Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations

We consider the time-dependent Schrödinger-Hartree equation (1) $$iu_t + \Delta u = \left( {\frac{1}{r}*|u|^2 } \right)u + \lambda \frac{u}{r},(t, x) \in \mathbb{R} \times \mathbb{R}^3 ,$$ (2) $$u(0,x) = \phi (x) \in \Sigma ^{2,2} ,x \in \mathbb{R}^3 ,$$ where λ≧0 and \(\Sigma ^{2,2} = \{ g \in L^2 ;\parallel g\parallel _{\Sigma ^{2,2} }^2 = \sum\limits_{|a| \leqq 2} {\parallel D^a g\parallel _2^2 + \sum\limits_{|\beta | \leqq 2} {\parallel x^\beta g\parallel _2^2< \infty } } \} \) . We show that there exists a unique global solutionu of (1) and (2) such that $$u \in C(\mathbb{R};H^{1,2} ) \cap L^\infty (\mathbb{R};H^{2,2} ) \cap L_{loc}^\infty (\mathbb{R};\Sigma ^{2,2} )$$ with $$u \in L^\infty (\mathbb{R};L^2 ).$$ Furthermore, we show thatu has the following estimates: $$\parallel u(t)\parallel _{2,2} \leqq C,a.c. t \in \mathbb{R},$$ and $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$      

Antiviral agents of plant origin. III. Scopadulin, a novel tetracyclic diterpene from Scoparia dulcis L

The structure and stereochemistry of scopadulin, a novel aphidicolane-type diterpene isolated from Scoparia dulcis L. have been established from spectral data and single-crystal X-ray analysis of its acetone solvate.     

Radiation sterilization of enzyme hybrids with biodegradable polymers

Ionizing radiations, which have already been utilized for the sterilization of medical supplies as well as gas fumigation, should be the final candidate to decontaminate “hybrid” biomaterials containing bio-active materials including enzymes because irradiation induces neither heat nor substances affecting the quality of the materials and our health. In order to check the feasibility of ⁶⁰Co-gamma rays on these materials, we selected commercial proteases including papain and bromelain hybridized with commercial activated chitosan beads and demonstrated that these enzyme-hybrids suspended in water showed the significant radiation durability of more than twice as much as free enzyme solution at 25-kGy irradiation. Enhanced thermal and storage stability of the enzyme hybrids were not affected by the same dose level of irradiation, either, indicating that commercial irradiation sterilization method is applicable to enzyme hybrids without modification.     

Additive telluromolybdates. Structure and catalysis in oxidation

Additive telluromolybdates, MoO₃·2TeO₂ and M^IIO·TeO₂·MoO₃ (M^IITeMoO₆; M^II = Co, Mn, Zn), converted ethyl lactate selectively to pyruvate in a vaporphase fixedbed flow system at 250–300 °C. A synergy in activity was observed for binary TeO₂–MoO₃, and crystalline Te₂MoO₇ was suggested as the active species. The Rietveld analysis of powder XRD patterns of ternary CoTeMoO₆ revealed the layer structure quite different from that of the reference Te₂MoO₇, but tellurium was again located adjacent to molybdenum linked through lattice oxygen.     

Chiral β-dimethylaminoalkylphosphines. Highly efficient ligands for a nickel complex catalyzed asymmetric grignard cross-coupling reaction

Chiral β-dimethylaminoalkylphosphines were prepared starting with amino acids, (S)-alanine, (S)-phenylalanine, (R)-phenylglycine, (S)-valine, and (R)-tert-leucine. The chiral phosphines were found to be highly efficient ligands for a nickel catalyzed asymmetric Grignard cross-coupling reaction (38～94% optical yield).     

