On the existence of Burgers vortices for high Reynolds numbers

Axisymmetric or non-axisymmetric Burgers vortices have been studied numerically as a model of concentrated vorticity fields. Recently it has been rigorously proved that non-axisymmetric Burgers vortices exist for all values of the vortex Reynolds number if an asymmetry parameter is sufficiently small. On the other hand, several numerical results indicate that Burgers vortices have simpler structures as the vortex Reynolds number is increasing, even when the asymmetry parameter is not sufficiently small. In this paper we give a rigorous explanation for this numerical observation and extend the existence and stability results of Burgers vortices for high vortex Reynolds numbers.     

High-dimensional asymptotic expansions for the distributions of canonical correlations

This paper examines asymptotic distributions of the canonical correlations between and with q≤p, based on a sample of size of N=n+1. The asymptotic distributions of the canonical correlations have been studied extensively when the dimensions q and p are fixed and the sample size N tends toward infinity. However, these approximations worsen when q or p is large in comparison to N. To overcome this weakness, this paper first derives asymptotic distributions of the canonical correlations under a high-dimensional framework such that q is fixed, m=n−p→∞ and c=p/n→c₀∈[0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher’s z-transformation is proposed. Then, the asymptotic distributions are improved further by deriving their asymptotic expansions. Numerical simulations revealed that our approximations are more accurate than the classical approximations for a large range of p,q, and n and the population canonical correlations.     

Reactions of 26-iodopseudodiosgenin and 26-iodopseudodiosgenone with various nucleophiles and pharmacological activities of the products

26-Iodopseudodiosgenin (8) and 26-iodopseudodiosgenone (9) were reacted with various nucleophiles (KSCN, KOCN, NaCN, NaN(3) and various amines) to give pseudodiosgenin derivatives (4, 12, 16-20, 26) and pseudodiosgenone derivatives (5, 13, 21-25, 27), respectively. The reactions of 8 and 9 with KOCN gave the elimination products (10) and (11), respectively. The reaction of 9 with NaCN gave 5alpha,26- (14) and 5beta,26-dicyanocholestan-3-one (15). The reaction of 8 with NaN3 gave triazepine derivative (30), while that of 9 gave 26-azidopseudodiosgenone (31). Compound 31 was converted into triazepine derivative (32) by heating at 120 degrees C. The cytotoxicity of the pseudodiosgenins and pseudodiosgenones on P-gp-underexpressing HCT 116 cells and P-gp-overexpressing Hep G2 cells was examined by MTT assay. Pseudodiosgenins 2, 4, 12 and 30 showed strong cytotoxic activity (IC50 values: 2.6+/-0.3-6.7+/-1.4 microM), as did pseudodiosgenones 3, 5, 11, 13, 21-25 and 27 (IC50 values: 1.3+/-0.3-6.4+/-0.3 microM) toward HCT 116 cells. Pseudodiosgenins 12, 16 and 30 (IC50 values: 1.2+/-0.7-2.2+/-0.6 microM) and pseudodiosgenones 22, 23, 25 and 27 (IC50 values: 0.6+/-0.1-2.5+/-0.3 microM) were highly cytotoxic to Hep G2 cells. Compounds 3 and 27 showed efficient antibacterial activity (MIC: 15.6, 10.4 microg/ml) and (MIC: 7.8, 15.6 microg/ml) against Bacillus subtilis and Staphylococcus aureus, respectively.     

Chiral resolution of monosaccharides as 1-phenyl-3-methyl-5-pyrazolone derivatives by ligand-exchange CE using borate anion as a central ion of the chiral selector

Six reducing monosaccharides (mannose, galactose, fucose, glucose, xylose, and arabinose) were derivatized with 1-phenyl-3-methyl-5-pyrazolone (PMP) and chiral resolution of these racemic PMP-monosaccharides was studied by ligand-exchange CE using borate anion as a central ion of the chiral selector and (S)-3-amino-1,2-propanediol (SAP) as a chiral selector ligand. PMP-mannose, PMP-galactose and PMP-fucose were successfully enantioseparated. Lowering the capillary temperature increased the resolution of PMP-mannose system, but decreased that of PMP-galactose and PMP-fucose systems. Whereas the maximum resolution was obtained at pH 8.9 in the PMP-mannose system, resolution increased gradually with pH in the PMP-galactose and PMP-fucose systems. Expecting the formation of the ternary borate complexes with SAP and PMP-monosaccharide in the CE experiments, the optimized structures of the borate diastereomers were obtained by semiempirical molecular orbital calculations to discuss the structural difference of the diastereomers in connection with the enantioseparation behaviors.     

