On the existence and the stability of solutions for higher-order semilinear Dirichlet problems

We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.     

Influence of organic modifiers on morphology and crystallization of poly(ϵ‐caprolactone)/synthetic clay intercalated nanocomposites

ε‐caprolactone was polymerized in the presence of neat montmorillonite or organomontmorillonites to obtain a variety of poly(ε‐caprolactone) (PCL)‐based systems loaded with 10 wt % of the silicates. The materials were thoroughly investigated by different X‐ray scattering techniques to determine factors affecting structure of the systems. For one of the nanocomposites it was found that varying the temperature in the range corresponding to crystallization of PCL causes reversible changes in the interlayer distance of the organoclay. Extensive experimental and literature studies on this phenomenon provided clues indicating that this effect might be a result of two‐dimensional ordering of PCL chains inside the galleries of the silicate. Small angle X‐ray scattering and wide angle X‐ray scattering investigation of filaments oriented above melting point of PCL revealed that polymer lamellae were oriented perpendicularly to particles of unmodified silicate, while in PCL/organoclay systems they were found parallel to clay tactoids. Calorimetric and microscopic studies shown that clay particles are effective nucleating agents. In the nanocomposites, PCL crystallized 20‐fold faster than in the neat polymer. The crystallization rate in nanocomposites was also significantly higher than in microcomposite. Further research provided an insight how the presence of the filler affects crystalline fraction and spherulitic structure of the polymer matrix in the investigated systems. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2350–2367, 2007     

Asymmetric synthesis XXVII: Asymmetric catalytic trimethylsilylcyanation of aldehydes by novel Ti-chiral Schiff base complexes

Enantioselective catalytic trimethylsilylcyanations of aldehydes with 48% to 92% e.e. have been studied using the novel Ti-chiral Schiff base complexes. We have found that the catalyst led to high enantoselectivity when the molar ratio of the Schiff base 1 to Ti(O-i-Pr)₄ was 2:1.     

Structure of 18-cyanoprogesterone,C22H29O2N

The crystal structure of 18-cyanoprogesterone was determined by X-ray diffraction methods:P2₁2₁2₁ a=7.436(2),b=11.322(2),c=22.642(2) Å. The structure was solved usingShelx-86. Final conventionalR=0.054.R _w =0.051 for 1841 reflections. TheA ring has an intermediate sofa-half-chair conformation with asymmetry parameters C _s ^/1 =11.0, C ₂ ^3,4 =14.9. The steroid skeleton exhibits a flattening of theA ring relative to the rest of the molecule. The progesterone side chain has a typical conformation, and the C16-C17-C20-O20 torsion angle is –19.0(6)°.     

Intra- versus intermolecular hydrogen bonds in salicylamide derivatives

The crystal structures, solid-state infrared patterns, and thermal properties of two polymorphs of 4-nitrosalicylanilide are presented. In both polymorphs, intramolecular hydrogen bonds are found between the phenol oxygen and the amide proton, and intermolecular hydrogen bonds are found between the amide carbonyl oxygen and the phenol proton. These hydrogen bond patterns are compared to those found in other known salicylamide derivatives and an analysis is given of the factors contributing to preferences for intra- or intermolecular hydrogen bonds in these structures. Crystal data: polymorph, orthorhombic,Pbca,a=11.003(4),b=27.959(7),c=7.622(5) Å,Z=4,V=2345(3) ų, andR=0.038 (1351 reflections); polymorph, monoclinic,P2₁/a,a=28.36(1),b=11.64(1),c=7.293(8) Å,=90.68(6)°,Z=8,V=2408 ų, andR=0.043 (2425 reflections).     

Protolytic reactions of 3,3'-dimethylnaphthidine and 3,3'-dimethoxybenzidine

The dissociation constants of diprotonated 3,3'-dimethylnaphthidine (DMN) and 3,3'-dimethoxybenzidine (DMB) have been determined spectrophotometrically. They are: pK(a1) = 2.62 +/- 0.03, pK(a2) = 3.33 +/- 0.09 for DMN: pK(a1) = 2.83 +/- 0.07, pK(a2) = 4.05 +/- 0.12 for DMB. The molar absorptivities (l.mole(-1).cm(-1)) of all forms of the indicators have been also determined: epsilon(B) = 1.68 x 10(4), epsilon(BH(+)) = 9.34 x 10(3), epsilon(BH(2+)(2)) = 1.80 x 10(3) at 300 nm for DMB; epsilon(B) = 7.33 x 10(3), epsilon(BH(+)) = 3.73 x 10(3), epsilon(BH(2+)(2)) = 0 at 330 nm for DMN.     

Thermal copolymerization of acrylonitrile with methacrylate units arranged in matrix

Copolymerization of acrylonitrile with methacrylates on a matrix has been examined (using methacrylate of p-cresol-formaldehyde resin). It has been found that the copolymerization proceeds at 70° without an initiator. The reactivity ratios depend on the length of the matrix used. The method of calculating Q and e according to the Alfrey-Price scheme has been discussed for the system under investigation.     

