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.     

A neuro-fuzzy system for X-ray spectra interpretation

A decision scheme for the interpretation of spectra from wavelength dispersive X-ray fluorescence spectrometry is described that encompasses elements from three areas of artificial intelligence: fuzzy logic, rule based expert systems and neural net technology.After transforming the recorded spectra to line spectra by appropriate background correction a reasoning scheme is applied that takes into account not only the observed spectra, but also the recording conditions and prior spectroscopic information regarding the relative emission probabilities and the usefulness of the different lines for the purpose of element identification. The latter is done on the basis of a previously described scheme to compute conditional a posteriori Bayes probabilities for a mean matrix. These different pieces of information are then assembled into a battery of fuzzy rules. The importance of the rules as well as the importance of the X-ray lines is determined in a training process, similar to the one in a feedforward back-propagation network.To further stabilize the results this network is pruned in a second training cycle. This, however, had little effect on the quality of interpretation.The advantages of this approach to the interpretation of X-ray spectra over older ones are numerous: the system adapts itself to better interpret spectra that are of greater importance to a laboratory as these are better represented in the training set; the fuzzy logic is capable of working with incomplete and uncertain knowledge, and the neural network results based on these fuzzy rules is readily interpretable by the X-ray spectroscopist as every rule can be expressed also in natural language as in any classical rule based system.On leave from Silesian University, Katowice, Poland     

Complete Oxidation of Methane over Palladium Supported on Alumina Modified with Calcium,Lanthanum,and Cerium Ions

The activity and thermal stability of Pd/Al_2O_3 and Pd/(Al_2O_3 MO_x)(M=Ca,La,Ce) palladium catalysts in the reaction of complete oxidation of methane are presented in this study.The catalyst supports were prepared by sol-gel method and they were dried either conventionally or with supercritical carbon dioxide.Then they were impregnated with palladium nitrate solution.The catalysts with unmodified alumina had a high surface area.The activity and thermal stability of the alumina- supported catalyst was also very high.The introduction of calcium,lanthanum,or cerium oxide into alumina support caused a decrease of the surface area in the way dependent on the support precursor drying method.These modifiers decreased the activity of palladium catalysts,and they required higher temperatures for the complete oxidation of methane than unmodified Pd/Al_2O_3.The improvement of the palladium activity by lanthanum and cerium support modifier was observed only at low temperatures of the reaction.     

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 and characterization of metal polycarboxylates constructed from lanthanides(iii) and 1,2,4,5-benzenetetracarboxylic acid

The complexes of yttrium(III) and lanthanides(III) with 1,2,4,5-benzenetetracarboxylic acid were prepared as crystalline solids of the general formula Ln₄(C₁₀H₂O₈)₃⋅14H₂O. They are insoluble in water. On heating in air or inert gas atmosphere all compounds lose water molecules; next anhydrous compounds decompose to oxides. The yttrium complex and heavy lanthanide (from Ho to Lu) ones crystallize in monoclinic crystal system. The dehydration does not change the crystal structure of the compounds.     

The synthesis and the solvent and substituent effect on the spectroscopic characteristic of 3-ethyl-2-(p-substitued styryl)benzothiazolium iodides

The photophysical and photochemical properties of p-substitued 2-styryl-ethylbenzothiazolium iodides, possessing different electron-withdrawing or electron-donating groups are described. The dyes were prepared by the condensation of 3-ethyl-2-methylbenzothiazole salts with p-substituted benzaldehydes. The synthesis of suitable substrates is presented as well. We describe here the absorption, emission spectra and the luminescence quantum yield of hemicyanine dyes (SH) measured in 11 different organic solvents of varying polarity. Molecular structure of the synthesized dyes was established by (1)H NMR, electronic absorption and fluorescence spectrometry. The spectral data confirmed that all the compounds exist in E-configuration of their styryl residues. The planar molecular conformation is typical for the compounds with five-membered side aromatic moieties (for example benzothiazole). The compounds possessing N-alkyl substituent in phenyl ring, in contrast to the compounds with other substituents, exhibit low fluorescence quantum yield in THF solution. This indicates that for N-alkyl derivatives the non-radiative processes are much more effective than the radiative ones. The electronic absorption and fluorescence emission spectra of tested dyes demonstrate high sensitivity to the nature of substituent introduced into the aromatic ring.     

Synthesis, characterization and potential biomedical applications of N-succinimidyl ester functionalized, polypyrrole-coated polystyrene latex particles

N-Succinimidyl ester functionalized polypyrrole-coated polystyrene latex particles (PS_E-PPyNSE) were prepared by the in situ copolymerization of pyrrole and the active ester-functionalized pyrrole (pyrrole-NSE) in the presence of polystyrene latex particles. Polystyrene microspheres were prepared by emulsion polymerization (PS_E) leading to particles having a diameter of 450 nm. These PS_E particles were precoated with poly(N-vinylpyrrolidone) prior to the in situ copolymerization of pyrrole and pyrrole-NSE. The initial comonomer concentration fractions were 25/75, 50/50 and 75/25 for pyrrole and pyrrole-NSE, respectively. The PPy-coated PS_E particles were characterized in terms of morphology, particle size, electrophoretic mobility and chemical composition. The study of morphology by means of scanning electron microscopy showed roughening of the underlying PS_E particles owing to the addition of PPyNSE, the overlayer thickness of which was estimated to be around 7 nm. Moreover, loading PPyNSE overlayers resulted in a shift of the electrophoretic mobility from –5.31 m cm/V s to a very small but positive value (0.082–0.112 m cm/V s). X-ray photoelectron spectroscopy and IR spectroscopy permitted the detection of pyrrole-NSE repeat units at the surface indicating that pyrrole and pyrrole-NSE did indeed copolymerize. The PS_E-PPyNSE particles were further evaluated as bioadsorbents of human serum albumin used as a test protein. For this study, PS_E-PPyNSE₅₀ particles, synthesized from a comonomer feed ratio of 50/50 in pyrrole/pyrrole-NSE, were used and were shown to attach efficiently human serum albumin macromolecules with a maximum amount of 0.2 mg m^–2.