ON DIRECT METHOD OF SOLUTION FOR A CLASS OF SINGULAR INTEGRAL EQUATIONS

In this article, by introducing characteristic singular integral operator and associate singular integral equations (SIEs), the authors discuss the direct method of solution for a class of singular integral equations with certain analytic inputs. They obtain both the conditions of solvability and the solutions in closed form. It is noteworthy that the method is different from the classical one that is due to Lu.     

Novel flow injection-fluorometric method for the determination of trace silicate and its application to ultrapurified water analysis

A highly sensitive fluorescence quenching method for the determination of silicate based on the formation of an ion associate between molybdosilicate and Rhodamine B (RB) in nitric acid medium was developed. A flow injection system coupled with a fluorescence detector was used for the measurement of fluorescence intensity at 560 and 580 nm as excitation and emission wavelengths, respectively. The calibration graph for Si showed a linear range of 0.1–5 ng cm⁻³ with correlation coefficient of 0.9999, and the detection limit of 0.06 ng cm⁻³. The proposed method was successfully applied to the determination of silicate in ultrapurified water with satisfactory results.     

Membranes,peptides, and disease: Unraveling the mechanisms of viral proteins with solid state nuclear magnetic resonance spectroscopy

The interplay between peptides and lipid bilayers drives crucial biological processes. For example, a critical step in the replication cycle of enveloped viruses is the fusion of the viral membrane and host cell endosomal membrane, and these fusion events are controlled by viral fusion peptides. Thus such membrane-interacting peptides are of considerable interest as potential pharmacological targets. Deeper insight is needed into the mechanisms by which fusion peptides and other viral peptides modulate their surrounding membrane environment, and also how the particular membrane environment modulates the structure and activity of these peptides. An important step toward understanding these processes is to characterize the structure of viral peptides in environments that are as biologically relevant as possible. Solid state nuclear magnetic resonance (ssNMR) is uniquely well suited to provide atomic level information on the structure and dynamics of both membrane-associated peptides as well as the lipid bilayer itself; further ssNMR can delineate the contribution of specific membrane components, such as cholesterol, or changing cellular conditions, such as a decrease in pH on membrane-associating peptides. This paper highlights recent advances in the study of three types of membrane associated viral peptides by ssNMR to illustrate the more general power of ssNMR in addressing important biological questions involving membrane proteins.     

Formation of polymeric micelles with amino surfaces from amphiphilic AB‐type diblock copolymers composed of poly(glycolic acid lysine) segments and polylactide segments

Amphiphilic AB‐type diblock copolymers composed of hydrophobic poly(L ‐lactide) (PLA) segments and hydrophilic poly(glycolic acid lysine) [poly(Glc‐Lys)] segments with amino side‐chain groups self‐associated to form PLA‐based polymeric micelles with amino surfaces in an aqueous solution. The average diameter of the loose core–shell polymeric micelles for poly(Glc‐Lys) [number‐average molecular weight (M_n) = 1240]‐b‐PLA (M_n = 7000) obtained by a dimethyl sulfoxide/water dialysis method was estimated to be about 50 nm in water by dynamic light scattering measurements. The size and shape of the obtained polymeric micelles were further observed with transmission electron microscopy and atomic force microscopy. To investigate the possibility of applying the obtained PLA‐based polymeric micelles as bioabsorbable vehicles for hydrophobic drugs, we tested the entrapment of drugs in poly(Glc‐Lys) (M_n = 1240)‐b‐PLA (M_n = 7000) micelles and their release with doxorubicin as a hydrophobic drug. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 1426–1432, 2002     

Geometrical and Topological Properties of Real Polynomial Fibres

We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of ⁿ . For this we need to study topological properties of a generic hyperplane section of this fibre.     

IR spectra,conformational lability,and intermolecular interactions in long-chain aliphatic compounds

Investigations of the conformational lability and intermolecular interactions in long-chain aliphatic compounds (LACs), namely, in carboxylic acid derivatives (alkyl- and alkoxybenzoic acids; alkylcyclohexanecarboxylic acids and their completely or partially fluoroalkyl-substituted derivatives), 4-cyano-4-p-alkoxybiphenyls, 4-cyano-4-p-alkylbiphenyls, and cholesterol p-n-butyloxybenzoate are reviewed. Major attention is paid to experimental and theoretical IR spectroscopy data. Differential thermal analysis, polarization microscopy, and X-ray diffraction data are also taken into account. A more detailed treatment is presented on IR spectrum simulation based on data about the conformational lability of molecules and their specific (H-bonding) intermolecular interactions. The first mechanism is responsible for the conformational type of polymorphism in LACs and for the structure of the latter in solid crystal (SC) and liquid crystal (LC) states and in isotropic liquids (ILs). The second mechanism complements the structure-forming aspect of polymorphism in carboxylates, which is due to a rearrangement of hydrogen bond systems in H-complexes during polymorphic transitions to the LC and IL states. Both mechanisms are reflected in IR absorption spectra. A more adequate interpretation is possible in order to explain the many spectral features associated with the structure of LAC polymorphs and their H-complexes if these mechanisms are taken into account.Original Russian Text Copyright © 2004 by L.M. BabkovTranslated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 3, pp. 389–397, May–June, 2004.     

