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)     

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     

Rate constants of the O(D) reactions with N2, O2, N2O, and H2O at 295 K

Using a technique of laser flash photolysis coupled with vacuum ultraviolet laser-induced fluorescence spectroscopy, the rate coefficients of O(¹D) reactions with N₂, O₂, N₂O, and H₂O at 295 ± 2 K have been determined to be , k_O2=(4.06±0.24)×10^-11, k_N2O=(1.35±0.08)×10^-10 and . The quoted uncertainties include estimated errors and are the 95% confidence level. The k_N2 and k_N2O values obtained are larger than the current NASA/JPL recommendations by 26% and 16%, respectively, although they are still within the error limits associated with the recommendations.     

Fast enclosure for the minimum norm least squares solution of the matrix equation AXB = C

Fast algorithms for enclosing the minimum norm least squares solution of the matrix equation AXB = C are proposed. To develop these algorithms, theories for obtaining error bounds of numerical solutions are established. The error bounds obtained by these algorithms are verified in the sense that all the possible rounding errors have been taken into account. Techniques for accelerating the enclosure and obtaining smaller error bounds are introduced. Numerical results show the properties of the proposed algorithms. Copyright © 2015 John Wiley & Sons, Ltd.     

A new application of statistical moment theory to evaluate the swelling behavior of thermo-responsive gels

The loosely cross-linked poly(acryloyl-L -proline methyl ester) gel, which is known as one of the typical thermo-responsive gels, shows a volume transition around approximately 14°C in pure water. This volume transition is shifted to higher temperature by treatment in aqueous sodium dodecyl sulfate (SDS). The analysis of the swelling-temperature curve (frequency distribution) was performed according to a moment analysis, in which the area under the swelling-temperature curve (AUC), mean swelling transition temperature (MSTT) and variance of swelling transition temperature (VSTT) were calculated. It is shown that the apparent volume transition temperature can be estimated from MSTT and that VSTT can be used to characterize the shape of the corresponding curves.