The Rasmussen invariants and the sharper slice-Bennequin inequality on knots

Rasmussen introduced a knot invariant based on Khovanov homology theory, and showed that this invariant estimates the four-genus of knots. We compare his result with the sharper slice-Bennequin inequality for knots. Then we obtain a similar estimate of the Rasmussen invariant for this inequality.     

Recursive Fermion System in Cuntz Algebra. I

Embeddings of the CAR (canonical anticommutation relations) algebra of fermions into the Cuntz algebra ?₂ (or ?_{2 d} more generally) are presented by using recursive constructions. As a typical example, an embedding of CAR onto the U(1)-invariant subalgebra of ?₂ is constructed explicitly. Generalizing this construction to the case of ?_{2 p} , an embedding of CAR onto the U(1)-invariant subalgebra of ?_{2 p} is obtained. Restricting a permutation representation of the Cuntz algebra, we obtain the Fock representation of CAR. We apply the results to embed the algebra of parafermions of order p into ?_{2 p} according to Green's ansatz. Received: 3 September 2001 / Accepted: 19 January 2002     

Improvement of chemical analysis of antibiotics. X. Determination of eight tetracyclines using thin-layer and high-performance liquid chromatography

Analytical methods for eight tetracyclines (TCs) were established using silica gel high-performance thin-layer chromatography (HPTLC), reversed-phase thin-layer chromatography (RP-TLC) and high-performance liquid chromatography (HPLC). Good separations of eight TCs were obtained using chloroform-methanol-5% disodium ethylenediaminetetraacetate solution (65:20:5) (lower layer) and methanol acetonitrile 0.5 M oxalic acid solution (1:1:4) (pH 3.0) on silica gel HPTLC and C8 TLC plates, respectively. A combination of HPTLC and RP-TLC made possible the identification of the eight TCs. Each calibration graph was linear between 0.1 and 1.0 microgram using UV densitometry except for rolitetracycline. For detection reagents, the diazonium salts including Fast Violet B gave variously coloured spots with the eight TCs and good sensitivities were obtained except with minocycline. In HPLC, the simultaneous analysis of the eight TCs on a C8 column was possible using methanol-acetonitrile-0.01 M oxalic acid solution (1:1.5:7) adjusted to pH 3.0 as the mobile phase. A linear relationship was obtained between 1.0 and 10 ng using the usual sample preparation except for rolitetracycline. The direct determination of rolitetracycline was possible using tetrahydrofuran, dimethyl sulphoxide and the mobile phase as solvents for preparation of the sample. For the determination of residual rolitetracycline, it was effective to measure the amount of rolitetracycline as tetracycline by HPLC, HPTLC and RP-TLC after conversion of rolitetracycline to tetracycline by incubating for 5 min in methanol at 50 degrees C.     

A hybrid approach combining energy density analysis with the interaction energy decomposition method

We propose a new analysis technique for characterizing molecular interactions that combines an energy decomposition scheme, such as the Kitaura-Morokuma decomposition method, with energy density analysis, which partitions the total energy of the system into atomic contributions. The combined scheme, termed Interaction-EDA, enables us to estimate the local contribution of interaction energy components, such as electrostatic, exchange, polarization, and charge transfer. The evaluation of the local interaction energy is rather important in large systems. For a numerical assessment, the Interaction-EDA method is applied to the process of CO adsorption on Si(100) - (2 x 1) surface.     

Total synthesis of brevetoxin-B

Brevetoxin-B (BTX-B), produced by the red tide organism, Gymnodium breve Davis, is the first member of marine polycyclic ethers to be structurally elucidated and one of the most potent neurotoxins. The structural feature is a trans-fused polycyclic ether ring system with 23 stereocenters. Its unique, complex structure and potent biological activity have attracted the attention of synthetic organic chemists. Total synthesis of BTX-B has been accomplished via the coupling of the ABCDEFG and IJK-ring segments, each ether ring of which was stereoselectively and efficiently constructed on the basis of SmI2-induced intramolecular cyclization, 6-endo-cyclization of hydroxy epoxide, ring-closing olefin metathesis, and SmI2-induced intramolecular Reformatsky-type reaction. Several kinds of double reactions at the left and right sides were efficiently used through the synthesis.     

Bound site of Mo atoms and its local structure in a Mo/HY catalyst characterized by extended X-ray absorption fine structure and density functional calculation

The bound site of Mo atoms and its local structure in a Mo/HY catalyst have been determined by detailed analysis of extended X-ray absorption fine structure (EXAFS). Molybdenum was introduced in the supercage of HY zeolite by cycles of saturated adsorption of Mo(CO)6 at room temperature and subsequent thermal decomposition at 573 K. Two Mo atoms per supercage were immobilized in each CVD-thermal treatment cycle. The Mo loading increased linearly with the cycles up to three cycles at saturation, where six Mo atoms were supported. Temperature-programmed decomposition of the adsorbed Mo(CO)6 was also characterized by GC, QMS, and FT-IR, respectively. The EXAFS analysis including multiple scattering based on theoretical calculations revealed that Mo bound with two oxygen atoms connects to Al, where one of the two oxygen atoms had been associated with a proton. The bound site is called the S(III)' site. The zeolite framework was significantly distorted by the introduction of low-valent Mo, resulting in isolation of the [MoO2Al] unit from the surrounding zeolite framework due to a quasi-disruption of Si-O bonds adjacent to the unit. In the mild oxidation of the low-valent Mo/HY sample two Mo=O bonds were newly formed and the position of Mo was displaced by 0.06 nm so that the distortion of zeolite framework around the Al atom was relieved. The structures were also supported by DFT calculations. This study is the first example that the position of metal cation in zeolite was determined unambiguously by the EXAFS analysis.     

Synthesis and analgesic activity of novel heterocycles, [1]benzothiopyrano[3,4-b]pyrrole derivatives

In order to develop analgesic compounds possessing a sulfur atom in the alicyclic ring, novel cis-fused heterocycles, [1]benzothiopyrano[3,4-b]pyrrole derivatives (II) were synthesized via a unique cyclization reaction starting from 4-(4-methoxyphenylthio)-2-butanone (1) or 6-methoxy-3,4-dihydro-2H-1-benzothiopyran-4-one (7). The analgesic effects of benzothiopyranopyrroles (16, 18) were measured by means of the writhing test. The phenolic derivative 18 completely inhibited the appearance of writhing at the dose of 50 mg/kg, but the methoxy derivative 16 had no analgesic effect.     

Preparation of Sr2CeO4:Eu3+,Dy3+ white luminescence phosphor particles and thin films by using an emulsion liquid membrane system

Sr(2)CeO(4) and Sr(2)CeO(4):Eu(3+),Dy(3+) phosphor particles and thin films were prepared by using an emulsion liquid membrane (ELM, water-in-oil-in-water (W/O/W) emulsion) system, containing VA-10 (2-methyl-2-ethylheptanoic acid) as extractant (cation carrier). A two-step extraction enabled efficient extraction for Sr(3+) and rare earth ions, and the resulting precursor metal oxalate particles produced in the internal water phase of the ELM system were about 60 nm in diameter. Calcination of the oxalate particles in air gave submicrometer-sized Sr(2)CeO(4) and Sr(2)CeO(4):Eu(3+),Dy(3+) particles, which showed blue and white luminescence, respectively, by UV excitation. Blue and white luminescence phosphor thin films were also prepared by soaking alumina substrates into the W/O emulsion containing precursor oxalate particles, followed by calcination in air.