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     

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.     

Direct micropatterning of high dielectric BaTiO3 films by laser-induced pyrolysis with a nano-crystalline seeding technique

A direct patterning method of dielectric BaTiO₃ (BT) films is proposed, which applies laser-induced pyrolysis in combination with nano-crystalline seeding technique. A precursor solution of a BT complex alkoxide containing BT nano-crystalline particles with polyvinylpyrollidone (PVP) as dispersion stabilizer was spin-coated on Pt substrate. An Ar⁺ laser beam was focused and scanned on spin-coated BT films, which induced pyrolysis and crystallization of the films with spatial selectivity. Micropatterns were obtained by striping laser-unirradiated regions on the films with HCl aqueous solution. Raman spectra of the micropattern confirmed that the structures were tetragonal crystalline BT. Clear micropatterns with a line width of ca. 3 μm and an interval of 5 μm were formed at PVP concentrations of 25 and 50 kg/m³. The dielectric constant and dissipation factor of the film fabricated at a laser energy density of 27 MW/cm² and a scanning speed of 25 μm/s attained 76.2 and 0.07, respectively, for a measurement frequency of 100 kHz.     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009