Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

Reaction kinetics and pathway of hydrothermal decomposition of aspartic acid

The kinetics and pathway of hydrothermal decomposition of aspartic acid were studied using a continuous‐flow tubular reactor. The reaction was carried out in the temperature range of 200–260°C and at a pressure of 20 MPa. Deamination was the primary reaction, indicated by the presence of significant amount of ammonia, fumaric acid, or maleic acid in the products. Other reaction products were pyruvic acid, malic acid, and traces of succinic and lactic acid. Traces of alanine were also detected, showing the possibility of decomposing high‐molecular weight amino acids to obtain simple amino acids such as glycine or alanine. Results on the effect of reaction parameters demonstrated that decomposition of aspartic acid is highly temperature dependent under hydrothermal conditions. For a slight temperature difference of 60°C (from 200 to 260°C), the first‐order reaction rate constants of 0.003 significantly increased to 0.231 s^?1. The activation energy was 144 kJ/mol, as calculated by the Arrhenius equation. No significant effect was exhibited by other reaction parameters such as pH and pressure. The results are useful in controlling the hydrolysis of proteinaceous materials toward high yield of aspartic acid under hydrothermal conditions. © 2007 Wiley Periodicals, Inc. 39: 175–180, 2007     

Crystal and molecular structure of thiamine monochloride

The crystal and molecular structure of thiamine monochloride (C₁₂H₁₇N₄OSCl) was determined by X-ray diffraction and refined to a finalR value of 0.042. The compound crystallizes in the monoclinic system, space groupP2₁/a, with cell constantsa=18.929(4),b=11.663(2),c=6.376(2) Å and=96.72(8)°. The thiamine molecule is anhydrous and unprotonated, and the torsion angles at the methylene carbon show that it possesses anF conformation. The dihedral angle value of 84.16(6)° between thiazolium and pyrimidine rings is in the normal range found for the thiamine withF conformation, protonated or not, hydrated or not. Thiamine therefore has the same conformation notwithstanding protonation or hydration, with the rings similarly oriented in all the crystal structures containing thiamine.     

Preparation of bisdiazoalkane and related complexes from the reactions of diazo compounds with the dinitrogen complexestrans-[M(N2)2(Ph 2PCH2CH2PPh 2)2] (M=Mo or W)

Summary Reactions oftrans-[M(N₂)₂(dppe)₂] (A;M=Mo, W;dppe=Ph ₂PCH₂CH₂PPh ₂) with ethyldiazoacetate, N₂CHCOOEt, yield the bisdiazoalkane speciestrans-[M(N₂CHCOOEt)₂(dppe)₂], upon simple replacement of the dinitrogen ligand by ethyldiazoacetate. However, diazomethane, N₂CH₂, reacts withA with loss of N₂ to give products which we tentatively formulate as containing methylene ligands,trans-[M(CH₂)₂(dppe)₂].

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Herstellung von Bisdiazoalkan- und ähnlichen Komplexen aus den Reaktionen von Diazoverbindungen mit Distickstoffkomplexen des Typstrans-[M(N₂)₂(Ph ₂PCH₂CH₂PPh ₂)₂] mitM=Mo oder W

Zusammenfassung Die Reaktion vontrans-[M(N₂)₂(dppe)₂] (A:dppe=Ph ₂PCH₂CH₂PPh ₂ undM=Mo oder W) mit Ethyldiazoacetat, N₂CHCOOEt, ergab nach einfachem Austausch des Distickstoffliganden mit Ethyldiazoacetat die Bisdiazoalkanetrans-[M(N₂CHCOOEt)₂(dppe)₂]. Diazomethan (N₂CH₂) hingegen reagierte mitA unter Verlust von N₂ zu Produkten, die tentativ alstrans-[M(CH₂)₂(dppe)₂] mit Methylenliganden formuliert wurden.

     

The electronic properties of isocyanides at rhenium—dinitrogen binding sites. Preparation and redox properties of the isocyanide complexes trans-[ReCl(CNR)(Ph2PCH2CH2PPh2)2]

The isocyanide complexes trans-[ReCl(CNR)(dppe)₂] (R  Me, Bu^t, C₆H₄CH₃-4, C₆H₄CH₃-2, C₆H₄Cl-4, C₆H₄OCH₃-4 and C₆H₃Cl₂-2,6; dppe  Ph₂PCH₂CH₂PPh₂) have been prepared by isocyanide displacement of dinitrogen from the parent complex trans-[ReCl(N₂)(ddpe)₂]. Their redox properties have been studied by cyclic voltammetry and are interpreted on the basis of the electronic properties and the geometry of the ligating isocyanides which are believed to be bent in these complexes, appearing to exhibit ligand parameter (P_L) values ca. +0.3 V higher than those which would be expected for linear geometry. A very high polarisability (B ? 3.4) is observed for the {ReCl(dppe)₂} site.     

Solid-state photodimerization of steroid enones

Androst-4-ene-3,17-dione (1) and 17alpha-methyltestosterone (2) are dimerized in the solid-state by UV radiation. These substances were selected by a search in the CSD among the steroid enones presenting in the crystalline state an intermolecular short contact between a hydrogen alpha to a carbonyl group and the oxygen of an enone system. Dimerization occurs by transfer of the hydrogen to the oxygen and connection between the two involved carbons. Androst-4-ene-3,17-dione (1) affords dimer 3 and trimer 4, both formed by connection of the C-16 of a molecule with the C-3 of a near one. Irradiation of 17alpha-methyltestosterone (2) gives the isomeric trienones 5 and 6. These compounds are reasonably formed by dehydration of unisolated intermediate products 7 and/or 8 obtained by coupling of two molecules through a linkage between the C-2 and the C-3' carbons. The formation mechanisms of the photoproducts are satisfactory explained on the basis of the molecular arrangement of the monomers in the crystal state. Modeling of the dimeric molecules was done using molecular mechanics calculations. A single-crystal X-ray of the dimer of androst-4-ene-3,17-dione confirms the structural interpretation of spectral data. The conformer found in the solid-state agrees well with the results of molecular mechanics calculations.