On searching for solutions of the Diophantine equation

We propose a new search algorithm to solve the equation for a fixed value of . By parametrizing min, this algorithm obtains and (if they exist) by solving a quadratic equation derived from divisors of . By using several efficient number-theoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. We performed a computer search for 51 values of below 1000 (except ) for which no solution has previously been found. We found eight new integer solutions for and in the range of .

     

Association Schemes with Multiple Q-polynomial Structures

It is well known that an association scheme with has at most two P-polynomial structures. The parametrical condition for an association scheme to have two P-polynomial structures is also known. In this paper, we give a similar result for Q-polynomial association schemes. In fact, if , then we obtain exactly the same parametrical conditions for the dual intersection numbers or Krein parameters.     

Cutting Plane/Tabu Search Algorithms for Low Rank Concave Quadratic Programming Problems

In this paper, we will propose an efficient heuristic algorithm for solving concave quadratic programming problems whose rank of the objective function is relatively small. This algorithm is a combination of Tuy's cutting plane to eliminate the feasible region and a kind of tabu-search method to find a good vertex. We first generate a set of V of vertices and select one of these vertices as a starting point at each step, and apply tabu-search and Tuy's cutting plane algorithm where the list of tabu consists of those vertices eliminated by cutting planes and those newly generated vertices by cutting planes. When all vertices of the set V are eliminated, the algorithm is terminated. This algorithm need not converge to a global minimum, but it can work very well when the rank is relatively small (up to seven). The incumbent solutions are in fact globally optimal for all tested problems. We also propose an alternative algorithm by incorporating Rosen's hyperrectangle cut. This algorithm is more efficient than the combination of Tuy's cutting plane and tabu-search.     

Photometric determination of arsenic in silicate rocks

Summary The method described consists in decomposing the silicate rock sample by fusion with sodium hydroxide or sodium hydroxide-peroxide, leaching the melt with water, evolving arsine from the filtrate, and finally determining arsenic by photometric evaluation of molybdenum blue. Satisfactory accuracy has been demonstrated for the range 0.0 to 20 p. p. m. As, for which the method is particularly intended.

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Zusammenfassung Zur Bestimmung des Arsengehaltes in Silikatgesteinen wird die Probe durch Schmelzen mit Natriumhydroxyd und gegebenenfalls Natriumperoxyd aufgeschlossen. Aus dem Filtrat der wäßrigen Lösung dieser Schmelze wird Arsenwasserstoff entwickelt und in natriumhydrogenkarbonathältiger Jodlösung aufgefangen. Das hierbei entstehende Arsenat wird nach Zugabe von Molybdatreagens und Bisulfit photometrisch bestimmt. Für Arsengehalte unter 0,02% werden nach dieser Methode Resultate von zufriedenstellender Genauigkeit erhalten.

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Résumé La méthode décrite consiste en la décomposition de l'échantillon de roche silicatée par fusion avec la soude ou le peroxyde de sodium, reprenant la partie fondue par l'eau, libérant l'hydrogène arsénié du filtrat et finalement dosant l'arsenic par colorimétrie du bleu de molybdène. Une précision suffisante a été mise en évidence dans le domaine de 0,0 à 20 p. p. m. d'arsenic pour lequel la méthode convient particulièrement bien.

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Fulbright Scholar.     

Growth of MgO doped LiNbO3 single crystal fibers by a novel drawing down method

MgO-doped LN (LiNbO₃) fibers were automatically grown by an improved drawing down method. The smallest fiber diameter ever attained was 10 μm and the fluctuation in diameter was reduced to ±0.2 μm. The poling process was done during the growth process by the thermal electric effect. The dislocation which was observed in the X-ray topographs of the optical grade bulk crystals did not appear in the fiber. The fibers and optical grade bulk crystals did not have a uniform distribution of the MgO concentration as determined by electron probe micro analysis (EPMA).     

