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)     

Stability of porphyrin-calix[4]arene complexes analyzed by electrospray ionization mass spectrometry

The stability of some porphyrin-calix[4]arene sodium-ion complexes were determined by a collision-activated decomposition (CAD) method utilizing electrospray ionization mass spectrometry (ESI-MS). Comparing the values of E(1/2), the collision energy at which the relative intensity of the complex ion is 0.5, we found that the porphyrin-calix[4]arene complex with the higher value of E(1/2) corresponded to that with the larger association constant (Kass), as measured by 1H-NMR in CDCl3. Both our ESI-MS and NMR studies proved that the number of hydrogen bonds and the rigidity of the calix[4]arene stabilized the complex. The ESI-MS technique could be successful in screening the binding affinity in host-guest systems with a small amount of sample.     

Titanocene-catalyzed formation of allylsilanes from allyl ethers and chlorosilanes

A new method for silylation of allyl ethers with chlorosilanes has been developed by the use of Cp₂TiCl₂ as a catalyst. This reaction proceeds efficiently at −20 °C in THF using ⁿBuMgCl. A plausible reaction pathway via allyltitanocene intermediate was proposed.     

A concept for controlling singlet oxygen (1 Delta g) yields using nitroxide radicals: phthalocyaninatosilicon covalently linked to nitroxide radicals

In this study, we have investigated the singlet oxygen ((1)Delta(g)) generation mechanism using phthalocyaninatosilicon (SiPc) covalently linked to nitroxide radicals (NRs), and we succeeded in increasing the singlet oxygen quantum yield (Phi(Delta)) by linking the NRs. This originates from both an increase in the triplet quantum yield and excited-state lifetimes long enough to utilize photochemical reactions. Because the electron exchange interactions with paramagnetic species were known to result only in very fast excited-state relaxation, leading to a decrease in photochemical reaction yields, this increase in Phi(Delta) is an unusual and precious example for increasing photochemical reaction yields by electron exchange interactions with paramagnetic species. In addition, our experiments and theoretical analyses show that the spin-selective energy transfer rate constant is not influenced by linking the NRs and can be evaluated by the product of spin-statistical factors and matrix elements between the initial and final states.     

Free-fermions and skew stable Grothendieck polynomials

Journal of Algebraic Combinatorics - Motivated by the theory of correspondence functors, we introduce the notion of germ in a finite poset, and the notion of germ extension of a poset. We show that...     

The O(N) vector model in the large-N limit revisited: multicritical points and double scaling limit

The multicritical points of the O(N)-invariant N vector model in the large-N limit are re-examined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit N → ∞ while the coupling g → g_c in a correlated manner (the double scaling limit) a massless bound state O(N) singlet is formed and powers of 1/N are compensated by IR singularities. The persistence of the N → ∞ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.     

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.     

Highly efficient and selective epoxidation of alkenes by photochemical oxygenation sensitized by a ruthenium(II) porphyrin with water as both electron and oxygen donor

Visible light irradiation of a reaction mixture of carbonyl-coordinated tetra(2,4,6-trimethyl)phenylporphyrinatoruthenium(II) (Ru(II)TMP(CO)) as a photosensitizer, hexachloroplatinate(IV) as an electron acceptor, and an alkene in alkaline aqueous acetonitrile induces selective epoxidation of the alkene with high quantum yield (Phi = 0.6, selectivity = 94.4% for cyclohexene and Phi = 0.4, selectivity = 99.7% for norbornene) under degassed conditions. The oxygen atom of the epoxide was confirmed to come from a water molecule by an experiment with H(2)(18)O. cis-Stilbene was converted into its epoxide, cis-stilbeneoxide, without forming trans-stilbeneoxide. trans-Stilbene, however, did not exhibit any reactivity. Under neutral conditions, an efficient buildup of the cation radical of Ru(II)TMP(CO) was observed at the early stage of the photoreaction, while an addition of hydroxide ion caused a rapid reaction with the cation radical to promote the reaction with reversion to the starting Ru(II)TMP(CO). A possible involvement of a higher oxidized state of Ru such as Ru(IV), Ru(V), Ru(VI) through a dismutation of the Ru(III) species was excluded by an experiment with Ru(VI)TMP(O)(2). Decarbonylation of the Ru complex was also proven to be invalid. A reaction mechanism involving an electron transfer from the excited triplet state of Ru(II)TMP(CO) to hexachloroplatinate(IV) and subsequent formation of OH(-)-coordinated Ru(III) species, leading to an oxo-ruthenium complex as the key intermediate of the photochemical epoxidation, was postulated.     

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.     

Determination of chemical form of antimony in contaminated soil around a smelter using X-ray absorption fine structure.

Only limited information is available about the behavior of antimony (Sb) in contaminated soils. However, understanding the behavior of Sb in contaminated soils is important, because the toxicity or solubility of this element depends on its chemical state. In this study, we investigated the levels of Sb and the chemical forms of Sb in the soil around a smelter using X-ray absorption fine structure (XAFS) spectra. The highest Sb concentration in the contaminated soil was 2900 mg/kg dry soil. According to Sb-K edge X-ray absorption near edge (XANE) spectra, the Sb in the soil was in the form of Sb(V) compounds. The similarity of extended XAFS (EXAFS) spectra suggests that Sb speciation was independent of the sampling site, which indicates that Sb or Sb2O3 emitted from the smelter was converted into Sb(V) compounds in the soil.