Asymptotically independent topological indices on random trees

Topological indices are graph invariants used in computational chemistry to encode molecules. A frequent problem when performing structure-activity studies is that topological indices are inter-correlated. We consider a simple topological index and show asymptotic independence for a random tree model. This continues previous work on the correlation among topological indices. These findings suggest that a size-dependence in a certain class of distance-based topological indices can be eliminated.AMS subject classification: 05C80, 60E10, 92E10     

The formation of lactams of N-(2-amino)benzoylamino acids

N-(2-Nitro)benzoylamino acids were prepared by 2-nitrobenzoylation of amino acids via the mixed ethylcarbonic anhydride procedure. They were reduced catalytically to N-(2-amino)benzoylamino acids which underwent cyclization to the corresponding lactams under a variety of conditions. The use of this reaction sequence for stepwise degradation of peptides seems possible.     

Fast spatially localised electrooptical mode in vertically aligned nematic LCs with negative dielectric anisotropy

ABSTRACT

Electro-optical switching and the liquid crystal (LC) director distribution are studied in spatially periodic electric field for vertically aligned LC with negative dielectric anisotropy. Two electro-optical switching modes characterised by different switching times are observed. These modes are well distinguished optically by choosing proper geometry for the polarisers axes orientation. One of these modes is significantly faster as compared to the other. The fast switching is explained in terms of localised near-to-surface director reorientation. The 3D-numerical simulation shows very good agreement with the experiment: it points out the existence of the disclination lines and field-stabilised walls responsible for the localised director field switching and its relaxation. Possibilities of enhancing the fast mode for high-speed light modulators are discussed.     

Four cyclo­alkane­spiro‐4′‐imidazolidine‐2′,5′‐dithiones

The crystal structures of four cyclo­alkane­spiro‐4′‐imidazolidine‐2′,5′‐dithiones, namely cyclo­pentane­spiro‐4′‐imidazolidine‐2′,5′‐dithione {systematic name: 1,3‐diaza­spiro­[4.4]­nonane‐2,4‐dithione}, C₇H₁₀N₂S₂, cyclo­hexane­spiro‐4′‐imidazolidine‐2′,5′‐dithione {systematic name: 1,3‐diaza­spiro­[4.5]decane‐2,4‐dithione}, C₈H₁₂N₂S₂, cyclo­heptane­spiro‐4′‐imidazolidine‐2′,5′‐dithione {systematic name: 1,3‐diaza­spiro­[4.6]undecane‐2,4‐dithione}, C₉H₁₄N₂S₂, and cyclo­octane­spiro‐4′‐imidazolidine‐2′,5′‐dithione {systematic name: 1,3‐di­aza­spiro­[4.7]dodecane‐2,4‐dithione}, C₁₀H₁₆N₂S₂, have been determined. The three‐dimensional packing in all of the structures is based on closely similar chains, in which hydantoin moieties are linked through N—H⋯S hydrogen bonding. The size of the cyclo­alkane moiety influences the degree of its deformation. In the cyclo­octane compound, the cyclo­octane ring assumes both boat–chair and boat–boat conformations.     

Express detection of nonylphenol in water samples by fluorescence polarization immunoassay

The development of express method for detection of endocrine-disrupting chemicals (EDC) such as alkylphenols is required for ecological monitoring. Several attempts have been made to produce antibodies against 4-nonylphenol (NP) in recent years. This work describes the production of new antibodies against NP and also summarizes the characterization of antibodies obtained earlier. Three approaches used to produce alkylphenol-specific antibodies are compared; these are based on: 1. omega-(4-hydroxyphenyl)nonanoic or omega-(4-hydroxyphenyl)heptanoic acid NP derivatives designed to mimic the linear NP isomer; 2. 4-aminophenol, which potentially mimics various substituted phenolic compounds with different side-chain structures at position 4 of the benzene ring; and 3. a mixture of branched NP isomers, conjugated to the carrier protein via a benzene ring by the Mannich reaction, and expected to be the closest mimic of NP structure by preserving its natural alkyl moiety.Fluorescence polarization immunoassays based on different combinations of antibody and labeled antigen for screening detection of NP were developed and structural aspects of assay sensitivity and specificity were investigated. The assays based on the antisera raised against omega-(4-hydroxyphenyl)nonanoic acid and NP conjugate via Mannich reaction are capable of express detection of NP with detection limit of 7 microg mL(-1 )and assay dynamic range of 18-300 microg mL(-1).     

Fractional integrals and weakly singular integral equations of the first kind in then-dimensional ball

The purpose of the paper is to introduce and to investigate a new class of fractional integrals connected with balls in ?ⁿ. A Riesz potentialI _Ω ^α ρ over a ball Ω is represented by a composition of such integrals. Using this representation we obtain necessary and sufficient solvability conditions for the equationI _Ω ^α ρ =f in the space L_p(Ωw) with a power weight w(x) and solve the equation in a closed form. The investigation is based on a special Fourier analysis adopted for operators commuting with rotations and dilations in ?ⁿ.     

Quantum-algebras and elliptic algebras

We define a quantum-algebra associated to as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary-algebra of , or theq-deformed classical-algebra algebra of . We construct free field realizations of the quantum-algebra and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in.The research of the second author was partially supported by NSF grant DMS-9501414.     

Oxidative coupling of malononitrile with formation of 1,1,2,3,3-pentacyanopropene salts

A simple and convenient route for the synthesis of 1,1,2,3,3-pentacyanopropene salts is reported. These salts are formed by interaction of malononitrile with SeO₂ in presence of organic N-containing bases or pyridinium salts.     

Extraction of environmental information from large aerosol data sets through combined application of cluster and factor analyses

To reveal useful environmental information which is contained in large analytical data sets, an approach, based on the successive application of hierarchical cluster analysis and factor analysis, is proposed. Estimation criteria to determine the most suitable number of clusters and/or factors, are discussed and the interpretation of the cluster and factor analyses results is performed using visual techniques. The data sets were obtained by scanning electron microscope-energy-dispersive X-ray analysis of individual North Sea aerosol particles.