Bifurcation phenomena associated to a class of p-Laplacian like operators

 Global bifurcation of positive solutions for some degenerate quasilinear elliptic problems is considered. The uniform estimate of the gradient of weak solutions is given. This estimate is crucial in our arguments. Received: 10 August 2001 Supported in part by Grant-in-Aid for Scientific Research (No. 11640207), Ministry of Education, Science, Sports and Culture, Japan. Mathematics Subject Classification (2000): 35B32, 35J25, 35J70     

Laser spectroscopic investigation of salicylic acids hydrogen bonded with water in supersonic jets: Microsolvation effects for excited state proton dislocation

Geometric structures and excited-state proton dislocation of size-selected salicylic acid clusters (salicylic acid and 5-methoxysalicylic acid) with water were studied by using laser spectroscopic techniques. Fluorescence excitation, dispersed fluorescence, and infrared (IR) spectra of those clusters in supersonic jets were examined for both the electronic ground (S0) and first excited (S1) states. The geometric structures of the clusters were determined on the basis of the IR spectra of the OH stretch region with the help of quantum chemical calculations. The hydroxyl group of the water moiety in the clusters forms a ring involving the carboxylic group of the salicylic acid moiety. The IR spectra in S0 show that the intramolecular hydrogen bond in the salicylic acid moiety is still held upon cluster formation, but the phenolic OH stretch band intensity is remarkably weaken in the clusters. The IR spectra in the S1 state and dispersed fluorescence spectra indicated that the intramolecular excited state proton dislocation is hardly affected by the microsolvation with water, in contrast with the strong suppression of the dislocation in the self-solvation.     

Self-cooling effect on the kinetics of nonisothermal dehydration of lithium sulfate monohydrate

The effects of self cooling on the apparent kinetics of the nonisothermal dehydration of crushed crystals of lithium sulfate monohydrate were investigated using TG accompanied by DTA and power-compensation type DSC. Linearity of the sample heating rate on the TG-DSC system is much better than that on the TG-DTA. Kinetic obedience and Arrhenius parameters obtained from the TG-DTA deviate considerably from those obtained from the TG-DSC; the latter are the more accurate due to the better linearity of the sample heating rate.

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Zusammenfassung Mittels TG, ergänzt durch DTA und DSC mit Leistungskompensation wurde der Einfluß des Self-cooling-Effektes auf die scheinbare Kinetik der nichtisothermen Dehydratation von zerkleinerten Kristallen aus Lithiumsulfat-Monohydrat geschätzt. Die mittels TG-DTA erhaltene Kinetik und die Arrheniusschen Parameter weichen erheblich von denen ab, die mittels TG-DSC ermittelt wurden. DSC mit Leistungskompensation und TG-DSC haben gegenüber TG oder TG-DTA den großen Vorteil, das nichtisotherme kinetische Verhalten von Feststoffzersetzungen zu charakterisieren. Mittels Thermoanalyse nichtisotherm ermittelte kinetische Parameter sind ohne Anwendung von DSC eher unreell, besonders wenn sie bei größeren Aufheizgeschwindigkeiten und Probengrößen bestimmt wurden.

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We thank Dr. A. K. Galwey for reading the text and for valuable comments.     

Stereoselective ring-opening polymerization of racemic lactide using aluminum-achiral ligand complexes: exploration of a chain-end control mechanism

Stereoselective polymerization of racemic lactide (rac-LA) was examined using Al-achiral ligand complexes. By introduction of substituents in aromatic rings of Schiff base ligands, a higher selectivity was obtained without any chiral auxiliaries in the catalyst via a chain-end control mechanism. The T(m) values (T(m) 170-192 degrees C) were comparable to or higher than that of homochiral polymer, poly(L-LA) (T(m) 162 degrees C), and a thermally more stable polylactide than poly(L-LA) was prepared from rac-LA.     

Two-color double resonance in the four-photon ionization of nitric oxide

We have measured the two-color double resonance enhanced four-photon ionization and the fluorescence de-enhanced spectra of nitric oxide by using two tunable pulsed dye lasers. The spectra show clear structure in the third-photon (8.2 eV) region. Also discussed is the multiphoton ionization mechanism in the resonance state.     

Stereoselective syntheses of highly functionalized bicyclo[3.1.0]hexanes: a general methodology for the synthesis of potent and selective mGluR2/3 agonists

[Chemical reaction: See text] A Et3Al mediated intramolecular epoxide opening, cyclopropanation reaction is described. The transformation provided highly functionalized bicyclo[3.1.0]hexane systems in high efficiency and with perfect H or F endo selectivity. Application of this reaction to the synthesis of mGluR2/3 agonist 1 (43% overall yield) and a few intermediates suitable for the synthesis of other bicyclo[3.1.0]hexane mGluR2/3 agonists is discussed.     

Pheromone synthesis—63 Synthesis of both the enantiomers of 2,3-dihydro-2- isopropyl-2,5-dimethylfuran,a sex specific compound in females of the beetle hylecoetus dermestoidesL

Both the enantiomers of 2,3-dihydro-2-isopropyl-2,5-dimethylfuran were synthesized employing the Sharpless asymmetric epoxidation reaction. The (R)-(—)-enantiomer of this cyclic enol ether was also synthesized starting from (R)-(—)-linalool.