Nuclear magnetic resonance studies of alkaline earth phosphosilicate and aluminoborosilicate glasses

The ¹¹B, ²⁷Al, ²⁹Si and ³¹P magic angle spinning (MAS) NMR spectra of MO–P₂O₅, MO–SiO₂–P₂O₅ and MO(M^′₂O)–SiO₂–Al₂O₃–B₂O₃ (M=Mg, Ca, Sr and Ba, M^′=Na) glasses were examined. In binary MO–P₂O₅ (M=Ca and Mg) glasses, the distributions of the phosphate sites, P(Q_n), can be expressed by a theoretical prediction that P₂O₅ reacts quantitatively with MO. In the ternary 0.30MO–0.05SiO₂–0.65P₂O₅ glasses, the 6-coordinated silicon sites were detected, whose population increases in the order of MgOxCaO–0.05SiO₂–(0.95−x)P₂O₅ glasses, its population increases with an increase in f (=([P₂O₅]−[MO]−[B₂O₃]−[Na₂O])/[SiO₂]) and has maximum at f=9. The signal due to the 5-coordinated silicon atoms is also observed when x is smaller than 0.45. When three network-forming oxides such as SiO₂, Al₂O₃ and B₂O₃ coexist, Al₂O₃ reacts preferably with MO. The populations of 4-coordinated boron atoms, N₄, are expressed well with r/(1−r), where r=([Na₂O]−[Al₂O₃])/([Na₂O]−[Al₂O₃]+[B₂O₃]). The correlation of the Raman signal at 1210 and 1350 cm⁻¹ with the NMR signal of Si(Q₆) at −215 ppm is also seen.     

Solarization mechanism of glass containing Ce3+ and As5+

The solarization mechanism in a glass containing both Ce³⁺ and As⁵⁺, 16Na₂O·11CaO·73SiO₂:0.15AsO_x·0.015CeO_x (in mol.%), is newly proposed by elucidating the valence and coordination structure of arsenic after the photochemical reaction, the mechanism being traditionally expressed as

$\text{2}\text{Ce}{}^{\mathrm{3+}}\text{+}\text{As}{}^{\mathrm{5+}}\text{→}\text{hv}\text{2}\text{Ce}{}^{\mathrm{4+}}\text{+}\text{As}{}^{\mathrm{3+}}$

ESR hyperfine quartets due to an As⁴⁺ ranging from 0.1 to 0.5 T built up on UV-irradiation and their line shape varied with the duration of the irradiation. The line shape analysis of the ESR spectra employing a computer simulation technique has led to the following conclusions; (1) As⁵⁺ is reduced to As⁴⁺ in the solarization process. (2) The geometry around the As⁴⁺ in the solarized glass is tetrahedral during the early stage and trigonal-pyramidal during the latter stage of the reaction.     

Total synthesis of (-)-kainic acid via intramolecular Michael addition: a second-generation route

A total synthesis of (-)-kainic acid starting from the commercially available 2-azetidinone is described. The key delta-lactone intermediate was concisely prepared from the commercially available azetidinone through the Reformatsky-type reaction and an introduction of a glycine moiety. The construction of the functionalized pyrrolidine ring was executed by a one-pot sequential elimination-Michael addition protocol of a beta-amino-delta-lactone intermediate with high diastereoselectivity.     

Photophysical property and photostability of J-aggregate thin films of thiacyanine dyes prepared by the spin-coating method

By use of electrostatic interactions of dye molecules and poly(diallyldimethylammonium chloride) (PDDA), the spin-coating technique has been successfully applied to the preparation of stable J-aggregate thin films of thiacarbocyanine dyes on a polycarbonate or quartz plate. The J-aggregate thin films were prepared by the spin-coating of PDDA aqueous solution on dye thin films prepared on a substrate by the spin-coating of 2,2,3,3-tetrafluoro-1-propanol solution of dyes. Photophysical properties of the dye thin films and J-aggregate thin films were studied by measuring the fluorescence spectra, quantum yields, and lifetimes. Coherent size of the J-aggregates was estimated to be 3-12 by means of the absorption bandwidth (full width at half maximum) or radiative lifetime. Photostability of the J-aggregate thin films was also studied in terms of photodegradation efficiency under argon and oxygen in comparison with the dye thin films, and J-aggregate thin films were found to be more stable than the corresponding dye thin films.     

Relative and absolute stereochemistry of quinadoline B, an inhibitor of lipid droplet synthesis in macrophages

New fungal metabolites, designated quinadolines A (1) and B (2), were isolated from culture broth of Aspergillus sp. FKI-1746, and their structures were elucidated by NMR spectroscopy. The complete relative and absolute stereochemistry of 2 was determined by X-ray crystallography and amino acid analysis using a chiral column. Quinadolines moderately inhibited lipid droplet synthesis in mouse macrophages.