On interpolation of bilinear operators

In this paper we study interpolation of bilinear operators between products of Banach spaces generated by abstract methods of interpolation in the sense of Aronszajn and Gagliardo. A variant of bilinear interpolation theorem is proved for bilinear operators from corresponding weighted c₀ spaces into Banach spaces of non-trivial the periodic Fourier cotype. This result is then extended to the spaces generated by the well-known minimal and maximal methods of interpolation determined by quasi-concave functions. In the case when a maximal construction is generated by Hilbert spaces, we obtain a general variant of bilinear interpolation theorem. Combining this result with the abstract Grothendieck theorem of Pisier yields further results. The results are applied in deriving a bilinear interpolation theorem for Calderón-Lozanovsky, for Orlicz spaces and an embedding interpolation formula for (E,p)-summing operators.     

Die polarographische reduktion von NO3− in gegenwart von CrO42−

It has been observed, that on the d.c. polarograms of nitrate, even at the very small concentration of CrO₄^2? (of the order 10^?7 mol dm^?3) a maximum appears at the potential ?1.7 V. The maximum is of catalytic nature and may be used for analytical purposes.     

Polymer Inclusion Compounds by Polymerization of Monomers in β-Cyclodextrin Matrix in DMF Solution

The investigations of the synthesis of polyrotaxanes by the radical polymerization of monomers (vinylidene chloride, methyl acrylate, styrene, and methacrylonitrile) in DMF in the presence of β-cyclodextrin have been carried out. The possibility of formation β-cyclodextrin inclusion compounds with some vinyl monomers or some other organic substances in DMF solution has been established. We assume that the inclusion in presence of the solvent is related to the unusual phenomenon of β-cyclodextrin crystallization in hot DMF solutions. The polymerization of vinyl monomers in DMF solution at increased temperatures in the presence of β-cyclodextrin leads to compounds containing a great amount of cyclic compounds (up to 80%). Similar results have been obtained for monomers introduced as previously prepared adducts with β-cyclodextrin. Stable compounds of polymer and β-cyclodextrin have been obtained in the case of vinylidene chloride. The lack of carbohydrate moieties in the product obtained by polymerization of vinylidene chloride in the presence of linear dextrin suggest the inclusion character of the linkage between polymer and β-cyclodextrin molecules. The structure of a topological compound of polyrotaxane type is most feasible after dehydrochlorination.     

Magnetite nanowires in MCM-41 type mesoporous silica templates

MCM-41 mesoporous material was chosen as a template of very small Fe₃O₄ particles. The results of structural and magnetic studies of magnetite nanowires are reported. The average length of these nanowires is about 70 nm and their diameter is 3 nm. Magnetite polycrystalline nanowires were characterized by means of X-ray diffraction and ⁵⁷Fe Mössbauer spectroscopy (MS). Almost 80% of the particles exist in a superparamagnetic state at room temperature. Mössbauer measurements also provided evidence that the composites displayed a distribution of magnetic particles by size. As a result, strong changes of superparamagnetic and magnetic relative contributions along with temperature were observed.     

Products of operator ideals and extensions of Schatten classes

We study relations between Schatten classes and product operator ideals, where one of the factors is the Banach ideal Π_E,2 of (E, 2)‐summing operators, and where E is a Banach sequence space with ?₂ ? E. We show that for a large class of 2‐convex symmetric Banach sequence spaces the product ideal Π_E,2 ○ ??^a_q,s is an extension of the Schatten class ??_F with a suitable Lorentz space F. As an application, we obtain that if 2 ≤ p, q < ∞, 1/r = 1/p + 1/q and E is a 2‐convex symmetric space with fundamental function λ_E(n) ≈? n^1/p, then Π_E,2 ○ Π_q is an extension of the Schatten class ??r,q (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

New reactions of gamma-halocarbanions: simple synthesis of substituted tetrahydrofurans

The treatment of 4-chlorobutyronitrile, 3-chloropropyl phenyl sulfone, and other related compounds with a base afforded gamma-halocarbanions that undergo fast intramolecular substitution of the halogen to produce substituted cyclopropanes. We found that these short-lived carbanionic intermediates can be trapped with active external electrophilic partners, such as aldehydes, to give the aldol anions. These anions then undergo rapid intramolecular substitution of chloride to produce 2,3-disubstituted tetrahydrofurans. Under the right conditions, yields of tetrahydrofurans are excellent. Similar reactions with ketones gives 2,2,3-trisubstituted furans, but this process is usually less efficient. Ratios between the rates of intramolecular and intermolecular processes were qualitatively estimated by competitive experiments. It was shown that gamma-halo and gamma-trimethylammonium substituents substantially increase the kinetic CH acidity of alkane nitriles and sulfones.     

Influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium

This work concerns an analysis of the influence of a rigid skeleton pore structure on wave propagation in a fluid-filling porous medium. The analysis is based on the continuum theory of a deformable porous medium in which the pore structure is described by two macroparameters. Considerations comprise two questions: the influence of the pore structure on wave-propagation velocity analysed for the quasilinear case and the role of structure in the reflection-refraction wave phenomenon in fluid at the contact surface of two porous media. It has been shown that the pore structure reduces the velocity of wave and together with the angle of incidence it defines the reflection-refraction wave phenomenon.