Me‐BIPAM for the Synthesis of Optically Active 3‐Aryl‐3‐hydroxy‐2‐oxindoles by Ruthenium‐catalyzed Addition of Arylboronic Acids to Isatins

A chiral O‐linked C₂‐symmetric bidentate phosphoramidite (Me‐BIPAM) was found to be efficient for the ruthenium‐catalyzed addition of arylboronic acids to isatins. Asymmetric synthesis of 3‐aryl‐3‐hydroxy‐2‐oxindoles by 1,2‐addition of arylboronic acids to isatins was carried out in the presence of [RuCl₂(PPh₃)₃]/(R,R)‐Me‐BIPAM and KF, resulting in an enantioselectivity as high as 90 % ee. It was found that the reaction with N‐protected isatins proceeds with high yields and good enantioselectivities. The best protective groups on the nitrogen atom were different depending on the substituents on the aromatic ring. The use of a N‐benzyl group resulted in excellent enantioselectivities in many substrates compared with other groups.     

Numerical integration of atomic electron density with double exponential formula for density functional calculation

In the preceding study, we reported an application of the double exponential formula to the radial quadrature grid for numerical integration of the radial electron distribution function. Three-type new radial grids with the double exponential transformation were introduced. The performance of radial grids was compared between the double exponential grids and the grids proposed in earlier studies by applying to the electron-counting integrals of noble gas atoms and diatomic molecules including alkali metals, halogens, and transition metals. It was confirmed that the change in accuracy of the quadrature approximation depending on atomic or molecular species is not significant for the double exponential integration schemes rather than the other integration schemes. In the present study, we further investigate the accuracy of the double exponential formula for the electron-counting integrals of all the atoms from H to Kr in the periodic table to elucidate the stable performance of the double exponential radial grids. The electron densities of the atoms are calculated with the Gauss-type orbital basis functions at the B3LYP level. The quadrature accuracy and convergence behavior of numerical integration are compared among the double exponential formula and the formulas proposed by Treutler et al. and by Mura et al. The results reveal that the double exponential radial grids remarkably improve the convergence rate toward high accuracy compared with the previous radial grids, particularly for heavy elements in the 4th period, without fine tuning of the radial grids for each atom.     

A new geranylated aromatic compound from the mushroom Hericium erinaceum

A new geranylated aromatic compound, 5-[(2'E)-3',7'-dimethyl-2',6'-octadienyl]-4-hydroxy-6-methoxy-1-isoindolinone (1), was isolated from the fruiting bodies of the mushroom Hericium erinaceum (Bull.: Fr.) Pers. (Hericiaceae) together with three known sterols, 5alpha,6alpha-epoxy-(22E)-ergosta-8(14),22-diene-3beta,7alpha-diol (2), (22E)-ergosta-7,9(11),22-triene-3beta,5alpha,6beta-triol (3) and (22E)-ergosta-7,22-diene-3beta,5alpha,6alpha,9alpha-tetrol (4). The structure of the new compound was elucidated on the basis of spectral data.     

Spatial competition and collaboration networks

We model the formation of collaboration networks among firms that are located in a circular city as a two-stage game. In the first stage, the firms form collaboration links, and in the second stage, they engage in price competition. If two firms form a link, their production costs in the second stage are reduced. The second stage is a generalization of Salop??s (Bell J Econ 10(1):141?C156, 1979) circular city model. We provide a complete characterization of equilibrium prices of the model. We show that a firm prefers forming a link with a more distant firm if the cost-reducing effects are the same. We discuss the stability and social efficiency of the collaboration networks. When link costs are small, there is no conflict between efficiency and stability of networks. When link costs are significant, there is a conflict between efficiency and stability of networks. We also examine the average distances between linked firms.     

Total synthesis of antimalarial diterpenoid (+)-kalihinol A

Total synthesis of antimalarial diterpenoid (+)-kalihinol A, isolated from marine sponge Acanthella sp., is achieved. This total synthesis involves regioselective alkylation of an epoxide, construction of a tetrahydropyran ring by iodo-etherification, construction of a cis-decalin ring by intramolecular Diels-Alder reaction, isomerization of cis-decalin to trans-decalin, and subsequent functionalization of the trans-decalin ring.     

Development of an electrochemical cholesterol sensor system for food analysis

In this article, we report on a food-cholesterol monitoring sensor based on a non-enzymatic approach. Amorphous and single-crystal gold electrodes were modified with an alkanethiol self-assembled monolayer to quantify it by voltammetry. We first discuss the basic characteristics of these sensors and provide more information about the instrument developed by JSK Co. This instrument is a battery-operated handheld voltammetric analyzer, which mounts a sensor chip to monitor cholesterol contents in food samples. The sensor showed excellent linearity with the cholesterol concentration; egg-yolk samples were analyzed to give an excellent agreement between the values obtained by the sensor (1.4 mM) and chromatography (1.1 mM).