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.     

Separation of Monovinyl and Divinyl Protochlorophyllides Using C30 Reverse Phase High Performance Liquid Chromatography Column: Analytical and Preparative Applications

A new, high performance liquid chromatography method has been developed for the separation of monovinyl- and divinyl-protochlorophyllides, using commercially available, C₃₀ reverse phase column and isocratic elution. This method can be used both for analytical applications and preparative scale purification of monovinyl- and divinyl-protochlorophyllides using the same column where submilimolar concentrations of the crude protochlorophyllide extract can be separated in one run. The purity of the obtained protochlorophyllides was demonstrated by spectroscopic methods, as well by the formation of aggregates in toluene.     

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.     

A fading effect in the X-ray diffraction contrast of dislocations

Fringes in the dislocation image in X-ray section topography are shown to fade away partially when unpolarized radiation is used. The fading effect is explained in terms of an analogy with the polarization beat in a wedge crystal. The polarization nature of the phenomenon is confirmed through numerical simulations of the contrast.Dedicated to Professor Dr. Ulrich Bonse on the occasion of his 60th birthday     

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.     

Origin of organic gaseous products formed in the thermal decomposition of formates

The gaseous products of the thermal decomposition of formates have been investigated and compared with the products of formaldehyde and synthesis gas transformation under analogous conditions in the presence of the solids formed in the thermal decomposition of particular formates. It was found that formaldehyde transformation leads to organic compounds identical to those obtained in the thermal decomposition of the respective formates, while synthesis gas does not react under such conditions. This fact substantiates the hypothesis that formaldehyde is a precursor of the organic compounds identified in the thermal decomposition of formates. The nature of the organic componds obtained in the thermal decomposition of formates indicates that the formaldehyde formed in the initial stages is then transformed in the Cannizzaro or Tishchenko reactions.

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Zusammenfassung Die gasförmigen Produkte der thermischen Zersetzung von Formiaten wurden untersucht und mit den Produkten verglichen, die bei der Umwandlung von Formaldehyd und Synthesegas unter analogen Bedingungen in Gegenwart von bei der thermischen Zersetzung von speziellen Formiaten gebildeten Feststoffen entstehen. Formaldehydumwandlungen führen zu organischen Verbindungen, die identisch mit denen sind, die bei der thermischen Zersetzung des betreffenden Formiats gebildet werden, während Synthesegas unter solchen Bedingungen nicht reagiert. Dies erhärtet die Hypothese, daß Formaldehyd eine Vorstufe der bei der thermischen Zersetzung von Formiaten identifizierten organischen Verbindungen ist. Die Natur der bei der thermischen Zersetzung von Formiaten auftretenden organischen Verbindungen weist darauf hin, daß das in den ersten Reaktionsschritten gebildete Formaldehyd nach der Cannizzaro-oder Tishchenko-Reaktion weiterreagiert.

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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.     

Quantum spheres

Spaces homogeneous under the action of the quantum SU(2) group are introduced and investigated. These spaces can be considered as noncommutative two-dimensional spheres of different radii. The geometry of the space built from those spheres makes possible one-particle dipole electric transitions with l=0.     

2,2,5,5-tetramethylpyrrolidin-3-one-1-sulfinyl group for 5'-hydroxyl protection of deoxyribonucleoside phosphoramidites in the solid-phase preparation of DNA oligonucleotides

Several nitrogen-sulfur reagents have been investigated as potential 5'-hydroxyl protecting groups for deoxyribonucleoside phosphoramidites to improve the synthesis of oligonucleotides on glass microarrays. Out of the nitrogen-sulfur-based protecting groups so far investigated, the 2,2,5,5-tetramethylpyrrolidin-3-one-1-sulfinyl group exhibited near optimal properties for 5'-hydroxyl protection by virtue of the mildness of its deprotection conditions. Specifically, the iterative cleavage of a terminal 5'-sulfamidite group in the synthesis of 5'-d(ATCCGTAGCCAAGGTCATGT) on controlled-pore glass is efficiently accomplished by treatment with iodine in the presence of an acidic salt. Hydrolysis of the oligonucleotide to its 2'-deoxyribonucleosides upon exposure to snake venom phosphodiesterase and bacterial alkaline phosphatase did not reveal the formation of any nucleobase adducts or other modifications. These findings indicate that the 2,2,5,5-tetramethylpyrrolidin-3-one-1-sulfinyl group for 5'-hydroxyl protection of phosphoramidites, such as 10a-d, may lead to the production of oligonucleotide microarrays exhibiting enhanced specificity and sensitivity in the detection of nucleic acid targets.