Vibrational Spectroscopic Analysis of L,D-Dipeptides

Raman and infrared spectra of Boc-D-Leu-L-Leu-OMe, Boc-L-Ile-D-aIle-OMe and its N-deuterated derivative have been obtained. Normal mode frequencies on the models of these dipeptides have been calculated and the conformationally sensitive amide I, II, III and V modes are compared with the experimentally observed frequencies. The calculated frequencies are in good agreement with the observed frequencies. It is observed that the amide frequencies in these dipeptides are not very sensitive to their backbone conformation. This is in contrast to the well established conformational dependence of the amide modes in peptides, polypeptides and proteins. The normal mode calculations on these peptides also show absence of mixing in amide I and II modes, and hence lack of appreciable splitting in these modes due to transition dipole coupling.

     

Deformation of a singularity of type E8 and Mordell‐Weil lattices in characteristic 2

In this paper, we study the Mordell‐Weil lattices of the family of elliptic surfaces which is arising from the E₈⁴ singularity, one of the ADE singularities in characteristic 2. And we construct a subfamily of the universal family of supersingular K 3 surfaces in characteristic 2 as an application (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local existence and uniqueness of solutions to approximate systems of 1D tumor invasion model

In the present paper, we propose a modified tumor invasion model which was originally proposed in Chaplain and Anderson (2003) [1]. And we show the local existence and uniqueness of solutions to approximate systems of the 1D modified tumor invasion model. Especially, we introduce a new function and show that our system is equivalent to the nonlinear second-order PDE, which should be reformulated by the new function. Roughly speaking, our system can be rewritten into only one second-order PDE and this fact is quite essential to show the local existence of solutions to the approximate systems.     

Quantitative determination of E5880 in rat plasma by high-performance liquid chromatography/electrospray ionization tandem mass spectrometry

A simple and sensitive method is described for the determination of E5880 in rat plasma. The method is based on high-performance liquid chromatography/electrospray ionization mass spectrometry, using deuterated E5880 as an internal standard. Selected reaction monitoring is employed for selectivity and sensitivity, this in turn enables quantification in a short period of time (within 7 minutes) over the extended range of 0.1-1000 ng/ml with acceptable precision and accuracy. The method demonstrated to be suitable for the quantitative analysis of E5880 in rat plasma. The pharmacokinetic profile of E5880 after a single intravenous administration of E5880 was elucidated.     

Physarigins A-C, three new yellow pigments from a cultured myxomycete Physarum rigidum

Physarigins A-C (1-3), three new pigments have been isolated from a cultured plasmodium of myxomycete Physarum rigidum and their structures were elucidated by spectral data.     

Asymmetric reduction of benzil to (S)-benzoin with whole cells of Bacillus cereus

Benzil (1) was selectively reduced to (S)-benzoin (2) in the presence of a wild-type Bacillus cereus Tim-r01. A 92% yield of 2 with 94% enantiomeric excess ratio was attained in phosphate-buffered saline (PBS) (pH 7.5) by using glucose as a nutrient at 37 degrees C for 12 h. Compound 2 was not reduced further to hydrobenzoin (3) at all. The reduction activity differed greatly depending on the strain of B. cereus. Under these conditions the B. cereus strains IFO3001, IFO15305, IAM1110, IAM1229, IAM1656, and IAM1729 gave 2 in yields ranging from 23 to 46% and the configuration of 2 was (S)-form (7 to 86% ee).     

Best constants in Korn-Poincaré's inequalities on a slab

We establish the best constants in the Poincaré-type and the trace-type inequalities for the quadratic form $ \lambda ||\,{\rm div}\,{\rm u}\,||_{L^2 }^2 \, + \,2\,\mu \,||\,\,(\nabla {\rm u}\, + \,\nabla {\rm u}^{\rm T})/2\,||_{L^2 }^2 $ which is fundamental in elasticity theory, on the space of H¹ vector fields u on a slab vanishing on one or both of its sides. We similarly calculate those constants for the case of H¹ divergence-free vector fields. Our method, which is fairly general, has another practical application to the quadratic form ∑_j,k(a^jk?_ku, ?_ju)_L² with coefficients a ^jk = a^kj ε C in H¹ scalar functions u on a slab.