Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

On existence and asymptotic stability of solutions of a nonlinear integral equation

We prove an existence theorem for a nonlinear integral equation being a Volterra counterpart of an integral equation arising in the traffic theory. The method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question.     

Sensitised decomposition of microcystin-LR using UV radiation

UV radiation was applied to degrade cyanobacterial hepatotoxin, microcystin-LR in the presence of phycocyanin as a model natural sensitiser. The concentrations of both the toxin and the pigment used in the experiments were higher by several orders of magnitude than found in the environment. The photoreaction parameters were optimised. The process was found to be of limited use for water treatment due to its low efficacy. Additionally, pronounced UV-induced bleaching of the pigment significantly reducing the photoreaction rates of the toxin was observed for the highest UV radiation intensities applied.     

Structure and properties of the ion pair charge-transfer complex of octacyanotungstate(IV) with the 2,2′-bipyridinium dication

The X-ray crystal structure of (bpyH2)2[W(CN)8]·4H2 O (bpyH2=2,2-bipyridinium) is described. The [W(CN)8]4– anion has an approximately square antiprismatic (D4d) conformation, seemingly imposed by strong anion–water–cation hydrogen-bonding interactions. Bond distances in the anion are: WC 2.150(5), 2.163(5); CN 1.128(6), 1.145(6)Å and the angles WCN are 177.6(5), 178.3(5)°. The dihydrate and the anhydrous salt are both intensely black solids, exhibiting ion-pair charge-transfer interaction between cation and anion. E.s.r. spectra indicate that 30% of the tungsten is present as WV in the solid state, but that in solution only the WIV complex is present. The electron withdrawing effect of the cation is discussed and compared with that in a series of salts with different bipyridinium cations.     

Synthesis of corroles bearing up to three different meso substituents

[reaction: see text] We have developed a new method that affords regioisomerically pure corroles possessing up to three different substituents at the meso positions. The corrole formation reaction involves the acid-catalyzed condensation of a dipyrromethane-dicarbinol with pyrrole followed by oxidation with DDQ. ABC-Type corroles were synthesized for the first time according to this procedure.     

New insights into the reaction of zinc alkyls with dioxygen

Studies on the reaction of zinc alkyls with O2 are reported which demonstrate that the selective oxygenation of organozinc compound is viable. The reaction of [EtZn(azol)]n (azol = deprotonated 1-aziridineethanol) with an excess of dry O2 in toluene affords the zinc ethylperoxide [EtOOZn(azol)]2[EtZn(azol)]2, while the analogous reaction between Me2Zn and O2 results in the isolation of the Me6Zn7(OMe)8 cluster in high yield.     

Characterization of Titania/Silica Gel by Means of Low-Pressure Nitrogen Adsorption

Adsorbents synthesized by grafting of titania onto mesoporous silica gel surfaces at different temperatures were studied by means of nitrogen adsorption–desorption and water desorption. The pore size distribution f(R_p) of titania/silica gel depends on the titania concentration (C_TiO2) and the temperature of titania synthesis. Nonuniformity of TiO₂ phase is maximal at a low C_TiO2 value (3.2 wt.% anatase deposited at 473 K), and two peaks of the fractal dimension distribution f(D) are observed at such a concentration of titania, but at larger C_TiO2 values, only one f(D) peak is seen. More ordered filling of pores and adsorption sites by nitrogen, reflecting in the shape of adsorption energy distributions f(E) at different pressures of adsorbate, is observed for adsorbent with titania (rutile+anatase) grafted on silica gel at a higher temperature (673 K).     

The analysis of the zero-order and the second derivative spectra of retinol acetate, tocopherol acetate and coenzyme Q10 and estimation of their analytical usefulness for their simultaneous determination in synthetic mixtures and pharmaceuticals

The aim of the present work was to develop a simple and rapid method of retinol acetate, tocopherol acetate and coenzyme Q(10) determination in pharmaceuticals without involving any preparation operations like separation or masking. The values of second derivative amplitude at 212 nm for tocopherol, 351 nm for retinol and 222 nm for coenzyme were used for construction of calibration graphs. Beer's law is obeyed in the concentration range 0.5-20, 0.5-7.5 and 0.5-30 microg ml(-1) for retinol acetate, tocopherol acetate and coenzyme, respectively. The elaborated procedures were successfully applied to the simultaneous determination of studied compounds in their binary synthetic mixtures and in commercial preparations with high reliability and repeatability. Spectral properties of retinol acetate allows to determine its contents in ternary mixture which includes Vitamin E and coenzyme Q(10).     

Fluorescence lifetimes and spectral properties of protochlorophyllide in organic solvents in relation to the respective parameters in vivo

In this work, absorption and fluorescence spectra of protochlorophyllide (Pchlide), as well as its fluorescence lifetime, were investigated in organic solvents having different physical properties. The obtained Pchlide spectral features are discussed in relation to the parameters describing solvent properties (refractive index and dielectric constant) and taking into account the specific solvent-Pchlide interaction. The correlation of Pchlide Qy and Soret absorption bands with solvent polarizability function ((n2 - 1)/(n2 + 2)) has been found; however, the dispersion of the observed points was rather high. A small Stokes shift of a magnitude between 50 and 300 cm(-1) was found, which indicates low sensitivity of Pchlide to nonspecific solvation. The fluorescence decay of Pchlide was single exponential in all the investigated solvents, with the lifetime value ranging from 5.2 ns for dioxane to 3.5 ns for methanol. Dependence of the obtained fluorescence lifetimes on the solvent orientation polarizability, a parameter being the function of both refractive index and dielectric constant, was discussed. In water-methanol mixtures, a further decrease of the fluorescence lifetime was observed, giving values of 2.9 ns for 25% methanol. Double-exponential decay of Pchlide fluorescence was found for Pchlide in a solution of 15% methanol with the lifetimes of 4.5 +/- 0.5 ns and 1.2 +/- 0.3 ns and in pure water with the lifetimes of 2.5 +/- 0.5 ns and 0.4 +/- 0.1 ns. The obtained results are discussed in relation to spectroscopic properties of Pchlide in vivo.     

Chromatographic and spectroscopic investigation of the associative changes with the selected higher fatty alcohols

An attempt was made to compare usefulness of the ir spectroscopic technique with paper chromatography in the investigations concerning self-association of higher fatty alcohols. A conclusion was drawn that only the complementary application of both analytical methods better enabled to trace the establishing of association equilibria in the given experimental conditions.