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     

Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Prolonged release of drug from triacetyl-β-CyD complex for oral and rectal administration

Triacetyl--cyclodextrin (TA--CyD), a hydrophobic cyclodextrin derivative, that is insoluble in water, was used to form a complex with flufenamic acid (FA). FA-TA--CyD complex formation was demonstrated by differential scanning calorimetry and powder X-ray diffractometry. The release rate of FA from the FA-TA--CyD complexes in phosphate buffer pH 6.8 was significantly retarded compared to that of FA from the FA and glucose mixture. When the FA-TA--CyD complexes were administered directly into the intraduodenal lumen, the plasma concentration of FA remained at a plateau level (10-18 g/ml) for 6–8 h. An increased mean residence time of FA following FA-TA--CyD complexes administration was observed. These results indicate that TA--CyD may serve as a hydrophobic carrier in prolonged-release preparations of FA.     

Mass spectrometric determination of glycosylation sites and oligosaccharide composition of insect-expressed mouse interleukin-3

The primary structure of Baculovirus-expressed mouse interleukin-3 produced in infected Bombyx mori larvae was characterized by liquid secondary ion mass spectrometry and 252Cf-plasma desorption mass spectrometry in combination with selected protein microchemical reactions. Interleukin-3 was found to consist of at least two glycoprotein species of ca. 17,000 dalton. Characterization of tryptic and S. aureus V8 protease peptides by Edman degradation combined with plasma desorption mass spectrometry showed that two N-glycosylation sites. Asn-16 and Asn-86, were present. N-Glycan residues were shown by liquid secondary ion mass spectrometry and high-performance liquid chromatography to consist of mannose, fucose, and glucosamine. The presence of galactosamine indicated that O-glycosylated residues were present, in addition to the N-glycosylated residues. Glucose was also present, which indicated incomplete processing of the insect-expressed N-linked oligosaccharides.     

Effect of TRX-liposomes size on their prolonged circulation in rats

Newly formulated cationic liposomes (TRX-liposomes) with four different mean diameters were injected into twelve male rats via the lateral tail vein in order to evaluate the effect of liposomal size on pharmacokinetic parameters. TRX-liposomes disappeared from the blood according to the one-compartment model and demonstrated maximum and minimum half-lives of ca. 14 h (mean diameter of 114.3 nm) and ca. 5 h (mean diameter of 285.9 nm), respectively. This prolonged half-life tended to decrease at the boundary of 114.3 nm mean diameter. The optimal size (114.3 nm) for prolonged circulation of TRX-liposomes was consistent with that of pegylated liposomes such as Doxil((R)), however, the half-life was different among these liposomes. The electric charge of the TRX-liposomal surface is assumed to be responsible for this difference. The results of the present study will be very useful in the design of long-circulating cationic liposomes.     

Product-retardation and -activation of catalytic hydrolysis by phospholipase D in small unilamellar vesicles of egg yolk phosphatidylcholine

 We evaluated the hydrolysis of egg yolk phosphatidylcholine (PC) by phospholipase D from Streptomyces chromofuscus (PLD) in small unilamellar vesicles (SUV) in presence of 50 μM Ca²⁺. After initial choline production (hydrolysis of 1.5% of the PC at the outer leaflets of the vesicle bilayers), the hydrolysis was reduced to 5% of the initial velocity. The kinetic behavior in SUV of premixed PC and a low percentage of the hydrolysis product, phosphatidic acid (PA), was similar to that of PC SUV. The reduced velocity disappeared when the membrane structure was disintegrated by means of a nonionic surfactant. In the retardation phase, the partially hydrolyzed vesicles (postsubstrates) had much higher affinity for PLD than fresh PC SUV. These results indicated that small clusters of the product, PA, at the vesicle surface were responsible for the reduced velocity of hydrolysis. The initial velocity increased in a biphasic manner with the substrate concentration. At a PC concentration range up to 4 mM, the experimental data fit Michaelis–Menten kinetics. At concentrations above 6 mM, the velocity again markedly increased. Negatively charged mixed vesicles of PC and PA did not have such kinetics. Furthermore, adding PC SUV to the postsubstrates, where the fraction of free PLD was less than 0.05, induced steep choline production. These results showed that PLD bound to vesicles had higher activity than free PLD. We speculated that PLD bound to vesicles collided with and was directly transferred to PC SUV when the fraction of free PLD in aqueous medium was very small. Received: 5 November 1996 Accepted: 26 February 1997