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 $$\parallel u(t)\parallel _\infty \leqq C(1 + |t|)^{ - 1/2} ,a.e. t \in \mathbb{R}.$$      

Stereoselective nucleophilic addition reactions to nitro sugars

Nucleophile(s) almost exclusively added from the equatorial side of 2-nitro-β-$\text{D}$-2-enopyranoside and the axial side of 2-nitro-$\text{D}$-$\text{ribo}$-1-enitol. On the other hand, methoxide and $\text{tert}$-butyl peroxide ions approached from the equatorial side of 2-nitro-α-$\text{D}$-2-enopyranoside, whereas methanol and hydrogen peroxide ion from the axial side.     

Ru3(CO)12-catalyzed silylation of benzylic C-H bonds in arylpyridines and arylpyrazoles with hydrosilanes via C-H bond cleavage

Ruthenium-catalyzed silylation of sp3 C-H bonds at a benzylic position with hydrosilanes gave benzylsilanes. For this silylation reaction, Ru3(CO)12 complex showed high catalytic activity. This silylation proceeded at the methyl C-H bond selectively. For this silylation reaction, pyridyl and pyrazolyl groups, and the imino group in hydrazones, can function as a directing group. Several hydrosilanes involving triethyl-, dimethylphenyl-, tert-butyldimethyl-, and triphenylsilanes can be used as a silylating reagent. Coordination of an sp2 nitrogen atom to the ruthenium complex is important for achieving this silylation reaction.     

Amphotericin B covalent dimers forming sterol-dependent ion-permeable membrane channels

Polyenemacrolides such as amphotericin B (AmB) were thought to assemble together and form an ion channel across plasma membranes. Their antimicrobial activity has been accounted for by this assemblage, whose stability and activity are dependent on sterol constituents of lipid bilayer membranes. The structure of this channel-like assemblage formed in biomembranes has been a target of extensive investigations for a long time. For the first step to this goal, we prepared several AmB dimers with various linkers and tested for their channel-forming activity. Among these, AmB dimers that bore an aminoalkyl-dicarboxylate tether covalently linked between amino groups of AmB showed potent hemolytic activity. Furthermore, K+ influx actions monitored by measuring the pH of the liposome lumen by 31P NMR revealed that the dimers formed the molecular assemblage similar to that of AmB in phospholipid membrane. Judging from changes in 31P NMR spectra, the dimers appeared to induce "all-or-none"-type ion flux across the liposome membrane in the presence of ergosterol, which suggested that the ion channel formed by ergosterol/dimer is similar to that of AmB. With these data in hand, we are now trying to elucidate the structure of the ion-channel complex by making the labeled conjugates of AmB for NMR measurements.     

Preparation and properties of molybdenum and tungsten dinitrogen complexes : `XVI. Electrochemical properties of tungsten and molybdenum diazoalkane complexes

Diazoalkane complexes of type [MF(NNCRR′)(dpe)₂][BF₄] (M = Mo or W; dpe = Ph₂PCH₂CH₂PPh₂), which are easily derived from bis(dinitrogen) complexes [M(N₂)₂(dpe)₂], undergo consecutive one- and two-electron oxidations and reductions under voltammetric conditions at a platinum electrode. The ESR spectra of the species generated by the controlled potential electrolysis show that primary oxidation occurred on the metal atom (M = Mo) and reduction on the two nitrogen atoms in the diazoalkane ligands (M = Mo or W).     

Control of viscoelasticity using redox reaction

The viscoelasticity of a fluid was tuned with the Faradaic reaction of (11-ferrocenylundecyl)trimethylammonium bromide (FTMA), a "redox-switchable" surfactant. An aqueous solution of the reduced form of FTMA exhibited a remarkable viscoelasticity in the presence of sodium salicylate (NaSal) because of the formation of three-dimensional entanglement of wormlike micelles. Electrolytic oxidation of FTMA caused the viscosity of the system to dramatically decrease and the elasticity to disappear. This drastic decrease in viscoelasticity arose from the disruption of wormlike micelles. This novel electrorheological phenomenon is expected to be applicable to ink for inkjet printers, the electrochemically controlled release of substances entrapped in wormlike micelles of FTMA, and fluid flow rate control using electric signals.     

Effect of sucrose on the structure of a cubic phase formed from a monoolein/water mixture

The effect of sucrose on the structure of molecular assemblies formed in an MO/H2O mixture has been studied using a small-angle X-ray scattering method. It was found that the phase transition Ia3d --> Pn3m --> H(II) occurs with increased sucrose concentration in the mixture with the composition 70 wt% MO at 20 degrees C. This structural change induced by sucrose addition would be ascribed to a cosmotropic property of sucrose, which leads to the dehydration of the MO head group and hence causes a decrease in the effective area occupied by the MO molecule at the polar/apolar interface, which facilitates the formation of molecular assemblies with a high curvature for the reversed liquid-crystal mesophase.     

Stimulatory effect of red light on starch accumulation in a marine green alga,chlamydomonas sp. strain MGA161

A marine green alga,Chlamydomonas sp. strain MGA161 was cultivated under illumination of red and white lights. The growth rate under red light illumination was almost the same as that in the basic conditions under white light illumination, but red light-grown cells accumulated almost twice as much starch as white light-grown cells. Although there was a slight decrease in carbonic anhydrase activity, red light-illuminated cells had almost 2.3 times the fructose-l,6-diphos-phatase activity of white light-illuminated cells. Red light might stimulate starch accumulation by increasing the amounts of enzymes related to carbon fixation through the phytochrome system. Cells grown under red light degraded 1.6 times as much starch and produced 1.7 times as much hydrogen and 1.6 times as much ethanol compared with cells grown under white light during 12 h of dark anaerobic fermentation.