On generalized energy equality of the Navier-Stokes equations

We show that for every initial dataa εL ²(Ω) there exists a weak solutionu of the Navier-Stokes equations satisfying the generalized energy inequality introduced by Caffarelli-Kohn-Nirenberg forn=3. We also show that if a weak solutionu εL ^s (0,T;L ^q (Ω)) with 2/q + 2/s ≤ 1 and 3/q + 1/s ≤ 1 forn=3, or 2/q + 2/s ≤ 1 andq ≥ 4 forn ≥ 4, thenu satisfies both the generalized and the usual energy equalities. Moreover we show that the generalized energy equality holds only under the local hypothesis thatu εL ^s (ε, T; L ^q (K)) for all compact setsK ⊂ ⊂ Ω and all 0 <ε <T with the same (q, s) as above when 3 ≤n ≤ 10.     

Lithium insertion behaviour of Li1+xV3O8 prepared by precipitation technique in CH3OH

Li_1+xV₃O₈ (LT-M sample) was obtained by the sol-gel method in CH₃OH. This sample, prepared at 350°C, possessed a smaller grain size and better electrochemical performance than the HT sample prepared by conventional high temperature synthesis. High discharge capacity (372 mAh g⁻¹: x=4.0) and reversible discharge and charge cycles were attained owing to improvement of insertion and extraction kinetics. When heated at 200°C, CH₃OH molecules remained in the compound and crystallinity became lower by lithium insertion over x=2.0. The lithium deintercalation was irreversible.     

Low-valent Nb(III)-mediated synthesis of 1,1,2-trisubstituted-1H-indenes from aliphatic ketones and aryl-substituted alkynes

A variety of 1,1,2-trisubstituted-1H-indenes are synthesized by the reaction of aliphatic ketones, aryl-substituted alkynes and NbCl3(DME) in 1,2-dichloroethane under reflux conditions.     

Texture change of ice on anomalously preserved methane clathrate hydrate

We used a confocal scanning microscope to observe growth and texture change of ice due to the dissociation of methane gas clathrate hydrate (CH(4) hydrate). The experiments were done under CH(4) gas atmospheric pressure and isothermal conditions between 170 and 268 K. Above 193 K, the dissociation of CH(4) hydrate resulted in many small ice particles that covered the hydrate surface. These ice particles had roughly the same shape and density between 193 and 210 K. In contrast, above 230 K the ice particles developed into a sheet of ice that covered the hydrate surface. Moreover, the measured release of CH(4) gas decreased when the sheet of ice formed at the surface of the hydrate. These findings can explain the anomalous preservation behavior of CH(4) hydrate; that is, the known increase of storage stability of CH(4) hydrate above 240 K is likely related to the formation of the ice that we observed in the experiments.     

Synthesis of DNA conjugate by mechanochemical solid-state polymerization and its affinity separation of oligonucleotides having single-base difference by capillary electrophoresis

In this communication, we discuss the characterization of DNA conjugate synthesized by mechanochemical polymerization, Con-M, on the separation of model oligo-DNA and its single nucleotide polymorphisms (SNPs) by affinity capillary electrophoresis, compared with that prepared by radical-initiated solution polymerization, Con-RL. The average molecular weight of Con-M was similar to that of Con-RL, although the molecular weight distribution of Con-M was narrower than that of Con-RL. Capillary electrophoresis of oligo-DNA was performed using the capillary filled with DNA conjugate. The resolution of the capillary filled with Con-M was apparently higher than with Con-RL. It is considered that higher resolution using the capillary filled with Con-M could be ascribed not only to the narrow molecular weight distribution but also to the difference of copolymer structure.     