The microstructure and Ruppeiner geometry of charged anti-de Sitter black holes in Gauss–Bonnet gravity: from the critical point to the triple point

Ruppeiner geometry has been successfully applied in the study of the black hole microstructure by combining with the small–large black hole phase transition, and the potential interactions among the molecular-like constituent degrees of freedom are uncovered. In this paper, we will extend the study to the triple point, where three black hole phases coexist acting as a typical feature of black hole systems quite different from the small–large black hole phase transition. For the six-dimensional charged Gauss–Bonnet anti-de Sitter black hole, we thoroughly investigate the swallow tail behaviors of the Gibbs free energy and the equal area laws. After obtaining the black hole triple point in a complete parameter space, we exhibit its phase structures both in the pressure–temperature and temperature–horizon radius diagrams. Quite different from the liquid–vapor phase transition, a double peak behavior is present in the temperature–horizon radius phase diagram. Then we construct the Ruppeiner geometry and calculate the corresponding normalized curvature scalar. Near the triple point, we observe multiple negatively divergent behaviors. Positive curvature scalar is observed for the small black hole with high temperature, which indicates that the repulsive interaction dominates among the microstructure. Furthermore, we consider the variation of the curvature scalar along the coexisting intermediate and large black hole curves. Combining with the observation for different fluids, the result suggests that this black hole system behaves more like the argon or methane. Our study provides a first and preliminary step towards understanding black hole microstructure near the triple point, as well as uncovering the particular properties of the Gauss–Bonnet gravity.     

Organosilica composite for preconcentration of phenolic compounds from aqueous solutions

A new adsorbent is proposed for the solid-phase extraction of phenol and 1-naphthol from polluted water. The adsorbent (TX-SiO₂) is an organosilica composite made from a bifunctional immobilized layer comprising a major fraction (91%) of hydrophilic diol groups and minor fraction (9%) of the amphiphilic long-chain nonionic surfactant Triton X-100 (polyoxyethylated isooctylphenol) (TX). Under static conditions phenol was quantitatively extracted onto TX-SiO₂ in the form of a 4-nitrophenylazophenolate ion associate with cetyltrimethylammonium bromide. The capacity of TX-SiO₂ for phenol is 2.4 mg g⁻¹ with distribution coefficients up to 3.4 × 10⁴ mL g⁻¹; corresponding data for 1-naphthol are 1.5 mg g⁻¹ and 3 × 10³ mL g⁻¹. The distribution coefficient does not change significantly for solution volumes of 0.025–0.5 L and adsorbent mass less than 0.03 g; 1–90 μg analyte can be easily eluted by 1–3 mL acetonitrile with an overall recovery of 98.2% and 78.3% for phenol and 1-naphthol, respectively. Linear correlation between acetonitrile solution absorbance (A ₅₄₀) and phenol concentration (C) in water was found according to the equation A ₅₄₀ = (6 ± 1) × 10⁻² + (0.9 ± 0.1)C (μmol L⁻¹) with a detection range from 1 × 10⁻⁸ mol L⁻¹ (0.9 μL g⁻¹) to 2 × 10⁻⁷ mol L⁻¹ (19 μL g⁻¹), a limit of quantification of 1 μL g⁻¹ (preconcentration factor 125), correlation coefficient of 0.936, and relative standard deviation of 2.5%. A solid-phase colorimetric method was developed for quantitative determination of 1-naphthol on adsorbent phase using scanner technology and RGB numerical analysis. The detection limit of 1-naphthol with this method is 6 μL g⁻¹ while the quantification limit is 20 μL g⁻¹. A test system was developed for naked eye monitoring of 1-naphthol impurities in water. The proposed test kit allows one to observe changes in the adsorbent color when 1-naphthol concentration in water is 0.08–3.2 mL g⁻¹.     

Applications of ion associates for the microdetermination of vardenafil using atomic emission spectrometry

A simple, accurate, precise and sensitive method has been developed for the determination of Vardenafil (Vd) using direct coupled plasma atomic emission spectrometry. The ion associates formed as a result of the reaction of vardenafil with ammonium reineckate, Mn(II) and Co(II) thiocyanates and sodium cobaltinitrite are precipitated. The solubility of the solid complexes under the optimum conditions of pH and ionic strength was studied. Saturated solutions of each ion associate at different temperatures under the optimum precipitation conditions were prepared, and the metal ion content in the supernatant was determined. The solubility products were thus calculated at different temperatures, and the thermodynamic parameters ΔH, ΔG and ΔS were calculated. The method has been used for the determination of vardenafil (1.36–68.32 μg·mL⁻¹) in pure solutions and in Levitra tablets.     

Group divisible designs with three unequal groups and larger first index

We show the necessary conditions are sufficient for the existence of group divisible designs (or PBIBDs) with block size k=3 with three groups of size (n,2,1) for any n≥2 and any two indices with λ₁>λ₂.