On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

On bounding the effective conductivity of isotropic composite materials

In this paper inequalities for the effective conductivity of isotropic composite materials are derived. These inequalities depend on several coefficients characterizing the microstructure of composites. The obtained coefficients can be exactly calculated for models of a two-component aggregate of multisized, coated ellipsoidal inclusions, packed to fill all space. As a result, new bounds for effective conductivity, considerably narrower than those of Hashin-Shtrikman, are established for such models of composite materials.     

Trace analysis of rapamycin in human blood by micellar electrokinetic chromatography

A capillary electrophoretic method with UV detection at 278 nm has been developed for analysis of the immunosuppressant rapamycin (sirolimus) in human blood at low microgram per liter levels. Separation has been achieved in an acidic carrier electrolyte containing sodium dodecylsulfate and 30% (v/v) acetonitrile. For sample clean-up and preconcentration, an off-line solid-phase extraction step using a silica-based reversed-phase material and an on-capillary focussing technique were employed. The latter allows the injection of increased sample volumes without excessive band broadening. Although this new method is less sensitive than existing liquid chromatographic procedures combined with mass spectrometry, it is fully suited to routine analysis of rapamycin in blood from patients treated with this drug. Last but not least the low costs make it an attractive alternative to established methods.     

Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

The chemistry of fluorine containing phosphaalkenes, arsaalkenes and selenocarbonyls

This review covers our extensive research activities in the area of fluorine containing phospha- and arsaalkenes as well as selenocarbonyls, which differ considerably in their properties and reactivities from their alkyl and aryl counterparts and thus contribute in a gratifying manner to the still growing field of unsaturated element-carbon compounds of 3rd and 4th row main group elements E. Of particular interest is the influence of the fluorine substituents and other small groups (OR, NR₂) with either inductive and/or mesomeric effects on the polarity and reactivity of the EC bond. Addition reactions of proton acidic and hydridic polar HX reactants as well as [2+2], [3+2] and [4+2] cycloadditions have been thoroughly studied. The results obtained allow a classification of the EC systems within five different types, A to E, and prove a change from “normal” to “inverse” heteroalkenes in this sequence. The ligand properties of some derivatives have also been investigated in some detail.     

Unexpected differences in the alpha-halogenation and related reactivity of sulfones with perhaloalkanes in KOH-t-BuOH

Most alkyl phenyl sulfones are readily alpha-chlorinated with CCl(4) and alpha-brominated with CBrCl3 in KOH-t-BuOH via radical-anion radical pair (RARP) reactions. While isopropyl mesityl sulfone (4) is easily alpha-chlorinated with CCl(4), it was completely recovered when treated with the more reactive CBrCl3. Subsequent investigations showed the latter result to be due to the poor acidity of 4 together with the rapid depletion of CBrCl3 and KOH by their reaction with each other, and led to a variety of other important results. 4-Hydroxyphenyl isopropyl sulfone (6) is unreactive with either CCl4 or CBrCl3 in KOH-t-BuOH, its phenoxide anion strongly reducing the electronegativity of the sulfonyl group, thereby inhibiting alpha-anion formation. This effect is reversed by the electron-withdrawing influence of two alpha-phenyls, so that benzhydryl 4-hydroxyphenyl sulfone (8) is readily alpha-halogenated in KOH-t-BuOH with CCl4 or CBrCl3. On further contact with KOH-t-BuOH the alpha-halogenated sulfones from 8 are decomposed into benzophenone and phenol. While the alpha-halogenated derivatives of 4-methoxyphenyl benzhydryl sulfone (9) are stable to base, they are decomposed even under mildly acidic conditions into 4-methoxyphenyl 4-methoxybenzenethiolsulfonate (9c), phenol, and benzophenone. Mono-alpha-halogenation of benzyl phenyl sulfone (10) enhances the rate of the subsequent halogenation, so that alpha,alpha-dihalogenation is attained while much substrate is still present and the mono-alpha-halogenated product is not detected. The ease of reductive debromination of alpha-bromo sulfones with Cl3C- was correlated with the stability of the formed alpha-anions, explaining the success with alpha-bromobenzylic sulfones but failure with alpha-bromoalkyl sulfones. In the presence of air and the absence of competing halogenation, formation of the alpha-anions of alkyl aryl sulfones is quickly accompanied by oxidative cleavage by atmospheric O2, leading to the formation of arenesulfonyl alcohols, arenesulfonyl halides, and haloarenes.     

Die Bildungsenthalpien einiger Siliciumtetrahalogenid—Pyridin-Addukte

The enthalpies of formation of the addition compounds F₄Si(py)₂, Cl₄Si(py)₂, Br₄Si(py)₂ and I₄Si(py)₄ have been measured calorimetrically by two different ways (see table 1). It was not possible to confirm enthalpy data published in^{7, 8}. The sequence SiF₄4～SiBr₄>SiI₄(?) is proposed for the acceptor power of the silicon tetrahalides towards pyridine.