Integral–geometrical consideration of density matrices

The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM ) as well as the problem of reconstruction of the N-particle system density matrices (N-DM ) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θ are represented using particular values (at specially chosen ) of the Radon transform of the N-DM spatial parts (or their sums) ??_Nλ(x′ | x″) (here, is a d-plane in the n-space ?ⁿ of x = (x′, x″)), with n = 6N, d = 3 (N ? k), x′ ≡ (r′₁, ?, r′_N), x′ ≡ (r₁″, ?, r″_N ()). In this way, the problem is reduced to investigation of the properties of the functions . For a normalizable N – DM , it is proved that are bounded functions. The properties of implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. © 1995 John Wiley & Sons, Inc.     

The polysaccharide extracts from the fungi Coprinus comatus and Coprinellus truncorum do exhibit AChE inhibitory activity

The polysaccharide (PSH) extracts from the edible mushroom species Coprinus comatus and Coprinellus truncorum were screened in liquid for their acetylcholinesterase inhibitory (AChE) activity. Both extracts were found to display inhibition of the aforementioned enzyme reaching similar IC₅₀ values of 0.62 ± 0.07 and 0.61 ± 0.03 mg/mL, respectively. According to the means of FTIR spectroscopy, these PSH extracts mostly contained β-glucans. However, the presence of some proteins and polyphenolics as minor ingredients were also detected. Compared with existing literature data for anti-AChE activity of the sugar samples, the findings within this study may be treated as a profound bioactivity. Consequently, this study puts some light on the possible use of the screened macrofungi in the palliative treatment of Alzheimer’s disease.     

Carbon-carbon coupling constants - a new guide in the stereochemistry of oximes

A positive contribution of more than 7 Hz to the direct ¹³C-¹³C spin-spin coupling constants induced by the proximity of the nitrogen lone pair in syn-orientation to the coupled nuclei allows an unambiguous configuration assignment of diverse oximes.     

Relating Total π-Electron Energy and Resonance Energy of Benzenoid Molecules with Kekulé- and Clar-Structure-Based Parameters

Within classes of isomeric benzenoid hydrocarbons various Kekulé- and Clar-structure-based parameters (Kekulé structure count, Clar cover count, Herndon number, Zhang–Zhang polynomial) are all mutually correlated. This explains why both the total π-electron energy (E), the Dewar resonance energy (DRE), and the topological resonance energy (TRE) are well correlated with all these parameters. Nevertheless, there exists an optimal value of the variable of the Zhang–Zhang polynomial for which it yields the best results. This optimal value is negative-valued for E, around zero for TRE, and positive-valued for DRE. A somewhat surprising result is that TRE and DRE considerably differ in their dependence on Kekulé- and Clar-structure-based parameters.     

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.