Affine selections of convex set-valued functions

Summary It is shown that every convex set-valued function defined on a cone with a cone-basis in a real linear space with compact values in a real locally convex space has an affine selection. Similar results can be obtained for midconvex set-valued functions.     

Natural calcium minerals as catalysts of oxidative conversion of methane

The studies of the influence of the kind of natural calcium mineral and the kind and amount of sodium promoter on the conversion degree of methane and oxygen, selectivity and yield of the oxidative conversion of methane have shown the usability of limestone as a basic component of the catalyst for this process.     

On measurable multifunctions in countably separated spaces

We use an idea of countable separability of points and sets in topological spaces to prove results on intersection of measurable multifunctions and an implicit function theorem. We generalize or extend in part some well known Himmelberg's theorems.     

Every triangle-free planar graph has a planar upward drawing

A planar ordered set has a triangle-free, planar covering graph; on the other hand, there are nonplanar ordered sets whose covering graphs are planar. We show thatevery triangle-free planar graph has a planar upward drawing. This planar upward drawing can be constructed in time, polynomial in the number of vertices.Our results shed light on the apparently difficult problem, of long-standing, whether there is aneffective planarity-testing procedure for an ordered set.Supported in part by the Alexander von Humboldt Stiftung.Supported in part by the Deutsche Forschungsgemeinschaft.     

Synthesis of arylboronates by the palladium catalysed cross-coupling reaction in ionic liquids

The palladium catalysed cross-coupling reaction of aryl iodides and bromides with pinacolborane in 1,3-dialkylimidazolium tetrafluoroborates and hexafluorophosphates producing arylboronates is described.     

Finite-field many-body perturbation theory quadrupole polarizability of Be

Many-body perturbation theory is used for the calculation of the quadrupole polarizability of the Be atom within the finite-field perturbation scheme. The correlation corrections exhibit a considerable dependence on the f-type orbital exponents and the final results are in the range 287–294 au. The convergence of the correlation perturbation series is discussed.     

Evolution and potential of the BiAS procedure for the determination of non-ionic surfactants

The evolution of the BiAS procedure is reviewed and its standard recommended version was compared with the modified version combined with the indirect tensammetric method (BiAS-ITM). New applications of the use of BiAS-ITM for the determination of nonionic surfactants (in the presence of hydrocarbons or adsorbed on particles) and polyethylene glycols were discussed.     

Synthesis and acid-base properties of (1H-benzimidazol-2-yl-methyl)phosphonate (Bimp2-). Evidence for intramolecular hydrogen-bond formation in aqueous solution between (N-1)H and the phosphonate group

The synthesis of (1H-benzimidazol-2-yl-methyl)phosphonic acid, H2(Bimp)+/-, is described: 2-chloromethylbenzimidazole was reacted with ethylchloroformate to give 1-carboethoxy-2-chloromethylbenzimidazole which was treated with trimethyl phosphite and after hydrolysis with aqueous HBr H2(Bimp)+/- was obtained. In H2(Bimp)+/- one proton is at the N-3 site and the other at the phosphonate group; both acidity constants were determined in aqueous solution by potentiometric pH titrations (25 degrees C; I = 0.1 M, NaNO3) and this furnished the pKa values of 5.37 +/- 0.02 and 7.41 +/- 0.02, respectively. The acidity constant for the release of the primary proton from the P(O)(OH)2 group of H3(Bimp)+ was estimated: pKa = 1.5 +/- 0.2. Moreover, Bimp2- can be further deprotonated at its neutral (N-1/N-3)H site to give the benzimidazolate residue, but this reaction occurs only in strongly alkaline solution (KOH); application of the H_ scale developed by G. Yagil (J. Phys. Chem., 1967, 71, 1034) together with UV spectrophotometric measurements gave pKa = 14.65 +/- 0.12. Comparisons with acidity constants taken from the literature show that this latter pKa value is far too large and this allows the conclusion that an intramolecular hydrogen bond is formed between the (N-1/N-3)H site and the phosphonate group of Bimp2-; the formation degree of this hydrogen-bonded isomer is estimated to be 98 +/- 2%. The general relevance of this and the other results are shortly discussed and the species distribution for the Bimp system in dependence on pH is provided.