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     

Syntheses and properties of dithia‐tetrahomodiaza‐calix[4]arenes bridged by cystine unit

Dithia‐tetrahomodiaza‐calix[4]arenes were synthesized by the cyclization reactions of bis(3‐(chloro‐methyl)‐2‐hydroxyphenyl)sulfide with cystine peptides in moderate yields. Conformational analysis of the macrocycles by using nmr spectroscopy reveled that the cyclophanes adopt a cone‐like form as a preferable conformation and the cystine bridge moiety is incorporated in the cavity. The calixarene analogs can extract transion metals such as Zn²⁺ and Cu²⁺ ions from an aqueous phase into chloroform.     

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.     

Efficient synthesis and hydrolysis of cyclic oxalate esters of glycols

Based on the mechanism postulated for the formation of the cyclic carbonates 3 in the reactions of glycols 1 with oxalyl chloride in the presence of triethylamine, we present here three efficient syntheses of the cyclic oxalates 2 of various glycols 1 by controlling the formation of 3: replacement of the base by pyridine markedly diminishes yields of 3 in all reactions, realizing dramatic reversals of the product ratios in the reactions with the (R*,R*)-compounds 1g-i,q,r and pinacol (1k); although considerable amounts of the oxalate polymers are formed in the reactions with some (R*,S*)-glycols, this drawback can be removed by the use of 2,4,6-collidine instead of pyridine; 1,1'-oxalyldiimidazole is useful for the synthesis of two selected cyclic oxalates 2e,f. The cyclic oxalates 2 other than trisubstituted and tetrasubstituted ones were found to be very reactive: kinetic studies on the hydrolysis of 1,4-dioxane-2,3-dione (2a) as well as its mono- and some selected 5,6-disubstituted derivatives 2 have revealed that they undergo hydrolysis 260-1500 times more rapidly than diethyl oxalate (12) in acetate buffer-acetonitrile (pH 5.69) at 25 degrees C. Although the cyclic oxalate 21 from cis-1,2-cyclopentanediol (11) was 1.5 times more reactive than 2a, it has been shown with other substrates that increasing number of the alkyl substituents decreases the rate of hydrolysis. On the contrary, the phenyl group was found to have somewhat accelerative effect.