Integral representation of solutions to Fuchsian system and Heun's equation

We obtain integral representations of solutions to special cases of the Fuchsian system of differential equations and Heun's differential equation. In particular, we calculate the monodromy of solutions to the Fuchsian equation that corresponds to Picard's solution of the sixth Painlevé equation, and to Heun's equation.     

Pd(0)‐catalyzed polycondensation of methyl propargyl carbonate and bisphenols under stoichiometrically imbalanced conditions

We found that a novel Pd(0)‐catalyzed polycondensation of methyl propargyl carbonate ( 1 ) and bisphenol analogs 4 such as 4,4′‐dihydroxydiphenyl ether (4b ) proceeded successfully and gave polyethers 5 having exomethylene groups. The polycondensation was affected by the kind of bisphenol analogs used. The molar ratio of 1 and 4 also affected the polymerization behavior. Polyethers 5 with higher molecular weights were obtained by polymerization with 0.5 equiv of 4 toward 1 . The use of 1 equiv of 4 gave poor results. When 4,4′‐dihydroxybenzophenone ( 4d ) was employed as a nucleophile, benzenesulfonamide ( 13 ) was needed as an additive for obtaining the corresponding polyether with higher molecular weight. The Pd(0)‐catalyzed condensation of 1 and p‐hydroxyacetophenone was conducted as a model reaction. The desired compound and three by‐products were produced. Two of the by‐products were formed by reaction of 1 and methanol liberated from 1 . The other one appeared to be formed via hydrogenolysis. The formation of the by‐products suggested that some terminal reactions took place in the polycondensation of 1 and 4 . © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 2250–2261, 2008     

Plant constituents biologically active to insects. VI. Antifeedants for larvae of the yellow butterfly, Eurema hecabe mandarina, in Osmunda japonica. (2)

Three antifeedants for larvae of the yellow butterfly, Eurema hecabe mandarina de l'Orza, were isolated from Osmunda japonica Thunb. and identified as osmundalin, parasorboside and methyl (3S,5S)-5-hydroxy-3-(beta-D-glucopyranosyloxy)hexanoate. In the course of isolation of the antifeedants, a new glycoside, dihydroisoosmudalin (9), was isolated together with maltol beta-D-glucopyranoside, 2-deoxy-L-ribopyranolactone, 5-hydroxymethyl.2-furfural and glycerin. The structure of 9 was elucidated as (4R,5S)-5-(beta-D-glucopyranosyloxy)hexan-4-olide on the basis of chemical and spectroscopic evidence.     

Nanopattern formation on Cu(0 0 1) surface coadsorbed with nitrogen and oxygen

Strain-induced nanopatterns formed by the coadsorption of nitrogen and oxygen atoms are studied on the Cu(0 0 1) surface by scanning tunneling microscopy. A square grid pattern similar to that on the N-adsorbed surface appears, and consists of square c(2 × 2) areas with adsorbed N and O atoms when the total density of the adsorbates is around 30% of the Cu atom density on the clean surface. We evaluated the surface strain using a first-principles calculation for a coadsorbed surface and compared it with those on the clean and N-adsorbed surfaces. The strain on the coadsorbed surface is smaller than that of the N-adsorbed surface. The observed size of the square c(2 × 2) area on the coadsorbed surface is larger than that on the N-adsorbed surface with increasing the density of the adsorbates on average as expected by the strain reduction. On the other hand, there is no significant difference in the period of the grid pattern.     

THE MECHANISM OF PHOTOSENSITIZATION IN PHOTODYNAMIC THERAPY: PHOSPHORESCENCE BEHAVIOR OF PORPHYRIN DERIVATIVES IN SALINE SOLUTION CONTAINING HUMAN SERUM ALBUMIN

The phosphorescence properties, especially the dynamic behavior of metal free and metal complexed porphyrins, have been studied in phosphate buffered saline (PBS) containing 0-3% human serum albumin (HSA). 6,7-Bisaspartyl-2,4-bis (1-hexyloxyethyl)-deutero- porphyrin (DP) and its gallium(III), zinc(II), and indium(III) complexes are used as photosensitizers. Upon irradiation, a solution of porphyrins containing more than 0.1% HSA shows phosphorescence with a lifetime longer than 1 ms. With an increase in irradiation time, phosphorescence intensities and lifetimes of porphyrins increase, depending upon their concentrations and triplet lifetimes, and approach saturated values close to those under deaerated conditions. The experimental results may be interpreted in terms of hypoxia induced by photosensitization in a local environment surrounding the sensitizer. The hypoxia is caused by the reaction between proteins and singlet molecular oxygen generated by photosensitization of porphyrins. Phosphorescence behavior of sensitizers in HSA PBS solution gives significant information for classifying photosensitizers as to their efficacy for photodynamic therapy.     

Pressure-induced structural phase transition of iodine

The structural phase transition of iodine was observed at about 210 kbar and at room temperature by the high-pressure x-ray diffraction technique using a diamond-anvil cell and a position-sensitive detector. It was found to occur reversibly in both processes of increasing and decreasing pressure.     

Two new dimeric acridone alkaloids from Glycosmis citrifolia

Two new acridone dimers, glycobismines-F (1) and -G (2), were isolated from the roots of Glycosmis citrifolia collected in Taiwan. The structures of the new compounds were determined based on spectral analysis.     

Some characterizations of minimal Markov basis for sampling from discrete conditional distributions

In this paper we given some basic characterizations of minimal Markov basis for a connected Markov chain, which is used for performing exact tests in discrete exponential families given a sufficient statistic. We also give a necessary and sufficient condition for uniqueness of minimal Markov basis. A general algebraic algorithm for constructing a connected Markov chain was given by Diaconis and Sturmfels (1998,The Annals of Statistics,26, 363–397). Their algorithm is based on computing Gröbner basis for a certain ideal in a polynomial ring, which can be carried out by using available computer algebra packages. However structure and interpretation of Gröbner basis produced by the packages are sometimes not clear, due to the lack of symmetry and minimality in Gröbner basis computation. Our approach clarifies partially ordered structure of minimal Markov basis.     

Complexes of ytterbium(III) nitrate and triflate with homoazacalix[n]arenes (n=3, 4)

The synthesis and crystal structures of three ytterbium(III) complexes of homoazacalixarenes are reported. In all cases, the complexes are obtained without addition of a base, the protons of the complexing phenolic moieties being transferred to the amine groups upon complexation. The 1:1 complex between p-chloro-N-benzylhexahomotriazacalix[3]arene (1) and Yb(NO₃)₃ is analogous to the neodymium(III) complex reported previously, with the metal ion bound to three phenoxide groups and three nitrate ions. A second 1:1 complex is obtained with Yb(NO₃)₃ and p-methyl-N-benzyltetrahomodiazacalix[4]arene (2), in which the metal ion is bound to two phenoxide groups only. The replacement of nitrate by triflate counter-ions results in the formation of a 1:2 ‘sandwich’ complex with 1, in which two divergent calixarene molecules are bridged by the metal ion, the counter-ions being non-bonding.