Relieving effect of saline on cephaloridine nephrotoxicity in rats

To elucidate the mechanism(s) of the relieving effect of saline on cephaloridine (CER) nephrotoxicity, rats were given CER in equal quantity (1 g/kg body weight; i.v.), but at two different concentrations (4 and 25%) in saline. Urinary excretion of glucose, which was investigated as an index for renal proximal tubular injury, revealed that the renal damage was less in the 4% CER 25 ml/kg group than in the 25% CER 4 ml/kg group. As to urinary excretions of CER, sodium, potassium and water, no significant differences were observed between the two groups in the first 2 h, but chloride in the 4% CER 25 ml/kg group showed higher values than in the 25% CER 4 ml/kg group. Plasma concentrations of sodium, potassium, chloride and CER, did not show any definite distinctions between the two groups. At the time-point of 20 min after the CER administration, renal CER content was significantly lower in the 4% CER 25 ml/kg group than in the 25% CER 4 ml/kg group. These results suggest that the sodium ion which is needed for cellular trapping of CER is competitively expended for cellular entry of the chloride ion in the kidney, and that the relieving effect of the saline on CER nephrotoxicity is ascribable to the loaded quantity of chloride ion.     

Relaxation dynamics in glycerol-water mixtures: I. Glycerol-rich mixtures

We discuss the relaxation dynamics of glycerol-water mixtures, as studied by dielectric spectroscopy in the frequency range from 1 Hz to 250 MHz and at temperatures between 173 and 323 K. The experimental results obtained for the glycerol-rich mixtures suggest that the main dielectric relaxation process, as well as the so-called high-frequency "excess wing" (EW) and dc conductivity, follow the same temperature dependence. This result indicates that all of these processes are induced by the same molecular origin. A new phenomenological function is proposed to describe the whole dielectric spectrum in the covered frequency range, and some possible mechanisms of dielectric behaviors through the dc conductivity, the main relaxation process, and the EW are discussed.     

Preparation and characterization of silica—polyimide composite membranes coated on porous tubes for CO2 separation

Silica-polyimide microcomposite membranes were prepared on γ-alumina-coated α-alumina support tubes, and their gas permeation properties were evaluated with He, N₂ and CO₂. Smoothing of the substrate surface and hybridization of silica and polyamic acid were both effective to form defect-free thin composite membranes. The CO₂ permeance of a membrane with a silica content of 68 wt% was one order of magnitude higher than that of a polyimide membrane having the same thickness. The permselectivity of CO₂ to N₂ was 30 at 30°C and 13 at 100°C. Contributions of the silica and polyimide phases to permeance of the composite membrane were analyzed with a two-phase permeation model. The effective thickness of the rate-controlling polyimide phase was less than one-tenth of the total thickness of the silica-polyimide membrane.     

Photoinduced ionic polymerization. VII. Cationic polymerization of cyclohexene oxide in solid state

Photopolymerization of cyclohexene oxide in the presence of electron acceptors was studied in a bulk system (in liquid as well as in solid states). The polymerization was proved to proceed by a cationic mechanism in both states by the effect of inhibitors. In a liquid phase the light intensity dependence of the rate of polymerization and the molecular weight distribution showed a contribution of a free ionic polymerization. Any discontinuous phenomenon in the rate as well as in the molecular weight was not discerned between liquid(above ?36°C) and plastic crystal (between ?36 and ?81°C) phases. A quantum yield of monomer consumption as high as 8 × 10³ was observed in the plastic crystal phase. Below ?81°C in the normal crystal phase the rate as well as the molecular weight was remarkably suppressed.     

A new route to methyl (R,E)-(-)-tetradeca-2,4,5-trienoate (pheromone of Acanthoscelides obtectus) utilizing a palladium-catalyzed asymmetric allene formation reaction

[reaction: see text] A formal total synthesis of the sex attractant of male dried bean beetle, methyl (R,E)-(-)-tetradeca-2,4,5-trienoate, was achieved by a new efficient route utilizing the Pd-catalyzed asymmetric allene synthesis reaction. It was found that the atropisomeric biaryl bisphosphine (R)-segphos showed better enantioselectivity than (R)-binap in the Pd-catalyzed reaction for preparing alkyl-substituted axially chiral allenes.