement of the amount of nicotinic acid used, by faster freezing, and by the combination of these two factors. The proof of inclusion formation was given by a combination of X-ray diffractography, differential scanning calorimetry, thermogravimetry and thermofractography.The freeze-dried preparations obtained with DIMEB were amorphous mixtures of the two components. No proof for inclusion of the nicotinic acid in the cyclodextrin cavity could be given. Higher (–40°C) or lower (–196°C) freezing temperatures and the running of the secondary drying process could not influence these results. The very low stability constant of the complex and steric reasons are responsible for this behavior.     

Direct and stepwise intercalation of alkylalcohols intoα-zirconium phosphate

Intercalation of alkylalcohols into -zirconium phosphate was investigated at 25°C and/or under reflux.n-Alcohols having two to five carbons and 2-propanol were taken up at 25°C. These alcohols, andn-hexanol and heptanol, also intercalated under reflux.n-Alcohols having eight to eighteen carbon atoms intercalated when a stepwise method was employed. 2-Butanol and tertiary amylalcohols intercalated under reflux using a butanol intercalate as a starting material. Ethanol-to-butanol intercalates were unstable at room temperature, losing alcohols and changing to -zirconium phosphate. The particle size of the -zirconium phosphate did not affect the intercalation of alcohols.     

Thermogravimetric properties of inclusion complexes ofβ-cyclodextrin with benzene,acetylsalicylic acid and methyl salicylate

This paper reports TG analyses of inclusion complexes of-cyclodextrin with benzene, acetylsalicylic acid and methyl salicylate. The data were used for calculation of the compositions of the three body complexes and the apparent kinetic parameters of the thermal decompositions. Water exclusion proceeds as a reaction with ordern=1 and an activation energy about 20 kJ/mol. The expulsion of aromatic guest molecules follows ann=1 order process with the activation energy above 155 kJ/mol, except that for the methyl salicylate complex, which was found to be ca. 64 kJ/mol.     

Synthesis of N-unsubstituted ketene aminals from β-ketocarboxylic esters and cyanamide

The interaction of cyanamide with -ketocarboxylic esters in the presence of Ni(acac)₂ affords N-unsubstituted aminals of acyl(alkoxycarbonyl)ketenes.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 419–421, February, 1993.     

Enantioselective synthesis of hydroxy-substituted α-methyl-α-amino acids using Al and Mn derivatives of cyclo-(L-Ala-L-AIa) bis-Iactim ethers

Aluminum and manganese derivatives of lithiated bis-lactim ethers of cyclo-(L-Ala-L-Ala) were used for the enantioselective synthesis of -hydroxy and polyhydroxy -amino acids of the 2-methyIserine series. A new variant of the synthesis of these acids via 3-acyl-2, 5-dialkoxy-3, 6-dimethyl-3, 6-dihydropyrazines is proposed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 590–595, March, 1993.     

Primal-dual interior point approach for computingl 1-solutions andl ∞-solutions of overdetermined linear systems

This paper concerns solving an overdetermined linear systemA ^T x=b in the leastl ₁-norm orl -norm sense, whereA ^m×n ,m<n. We show that the primal-dual interior point approach for linear programming can be applied, in an effective manner, to linear programming versions of thel ₁ andl -problems. The resulting algorithms are simple to implement and can attain quadratic or superlinear convergence rate. At each iteration, the algorithms must solve a linear system with anm×m positive-definite coefficient matrix of the formADA ^T , whereD is a positive diagonal matrix. The preliminary numerical results indicate that the proposed algorithms offer considerable promise.This research was supported in part by Grants NSF DMS-91-02761 and DOE DE-FG05-91-ER25100.     

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.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.