Cusp Cross-Sections of Hyperbolic Orbifolds by Heisenberg Nilmanifolds I

Long and Reid [Algebr. Geom. Topol. 2: 285–296, 2002] have shown that the diffeomorphism class of every Riemannian flat manifold of dimension n≥ 3 arises as a cusp cross-section of a complete finite volume real hyperbolic (n+1)-orbifold. For the complex hyperbolic case, McReynolds [Algebr. Geom. Topol. 4: 721–755, 2004] proved that every 3-dimensional infranilmanifold is diffeomorphic to a cusp cross-section of a complete finite volume complex hyperbolic 2-orbifold. Moreover, he gave a necessary and sufficient condition for a Heisenberg infranilmanifold to be realized as a cusp cross-section of finite volume (arithmetically) complex hyperbolic orbifold. We study these realization problems by using Seifert fibrations.     

Anisotropic friction model of DNA electrophoresis in polymer solutions: Comparison with direct observations

The electrophoresis of DNA chains in uncrosslinked polymer solutions with a Brownian dynamics simulation with an anisotropic friction tensor was analyzed. According to the degree of anisotropy, three types of migration behavior are obtained: fluctuation without or with periodicity between U‐shaped and compact conformations, or migration with linear conformation. We found good agreement between our simulation results and the direct observations of DNA by fluorescence microscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1316–1322, 2003     

Total synthesis of tylosin

Tylosin has been synthesized byregio- and stereoselective introduction of the amino disaccharide moiety and D-mycinose onto the previously synthesized 16-membered-ring aglycone.     

Frequency measuring system using mirror gap stabilized Fabry-Perot interferometer

The mirror gap of a Fabry-Perot interferometer was stabilized with two laser diodes; one locked to the line frequency 385,243,555.14445 MHz of the F=3<--1 in 5D(3/2)<--5S(1/2) (87Rb) and the other to the 385,284,566.3663 MHz of the F=4<--2 in 5D(5/2)<--5S(1/2) (87Rb) [Opt. Commun. 102 (1993) 432]. The length of the mirror gap was adjusted to generate the zero-cross points simultaneously at both of the two line positions. The fringe signals obtained from an interferometer thus stabilized can be used as frequency markers having accuracies of the order of 10(10) depending on the finesse of the interferometer used. Based on measurement using Cs D1 hyperfine lines reported by Udem et al. [Phys. Rev. Lett. 82 (1999) 3568], the uncertainty of markers in the region 50 THz apart from the reference lines is +/- 5 MHz.     

Effect of cationic surfactant on the formation of ferron complexes

In the spectrophotometric determination of aluminium and iron with ferron (7-iodo-8-quinolinol-5-sulphonic acid, H(2)L), the addition of cationic surfactants greatly improves the linearity of the calibration curve and widens the useful pH range. The effect of cetyltrimethylammonium chloride (CTMAC) on the stepwise stability constants (K(1),K(2) and K(3)) of the ferron complexes of aluminium and iron (ML(+), ML(-)(2) and ML(3-)(3)) and on the acid-dissociation constants (K(a1) and K(a2)) of ferron has been studied in connection with the role of the surfactant. CTMAC greatly increases the value of K(3) while exerting little effect on K(1) and K(2), thus rendering ML(3-)(3) the predominant species even at very low concentration of free L(2-). It also has some effect on the acid-dissociation constants of ferron, but sometimes it acts to decrease the free L(2-) concentration. At is therefore concluded that the improvements due to addition of surfactant should be attributed to the increased K(3) value. The presence of surfactant micelles is not essential, because the surfactant has a favourable effect when present at well below its critical micelle concentration, and because the continuous variations plots show a peak at a point corresponding to the composition M: L: Q (Q = cationic surfactant) = 1:3:3.     

Scale-up of high shear granulation based on the internal stress measurement

Scale-up of wet granulation in a vertical high shear mixer was conducted. Pharmaceutical excipient powders composed of lactose, cornstarch and micro-crystallinecellulose, and hydroxypropylcellulose as a binder were mixed together and then granulated with purified water under various operating conditions and vessel scales. A novel internal stress measurement system was developed and stress of normal and tangential directions that granules received from the agitator blade during the granulation was continuously measured. The results indicated that granules received stress mainly from the tangential direction, which also showed the largest value near at the vessel wall. The effects of the agitator tip speed and the centrifugal acceleration on the measured stress was investigated. It was found that the tip speed of the agitator blade could be the main factor for the granule growth. The physical properties such as strength, size distribution and compressibility of granules prepared by changing the operating conditions and the vessel scales were evaluated and the scale-up characteristics of high shear granulation were investigated experimentally. The results showed that these physical properties had linear correlations with the tip speed. It was finally concluded that the scale-up of high shear granulation could be well conducted by means of the tip speed of the agitator blade.     

Regioselectivity in palladium-indium iodide-mediated allylation reaction of glyoxylic oxime ether and N-sulfonylimine

Allylation reaction of electron-deficient imines with allylic alcohol derivatives in the presence of a catalytic amount of palladium(0) complex and indium(I) iodide was studied. The reversibility of allylation was observed in the reaction of glyoxylic oxime ether having camphorsultam. As the important effect of water on regioselectivity, the gamma-adducts were kinetically formed from monosubstituted allylic reagents in the presence of water. The selective formation of thermodynamically stable alpha-adducts was observed in anhydrous THF. In contrast, the allylation of N-sulfonylimine gave the gamma-adducts with high regioselectivities even under anhydrous reaction conditions.