Certain values of Hecke L-functions and generalized hypergeometric functions

We compare two calculations due to Bloch and the author of the regulator of an elliptic curve with complex multiplication which is a quotient of a Fermat curve, and express the special value of its L-function at s=0 in terms of special values of generalized hypergeometric functions.     

Competition between crystalline electric field singlet and itinerant states of f electrons

A new kind of phase transition is proposed for lattice fermion systems with simplified f ² configurations at each site. The free energy of the model is computed in the mean-field approximation for both the itinerant state with the Kondo screening, and a localized state with the crystalline electric field (CEF) singlet at each site. The presence of a first-order phase transition is demonstrated in which the itinerant state changes into the localized state toward lower temperatures. In the half-filled case, the insulating state at high temperatures changes into a metallic state, in marked contrast with the Mott transition in the Hubbard model. For comparison, corresponding states are discussed for the twoimpurity Kondo system with f ¹ configuration at each site.     

A new algorithm for surface tension model in moving particle methods

A new algorithm for the surface tension model was developed for moving particle methods. The algorithm is based on the link‐list search algorithm and the continuum surface tension (CST) model. The developed algorithm with the CST model was implemented to a kind of moving particle approach, the finite volume particle (FVP) method. The FVP method with the new algorithm was tested by oscillatory behaviour of a two‐dimensional droplet. The oscillatory period agrees well with analytical one, and the transient shape of the droplet is also in good agreement with that obtained by other numerical methods. The droplet impact on a liquid surface was also studied using the new algorithm. The deposition and splashing phenomena were clearly reproduced. Simulated spread radius of the splashing phenomena was consistent with a power law. Copyright © 2007 John Wiley & Sons, Ltd.     

Pulse radiolysis study of formation of poly(4-vinylbiphenyl) anions in 2-methyltetrahydrofuran solution at 100–120 K

The reactions of poly(4-vinylbiphenyl) (denoted as PVB) polymers and biphenyl molecules with solvated electrons in the 2-methyltetrahydrofuran (MTHF) solvent have been studied at 100–120 K by electron-pulse radiolysis. The formation of PVB polymer anions as well as biphenyl anions was observed by the electron-pulse irradiation of the MTHF-PVB(or biphenyl) solution. The anions are formed by two processes; a rapid formation during the pulse irradiation (<20 ns) and a slow formation after the pulse irradiation. The slow formation is due to a diffusion-controlled reaction between solutes, such as PVB and biphenyl, and solvated electrons. It was found that the reaction efficiency, expressed in monomer unit, of PVB polymers is 1/27 of that of biphenyl molecules. The reaction radius for the electron capture reaction of PVB polymers is estimated as 200–370 A, which is much larger than the gyration radius (107 A) of polymer coils in MTHF solution.     

UV-Vis spectroscopic study on effects of pressure for adsorption ofp-nitrotoluene at liquid-solid interface

The behavior ofp-nitrotoluene adsorbed at zeolite/n-heptane interface has been investigated by the electronic spectroscopy under pressure up to 300 MPa. The uv-vis absorption bands of adsorbedp-nitrotoluene were deconvoluted into ones for the species adsorbed on the cation sites, and one for that on the pore wall of zeolite. The peak of adsorbed species on the cation site red-shifted by 20–80 nm from the position of the same species in the liquid phase, and their magnitudes of shift depended on the strength of electric field generated by the cation in zeolites. The peak intensities of adsorbed species on the cation site were enhanced but these or the pore wall site were reduced with the increase in pressure, suggesting that a part ofp-nitroluene molecules on the pore wall site desorbed and the adsorption on the cation site was enhanced by compression. The pressure dependence of peak intensity indicated that the behavior of this adsorption system was strongly governed by the solvation structure of the adsorbate in the zeolite pore. In particular, it was found that the adsorption of solvent molecules on the cation site strongly affected the volume change of the adsorption system.     

High-power sub-100-fs UV pulse generation from a spectrally controlled KrF laser

High-power sub-100-fs UV pulses were generated from a KrF excimer laser by spectral control and chirped-pulse amplification. The spectral width was broadened to 1.6 nm, resulting in 72-fs, nearly transform-limited pulses. The average output powers at 1 kHz were 0.6 and 1.2 W for pulse widths of 72 and 110 fs, respectively.     

Bismuth‐ and Hafnium‐Catalyzed Hydroamination of Vinyl Arenes with Sulfonamides,Carbamates, and Carboxamides

Catalytic intermolecular hydroamination of vinyl arenes is described. Our initial investigation revealed that a Bi(OTf)₃/[Cu(CH₃CN)₄]PF₆ system previously developed for catalytic intermolecular hydroamination of 1,3‐dienes was suitable for hydroamination of a styrene with sulfonamides, but the substrate generality of this system was unsatisfactory. Several metals were screened to expand the substrate scope, and a new Hf(OTf)₄/[Cu(CH₃CN)₄]PF₆ system was determined to be highly suitable. The combination of Hf(OTf)₄ and [Cu(CH₃CN)₄]PF₆ efficiently promoted the hydroamination of various vinyl arenes, including less‐reactive vinyl arenes with electron‐withdrawing groups. This strategy was applied to sulfonamides, carbamates, and carboxamides, and products were obtained in up to 99 % yield with 0.3–10 mol % catalyst loading.     

Synthesis of 5 beta-cholestane-3 alpha,6 beta,7 alpha,25,26-pentol and identification of a novel bile alcohol, alpha-trichechol, present in the West Indian manatee bile

In order to confirm the structure of alpha-trichechol, the major bile alcohol of the West Indian manatee, chemical synthesis of 5 beta-cholestane-3 alpha,6 beta,7 alpha,25,26-pentol was carried out. The chain of 3 alpha-hydroxy-5 beta-chol-6-en-24-oic acid was elongated by an Arndt-Eistert reaction to form 3 alpha-hydroxy-26,27-dinor-5 beta-cholest-6-en-25-oic acid. The unsaturated C25 bile acid was converted into 3 alpha,6 beta,7 alpha-trihydroxy-25-homo-5 beta-cholan-25-oic acid by 1,2-glycol formation of the delta 6-double bond. The acetylated derivative of the trihydroxy C25 bile acid was then converted into 3 alpha,6 beta,7 alpha,26-tetraacetoxy-27-nor-5 beta-cholestan-25-one by successive treatment with thionyl chloride, diazomethane, and acetic acid. A Grignard reaction of the 25-oxo compound with methylmagnesium iodide afforded the desired bile alcohol, 5 beta-cholestane-3 alpha,6 beta,7 alpha,25,26-pentol. By direct comparison with the synthetic pentahydroxy bile alcohol, the structure of the naturally occurring alpha-trichechol was determined to be 5 beta-cholestane-3 alpha,6 beta,7 alpha,25,26-pentol.