Braiding a link with a fixed closed braid

We show that every oriented link diagram with a closed braid diagram as a sublink diagram can be deformed into a closed braid diagram by a deformation keeping the sublink diagram and, under a mild condition, the number of Seifert circles fixed. As an application, we give an upper bound for the braid index of the link obtained by reversing the orientation of its sublink by using only the information of an original link.     

Low-regularity bilinear estimates for a quadratic nonlinear Schrödinger equation

In this article we establish the bilinear estimates corresponding to the 1D and 2D NLS with a quadratic nonlinearity , which imply the local well-posedness of the Cauchy problem in Hs for s?−1 in the 1D case and for s>−1 in the 2D case. This is a continuation of our study [N. Kishimoto, Local well-posedness for the Cauchy problem of the quadratic Schrödinger equation with nonlinearity , Commun. Pure Appl. Anal. 7 (2008) 1123-1143] on the 1D NLS with nonlinearity . Previous papers by Kenig, Ponce and Vega, and Colliander, Delort, Kenig and Staffilani established local well-posedness for s>−3/4 in 1D and in 2D, respectively, and when the nonlinearity is restricted to cu², papers by Bejenaru and Tao, and Bejenaru and De Silva improved these results to s?−1 in 1D and s>−1 in 2D. The bilinear estimate for 2D also yields an improvement on the growth rate of Sobolev norms of finite energy global-in-time solutions to the 2D cubic NLS.     

Electronic conductivity of pure ceria

The electronic conductivity of pure ceria with two different impurity levels is examined by dc polarization technique based on the Hebb-Wagner ion blocking method. The impurity level for the ceria with 99.999% purity (5N-CeO₂) is about 1/100 of that with 99.9% purity (3N-CeO₂) as confirmed by the fluorescence intensity of impurities obtained by Raman spectroscopy. The electronic conductivity for the 5N-CeO₂ was measured at T = 973 K to 1173 K, and the results are essentially the same as those for the 3N-CeO₂. The electronic conductivity increases with decreasing of P(O₂) following slope values of − 1/4 to − 1/6. The − 1/4 dependent region becomes narrower for the 5N-CeO₂ than that for the 3N-CeO₂. For both types of ceria, the P(O₂) independent region appears in the same region of higher than 10^− 2 and 10^− 3 MPa at T = 1073 K and 973 K, respectively. Activation energies for the 5N-CeO₂ were 2.2 eV, 2.6 eV and 1.9 eV in P(O₂) dependent regions of − 1/6, − 1/4 and 0, respectively.     

Stability of a Composite Wave of Two Viscous Shock Waves for the Full Compressible Navier-Stokes Equation

In this paper we investigate the asymptotic stability of a composite wave consisting of two viscous shock waves for the full compressible Navier-Stokes equation. By introducing a new linear diffusion wave special to this case, we successfully prove that if the strengths of the viscous shock waves are suitably small with same order and also the initial perturbations which are not necessarily of zero integral are suitably small, the unique global solution in time to the full compressible Navier-Stokes equation exists and asymptotically tends toward the corresponding composite wave whose shifts (in space) of two viscous shock waves are uniquely determined by the initial perturbations. We then apply the idea to study a half space problem for the full compressible Navier-Stokes equation and obtain a similar result. Research is supported in part by NSFC Grant No. 10471138, NSFC-NSAF Grant No. 10676037 and 973 project of China, Grant No. 2006CB805902, in part by Japan Society for the Promotion of Science, the Invitation Fellowship for Research in Japan (Short-Term). Research is supported in part by Grant-in-Aid for Scientific Research (B) 19340037, Japan.     

Atom Michelson interferometer on a chip using a Bose-Einstein condensate

An atom Michelson interferometer is implemented on an "atom chip." The chip uses lithographically patterned conductors and external magnetic fields to produce and guide a Bose-Einstein condensate. Splitting, reflecting, and recombining of condensate atoms are achieved by a standing-wave light field having a wave vector aligned along the atom waveguide. A differential phase shift between the two arms of the interferometer is introduced by either a magnetic-field gradient or with an initial condensate velocity. Interference contrast is still observable at 20% with an atom propagation time of 10 ms.     

Oxidative trans to cis Isomerization of Olefins in Polyketide Biosynthesis

Geometric isomerization can expand the scope of biological activities of natural products. The observed chemical diversity among the pseurotin‐type fungal secondary metabolites is in part generated by a trans to cis isomerization of an olefin. In vitro characterizations of pseurotin biosynthetic enzymes revealed that the glutathione S‐transferase PsoE requires participation of the bifunctional C‐methyltransferase/epoxidase PsoF to complete the trans to cis isomerization of the pathway intermediate presynerazol. The crystal structure of the PsoE/glutathione/presynerazol complex indicated stereospecific glutathione–presynerazol conjugate formation is the principal function of PsoE. Moreover, PsoF was identified to have an additional, unexpected oxidative isomerase activity, thus making it a trifunctional enzyme which is key to the complexity generation in pseurotin biosynthesis. Through the study, we identified a novel mechanism of accomplishing a seemingly simple trans to cis isomerization reaction.