Certain Families of Elliptic Functions Defined by <Emphasis Type="Italic">q</Emphasis>-Series

We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear algebraic ordinary differential equations satisfied by some such elliptic functions. 2000 Mathematics Subject Classification: Primary–11M36, 33E05     

Generalized Zeta Regularizations,Quantum Class Number Formulas,and Appell's <Emphasis Type="Italic">O</Emphasis>-Functions

We introduce a generalized notion of the zeta regularization. As applications we show the quantum analogue of the Lerch formula and of the Dirichlet class number formulas. We also give some further examples related to Appell's O-functions. 2000 Mathematics Subject Classification: Primary—11M36 Work in part supported by Grant-in Aid for Scientific Research (B) No. 11440010, and by Grant-in Aid for Exploratory Research No. 13874004, Japan Society for the Promotion of Science.     

Dielectric properties of poly [3,3-bis(chloromethyl)oxacyclobutane] (Penton)

Ohne Zusammenfassung     

Beta-ray angular distribution in aligned 12B and 12N and G-parity irregular induced tensor current

We made an explicit formula for beta-ray angular distribution by taking into account the radiative corrections, Coulomb corrections of the finite-size nucleus, weak magnetism, induced pseudoscalar, second-class induced tensor, and contributions of the d-wave leptons. Experimental data on the beta decays of aligned ¹²B and ¹²N given at Osaka are carefully investigated, and it is shown that these data are compatible with no induced tensor current, $\text{?}{}_{\mathrm{T}}\text{?}{}_{\mathrm{A}}\text{=}\text{?(0.44 +-0.88)}\text{2M}$. The nuclear parameter y is 3.3±0.9 in excellent agreement with the predicted value 3.6.     

Raman scattering studies of the Ba2MnWO6 and Sr2MnWO6 double perovskites

Polycrystalline Ba2MnWO6 (BMW) and Sr2MnWO6 (SMW) samples were studied between 80 and 1200 K by Raman scattering spectroscopy. In the case of BMW (space group Fmm), four Raman active vibrational modes, predicted by factor group analysis, were identified. Raman scattering studies with different wavelengths revealed a resonant bands between 300 and 800 cm-1. The origin of these bands was related to the Franck-Condon process. Line broadening versus temperature and phonon frequency were studied, and a qualitative explanation was proposed. SMW samples had considerably more complex Raman spectra. It was found that SMW transformed from tetragonal (room-temperature space group P42/n) to the cubic phase between 670 and 690 K; the phase transition temperature was dependent on sample preparation conditions, and it was considerably lower than in the case of large grain size powders. The role of grain size in phase transition is discussed. Mn ions were found to have a crucial role in the lattice dynamics of both materials.     

Asymmetric total synthesis of (+)-K01-0509 B: determination of absolute configuration

K01-0509 B is a novel natural product which contains a carbamoylated cyclic guanidine. Our asymmetric total synthesis features a Sharpless asymmetric epoxidation and a stereocontrolled construction of the cyclic guanidine via an asymmetric nitroaldol reaction, followed by intramolecular SN2 cyclization. These reactions allowed the cyclic guanidine and the adjacent hydroxy group to be assembled, facilitating the asymmetric total synthesis and determination of the absolute stereochemistry of K01-0509 B. [reaction: see text].     

Synthesis of Non-natural Xyloglucans by Polycondensation of 4,6-Dimethoxy-1,3,5-triazin-2-yl Oligosaccharide Monomers Catalyzed by Endo-β-1,4-glucanase

Summary: A cellotetraose-backboned hepta-saccharide (XXXG) (a capital X represents a glucopyranose residue that is substituted with a xylopyranose through an α-1,6 glycosidic bond, and a capital G represents a non-substituted glucopyranose residue) and a nona-saccharide (XLLG) (a capital L represents a glucopyranose residue that is substituted with a galactopyranoseβ(1-2)xylopyranose through an α-1,6 glycosidic bond) have directly been converted to the corresponding 4,6-dimethoxy-1,3,5-triazin-2-yl derivatives (DMT-β-XXXG 1 and DMT-β-XLLG 2 , respectively) by the action of 4-(4,6-dimethoxy-1,3,5-triazin-2-yl)-4-methyl morpholinium chloride (DMT-MM). The selective nucleophilic attack of the anomeric hydroxyl group to DMT-MM has been achieved in water without using any protection of the hydroxyl groups. The resulting activated oligosaccharide derivatives ( 1 and 2 ) were found to polymerize catalyzed by an endo-β-1,4-glucanase as catalyst. The polymerization took place in a complete regio- and stereo-selective manner, affording non-natural polysaccharides having a XXXG-repeating unit and a XLLG-repeating unit, respectively, in the main chain. It is extremely difficult to construct such definite repeating structures via the conventional synthetic routes including protection-deprotection procedures.