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)     

Selective chemical vapor deposition synthesis of double-wall carbon nanotubes on mesoporous silica

Double-wall carbon nanotubes (DWNTs) have been selectively synthesized over Fe/Co loaded mesoporous silica by catalytic chemical vapor deposition of alcohol. Several silica materials with desired pore diameter and morphology have been investigated for the DWNT growth. The diameter distribution and selectivity of the DWNT are found to depend on the reaction temperature, pore size, and thermal stability of the support material. A high-yield synthesis of DWNTs has been achieved at 900 degrees C over high-temperature stable mesoporous silica. The outer diameter of DWNTs is found to be in the range of 1.5-5.4 nm with a "d" spacing of 0.38 +/- 0.02 nm between inner and outer layers, which is much larger than those of multiwall carbon nanotubes.     

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     

Efficiently Synthesizing Lacto-Ganglio-Series Gangliosides by Using a Glucosyl Ceramide Cassette Approach: The Total Synthesis of Ganglioside X2

The first total synthesis of the hybrid ganglioside X2, which consisted of a highly branched octasaccharide and ceramide moieties, was accomplished by using a glucosyl ceramide cassette approach. With a disaccharyl donor, the heptasaccharide could not be constructed by glycosylation of the C4 hydroxy group of galactose at the reducing end of the pentasaccharide. In contrast, through an alternative approach with two branched glycan units, a GM2-core trisaccharide, and a lacto-ganglio tetrasaccharide, the heptasaccharyl donor could be prepared and subsequently joined with a glucosyl ceramide cassette to afford the protected ganglioside, X2. Finally, global deprotection completed the synthesis, thus affording the pure ganglioside X2.     

Molecular Insights into the Ligand-Based Six-Proton- and Six-Electron-Transfer Processes Between Tris-ortho-Phenylenediamines and Tris-ortho-Benzoquinodiimines

The global demand for energy and the concerns over climate issues renders the development of alternative renewable energy sources such as hydrogen (H₂) important. A high-spin (hs) Fe^II complex with o-phenylenediamine (opda) ligands, [Fe^II(opda)₃]²⁺ (hs- [6R] ²⁺), was reported showing photochemical H₂ evolution. In addition, a low-spin (ls) [Fe^II(bqdi)₃]²⁺ (bqdi: o-benzoquinodiimine) (ls- [0R] ²⁺) formation by O₂ oxidation of hs- [6R] ²⁺, accompanied by ligand-based six-proton and six-electron transfer, revealed the potential of the complex with redox-active ligands as a novel multiple-proton and -electron storage material, albeit that the mechanism has not yet been understood. This paper reports that the oxidized ls- [0R] [PF₆]₂ can be reduced by hydrazine giving ls-[Fe^II(opda)(bqdi)₂][PF₆]₂ (ls- [2R] [PF₆]₂) and ls-[Fe^II(opda)₂(bqdi)][PF₆]₂ (ls- [4R] [PF₆]₂) with localized ligand-based proton-coupled mixed-valence (LPMV) states. The first isolation and characterization of the key intermediates with LPMV states offer unprecedented molecular insights into the design of photoresponsive molecule-based hydrogen-storage materials.     

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.