The polymorphic transformations of cobalt molybdate

Polymorphic transformations of CoMoO₄ were studied by means of high temperature X-ray measurements within the temperature range 25–1200°C. On heating phase a obtained from low temperature modification b a new modification a′ was discovered. Phase a obtained by thermal decomposition of solvated α-CoMoO₄ shows different behaviour. At 700–930°C depending on the conditions of preparation it transforms irreversibly into still another modification a″. On cooling, a mixture of phases a + a″ is obtained, the presence of a″ being responsible for the explosionwise transition into b, observed around the room temperature.     

Über eine neue automatische Apparatur zur Zentigramm-Bestimmung von Kohlenstoff und Wasserstoff in organischen Substanzen

Zusammenfassung Das vom Verfasser undE. Sucharda schon 1928 angewandte Prinzip, die durch das Verhalten der Substanz beim Erhitzen bewirkten Druckschwankungen im Verbrennungsrohre zum Zwecke der automatischen Regulierung der Vergasungsgeschwindigkeit der Substanz bei der Elementaranalyse auszunutzen, wurde bei der Konstruktion einer neuen, elektrisch betriebenen, automatischen Apparatur angewandt. Hierbei wird das mit der Substanz gefüllte Mikroschiffchen mittels eines elektrischen Hochfrequenzgenerators erhitzt. Der Stromzufluß zu dem Hochfrequenzgenerator wird durch die erwähnten Druckschwankungen einoder ausgeschaltet. Die Verbrennung verläuft dann bei praktisch konstantem Druck im Verbrennungsrohre, also auch bei konstantem Sauerstoffüberschuß. Die neue Apparatur wird an Hand beigefügter Abbildungen beschrieben. Als Absorptionsmittel für Stickstoffoxyde werden 1 bis 2 g Bleidioxyd in einem 12 cm langen Porzellanschiffchen bei 190° angewandt. Die Absorption des Wassers erfolgt durch wasserfreies Kobaltchlorid, die der Kohlensäure ausschließlich durch Ascarit. Die Sauerstoffgeschwindigkeit im Verbrennungsrohre beträgt 8 ml pro Minute. Bei Substanzen, die mehr als 10% N enthalten, wird zwischen den Kohlensäureabsorptionsapparat und den Wasserabsorptionsapparat ein mit Mangandioxyd gefüllter Apparat eingeschaltet.

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Summary The principle used by the author andE. Sucharda as early as 1928, which employs the variations in pressure in the combustion tube resulting from the behavior of the substance when heated, for automatically regulating the rate of gasifying the substance was applied in the construction of a new electrically operated automatic apparatus. The micro boat charged with the sample is heated by means of a high frequency generator. The flow of current to the high frequency generator is switched on and off by the variations in pressure mentioned above. The combustion then proceeds at practically constant pressure in the combustion tube, and even when there is a constant excess of oxygen. The new apparatus is described in the accompanying figures. The nitrogen oxides are absorbed in 1 to 2 grams of lead dioxide contained in a porcelain boat (12 cm long) at 190°. The absorption of the water is by means of anhydrous cobalt chloride, while the carbon dioxide is taken up in ascarite. The speed of the oxygen in the combustion tube is 8 ml per minute. In the case of samples that contain more than 10% nitrogen, an apparatus filled with manganese dioxide is placed between the carbon dioxide absorber and the apparatus for taking up the water.

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Résumé Le principe de l'utilisation des variations de pression qui se produisent dans un tube à combustion en analyse élémentaire, lors du chauffage de la substance, a été utilisé dès 1928 par l'auteur etE. Sucharda pour la régulation automatique de la gazéification de cette substance. Il a été appliqué à la construction d'un nouvel appareil automatique commandé électriquement. La micronacelle qui contient la substance est chauffée électriquement à l'aide d'un générateur de courant de haute fréquence. Les variations de pression pendant la combustion provoquent l'ouverture ou la fermeture du circuit d'alimentation de ce générateur. Il en résulte que la combustion est effectuée à pression pratiquement constante ainsi qu'à excès d'oxygène constant. Ce nouvel appareil est décrit sur les figures de la publication.On utilise 1 à 2 grammes de bioxyde de plomb disposés dans une nacelle de porcelaine de 12 cm de longueur, portée à 190° pour absorber les oxydes de l'azote. L'eau est absorbée par du chlorure de cobalt anhydre et l'anhydride carbonique exclusivement par de l'ascarite. Le débit du courant d'oxygène dans le tube de combustion est de 8 ml par minute. Pour les substances contenant plus de 10% d'azote, on intercale un absorbeur à bioxyde de manganèse entre l'absorbeur à anhydride carbonique et l'absorbeur à eau.