Intercalation compound of diclofenac sodium with layered inorganic compounds as a new drug material

The intercalation reaction of diclofenac sodium (DFS) with layered inorganic compounds, gamma-titanium phosphate (gamma-TiP), proton type titanium oxide (H-TiO2) and sodium type synthetic mica (Na-TSM), was examined on. The direct reaction of DFS in ethanol-water mixed solvent resulted in the large amount accommodation of DFS. The amount of intercalated DFS was the order of gamma-TiP>H-TiO2>Na-TSM corresponding to the order of acidity. The intercalation using phospholiopids was also examined to assist the intercalation reaction. However, the amount of intercalated DFS was rather small in comparison with those in the direct reaction. DFS accommodated in gamma-TiP dissolved into neutral and basic buffer solution stoichiometry while scarcely dissolved in the acidic solution. The mechanism of the intercalation and reverse dissolution was successfully accounted according to the ion-exchange mechanism between Na+ in DFS and H+ in gamma-TiP. The dissolution from tablet of DFS/gamma-TiP intercalation compound was examined by using a disintegrator. It was found that the dissolution rate appropriately controlled by mixing the disintegrator. The present results suggested the different possibilities in the clinical field to use layered inorganic compounds such as drug delivery system (DDS).     

Synthesis of water-soluble polymeric prodrugs possessing 4-methylcatechol derivatives by mechanochemical solid-state copolymerization and nature of drug release

In this study we synthesized the water-soluble polymeric prodrugs possessing a 4-methylcatechol (4MC) derivative as a side chain by mechanochemical solid-state copolymerization. 1-benzoyl-4-methylcatechol (Bz4MC) was selected as a model compound of 4MC, and its methacryloyl derivative (1) was synthesized. 6-O-methacryloyl-D-galactose (2) was also prepared as a water-soluble monomer. The mechanochemical solid-state copolymerization of 1 and 2 was carried out to obtain the water-soluble polymeric prodrug possessing the Bz4MC as a side chain. The mechanochemical copolymerization of 1 and 2 proceeded to completion, and the polymeric prodrug produced possessed a narrow molecular weight distribution. Three kinds of polymeric prodrugs, whose compositions were different from one another, were hydrolyzed in vitro. The hydrolysis of these polymeric prodrugs proceeded to completion. The rate constants of hydrolysis decreased with increasing the mole fraction of 1 in polymeric prodrug. It was suggested that the rate constant of hydrolysis could be controlled by the composition, the mole fraction of 1 in the polymeric prodrug.     

Configuration Spaces of Points on the Circle and Hyperbolic Dehn Fillings, II (Dedicated to Professor Mitsuyoshi Kato on his 60th birthday)/atl>

In our previous paper (Topology 38 (1999), 497–516), we discussed the hyperbolization of the configuration space of n ( 5) marked points with weights in the projective line up to projective transformations. A variation of the weights induces a deformation. It was shown that this correspondence of the set of the weights to the Teichmüller space when n = 5 and to the Dehn filling space when n = 6 is locally one-to-one near the equal weight. In this paper, we establish its global injectivity.     

Characterization of the refolding and reassembly of an integral membrane protein OmpF porin by low-angle laser light scattering photometry coupled with high-performance gel chromatography

The refolding and reassembly of an integral membrane protein OmpF porin denatured in sodium dodecylsulfate (SDS) into its stable species by the addition of n-octyl-beta-D-glucopyranoside (OG) have been studied by means of circular dichroism (CD) spectroscopy and low-angle laser light scattering photometry coupled with high-performance gel chromatography. The minimal concentration where change in the secondary structure was induced by the addition of OG was found to be 6.0 mg/ml in CD experiments. A species unfolded further than the SDS-denatured form of this protein was observed at an early stage (5-15 min) of refolding just above the minimal OG concentration. In addition, the CD spectrum of protein species obtained above the minimal OG concentration showed that the protein is composed of a beta-structure which is different from the native structure of this protein. In light scattering experiments, no changes in molecular assemblies were observed when the OG concentration was below its minimal refolding concentration determined by CD measurements. Above the minimal concentration, a compact monomeric species was observed when denatured OmpF porin was incubated for 5 min at 25 degrees C in a refolding medium containing 1 mg/ml SDS and 7 mg/ml OG, and then injected into columns equilibrated with the refolding medium. After an incubation of 24 h before injection into the columns, predominant dimerization of this protein was observed in addition to incorrect aggregation.