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     

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.     

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.     

Kinetics of thermal decomposition of MCO3 to MO (M=Ca,Sr and Ba)

The kinetics of the thermal decompositions of CaCO₃, SrCO₃ and BaCO₃ into their oxides were studied by thermogravimetry at constant and linearly increasing temperatures. The kinetics of the isothermal decompositions of calcium and strontium carbonates were described by the lawR _n =1–(1–)^1/n , wheren=1.8 and 1.2, respectively. The kinetics of the non-isothermal decompositions of the two carbonates, analysed by the Ozawa and Coats-Redfern methods, were in keeping with the isothermal kinetics. True kinetic compensation laws were established for each decomposition of the two carbonates, including the data under both isothermal and non-isothermal conditions.As concerns the decompositions of BaCO₃, however, there was some difference between the kinetic features relating the isothermal and non-isothermal conditions. A true kinetic compensation law was not established in this case.

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Zusammenfassung Die Kinetik der thermischen Zersetzung von CaCO₃, SrCO₃ und BaCO₃ zu den Oxiden wurden durch Thermogravimetrie bei konstanter und linear ansteigender Temperatur untersucht. Die Kinetik der isothermen Zersetzung von Calcium- und Strontium-carbonat folgt dem GesetzR _n =1–(1 –)^1/n, won=1,8 bzw. 1,2. Die Kinetik der nichtisothermen nach den Methoden von Ozawa und Coats-Redfern analysierten Zersetzung der zwei Carbonate ist in Übereinstimmung mit der isothermen Zersetzung. Wahre kinetische Kompensationsgesetze wurden für die Zersetzung der beiden Carbonate erhalten, einschließlich der sich sowohl auf isotherme als auch auf nichtisotherme Bedingungen beziehenden Daten. Was die Zersetzung von Bariumcarbonat betrifft, so wurden einige Unterschiede im kinetischen Verhalten bei der Zersetzung unter isothermen und nichtisothermen Bedingungen festgestellt. Ein wahres kinetisches Kompensationsgesetz konnte in diesem Falle nicht ermittelt werden.

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, . R _n =1–(1–)^1/n , , , 1,8 1,2. , -, . « » , . , , . - «» .

     

Thermal dehydration of lithium metaborate dihydrate and phase transitions of anhydrous product

Reaction steps and mechanisms of the thermal dehydration of lithium metaborate dihydrate were investigated by means of thermoanalytical measurements, high temperature powder X-ray diffractometry, FT-IR spectroscopy, and microscopic observations. The first half of thermal dehydration was characterized by the melting of the sample producing viscous surface layer, the formation of bubbles on the particle surfaces, and the sudden mass-loss taking place by an opportunity of cracking and/or bursting of the bubble surface layer. The second half of the dehydration with a long-tailed mass-loss process in a wide temperature region was divided further into three distinguished reaction steps by the measurements of controlled rate thermal analysis. During the course of the thermal dehydration, four different poorly crystalline phases of intermediate hydrates were observed, in addition to an amorphous phase produced by an isothermal annealing. Just after completing the thermal dehydration, an exothermic DTA peak of the crystallization of β-LiBO₂ was appeared at around 750 K. The phase transition from β-LiBO₂ to α-LiBO₂ was observed in the temperature range of 800-900 K, which subsequently melted by indicating a sharp endothermic DTA peak with the onset temperature at 1101.4 ± 0.6 K.     

Heterodimerization of olefins. 1. Hydrovinylation reactions of olefins that are amenable to asymmetric catalysis

Through a systematic examination of ligand and counterion effects, new protocols for a nearly quantitative and highly selective codimerization of ethylene and various functionalized vinylarenes have been discovered. In a typical reaction, 4-bromostyrene and ethylene undergo codimerization in the presence of 0.0035 equiv each of [(allyl)NiBr]2, triphenylphosphine, and AgOTf in CH2Cl2 at -56 degrees C to give 3-(4-bromophenyl)-1-butene in >98% yield and selectivity. Corresponding reactions with [(allyl)PdX]2 are much less efficient and less selective and may require further optimization before a viable system can be identified. Another useful protocol that gives comparable yield and selectivity involves the use of a single-component catalyst prepared from allyl 2-diphenylphosphinobenzoate, Ni(COD)2, and (C6F5)3B. Recognition of a synergistic relationship between a chiral hemilabile ligand (for example, (R)-2-methoxy-2'-diphenylphosphino-1,1'-binaphthyl, MOP) and a highly dissociated counteranion (BARF or SbF6) in an enantioselective version of the Ni-catalyzed reaction raises the prospects of developing a practical route for the synthesis of 3-arylbutenes. Several pharmaceutically relevant compounds, including widely used 2-arylpropionic acids, can be synthesized from these key intermediates. This reaction appears to be quite general. Synthesis of several new 2-diphenylphosphino-1,1-binaphthyl derivatives, prepared to probe the effect of hemilabile coordination on the efficiency and selectivity of the reaction, are also described.