A category Ψ-density topology

Ψ-density point of a Lebesgue measurable set was introduced by Taylor in [Taylor S.J., On strengthening the Lebesgue Density Theorem, Fund. Math., 1958, 46, 305–315] and [Taylor S.J., An alternative form of Egoroff’s theorem, Fund. Math., 1960, 48, 169–174] as an answer to a problem posed by Ulam. We present a category analogue of the notion and of the Ψ-density topology. We define a category analogue of the Ψ-density point of the set A at a point x as the Ψ-density point at x of the regular open representation of A.     

Small cliques in random graphs

For d ≥ 1, a d-clique in a graph G is a complete d-vertex subgraph not contained in any larger complete subgraph of G. We investigate the limit distribution of the number of d-cliques in the binomial random graph G(n, p), p = p(n), n→∞.     

Liquid phase hydrogen transfer to cyclopentanone over MgO-I2 and MgO-RI catalysts

Instead of cyclopentanol, 2-cyclopentylidene-cyclopentanone is the main product of liquid phase hydrogen transfer from secondary alcohols to cyclopentanone in the presence of pure MgO [1]. In the present work it has been shown that a significant increase in the selectivity towards cyclopentanol has been observed for MgO treated with I₂ or alkyl iodides.     

Spectroscopic, mass spectrometry, and semiempirical investigations of a new 2-(2-methoxyethoxy)ethyl ester of Monensin A and its complexes with monovalent cations

A new 2-(2-methoxyethoxy)ethyl ester of Monensin A (MON7) has been synthesized and its capability of complex formation with Li⁺, Na⁺, and K⁺ cations has been studied by ESI MS, ¹H and ¹³C NMR, FT-IR, and PM5 semiempirical methods. ESI mass spectrometry indicates that MON7 forms complexes with Li⁺, Na⁺, and K⁺ of exclusively 1:1 stoichiometry which are stable up to cv = 70 V. The formation of complexes between MON7 and Na⁺ cations is strongly favored. Starting from about cv = 90 V fragmentation of the respective complexes is observed, primarily characterized by several dehydration steps. The structures of the MON7 complexes with Li⁺, Na⁺, and K⁺ cations are stabilized by intramolecular hydrogen bonds in which the OH groups are always involved. The structures are visualized and discussed in detail. It has been proved that the formation of a pseudo crown ring structure formed by MON7 is preferred in complexes with Na⁺ cations.     

Accurate determination of individual lanthanides in biological materials by NAA with pre-and post-irradiation separation

An intelligent hydrogel with both pH and temperature sensitivity was obtained by grafting acrylic acid and dimethylaminoethylmethacrylate onto preirradiated polypropylene (PP) film by two-step reactions. The effect of first and second reactions on the degree of grafting was studied. The grafted sample films were checked by Fourier transform infrared spectrophotometry in the attenuated total reflectance mode. The morphology of the PP samples was observed by scanning electron microscope in different conditions before and after grafting, respectively.     

Hypergeometric Type Functions and Their Symmetries

The paper is devoted to a systematic and unified discussion of various classes of hypergeometric type equations: the hypergeometric equation, the confluent equation, the F ₁ equation (equivalent to the Bessel equation), the Gegenbauer equation and the Hermite equation. In particular, recurrence relations of their solutions, their integral representations and discrete symmetries are discussed.     

New lacunar-type and pendant groups containing derivatives of β-unsubstituted dibenzotetraaza[14]annulenes—syntheses and crystal structures

Three new lacunar-type derivatives of β-unsubstituted dibenzotetraaza[14]annulene have been synthesized along with a range of their open-chain pendant group containing counterparts. The crystal structures of two representative products have been determined and the noncovalent interactions explored. A number of C-H?π and π?π interactions involving aliphatic chains and aromatic regions of the macrocycle have been evidenced. The relative ease and high yield of lacunization are suggested to be largely due to self-assembly processes, driven by favorable noncovalent interactions between reacting units.