Synthesis of porous vinylnaphthalene/divinylnaphthalene copolymers and their sorptive properties towards phenol and its derivatives

Four porous vinylnaphthalene/divinylnaphthalene (VN/DVN) polymers having three different nominal crosslinking degrees (60, 80 and 100 wt.%) have been synthesized using the suspension polymerization method in the presence of toluene and decane.The use of various crosslinking levels and inert diluents was aimed at changing the extent of polymeric network-diluent interactions. The resultant polymers have specific surface area in the range 450-700 m²/g depending on the DVN content. Two sets of pores were detected in all resins: one with the diameter of ≈2 nm and the second one in the range of 30-40 nm. Their sorptive properties have been studied using dilute (0.5 mmol/l) solutions of phenol and its derivatives (o-chlorophenol, 2-methylphenol, o-nitrophenol, m-nitrophenol and p-nitrophenol). It has been found that sorption, at low equilibrium concentration, follows the order: o-nitrophenol > o-chlorophenol > m-nitrophenol > o-methylphenol > p-nitrophenol > phenol. Full characteristics of the porous structure of resultant polymers was obtained by nitrogen adsorption at 77 K and their surface properties analyzed using Inverse Gas Chromatography.     

Semigroups of Jensen set-valued functions

A set-valued function F defined on a convex cone S in a real vector space X into the set n(Y) of all non-empty subsets of a real vector space Y is said to be the Jensen function iff $${1\over 2}\lbrack F(x)+F(x)\rbrack=F\lbrack{1\over 2}(x+y)\rbrack$$ for all x, y ∈ S. This note deals with iteration semigroups of Jensen set-valued functions on S.     

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.