Nonrelativistic limit in the energy space for nonlinear Klein-Gordon equations

We study the nonrelativistic limit of the Cauchy problem for the nonlinear Klein-Gordon equation and prove that any finite energy solution converges to the corresponding solution of the nonlinear Schr?dinger equation in the energy space, after the infinite oscillation in time is removed. We also derive the optimal rate of convergence in . Received: 13 July 2000 / Published online: 1 February 2002     

Spatial distribution and formation of nitrate radical NO<Stack><Subscript>3</Subscript><Superscript>2−</Superscript></Stack> in Antarctic calcitic evaporates

Nitrate radical NO₃²⁻ in calcitic evaporate was discovered in Antarctica. The distribution and formation of nitrate radical NO₃²⁻ in the calcite have been studied by pulse and continuous-wave electron spin resonance. In samples that had been annealed to destroy the NO₃²⁻, regeneration of the radical by γ-rays or UV light indicated that the radical was formed by UV light (with wavelengths less than 340 nm) from solar rays, not by environmental radiation. The nonuniform spatial distribution of the nitrate radical, which was deduced from high ratios of local spin density to total spin density, suggests that the nitrate impurity was introduced into the calcium carbonate after carbonate grain formation. Formation of the carbonate-containing nitrate requires the presence of high amounts of nitrate and a dry climate. Formation of the nitrate radical requires sample exposure to UV light. These conditions are satisfied in the environment of Antarctica.     

Preparation and condensation reactions of a new light-fluorous Mukaiyama reagent: reliable purification with fluorous solid phase extraction for esters and amides

A modified light-fluorous Mukaiyama reagent bearing a C₈F₁₇ tag was prepared and examined in ester and amide forming condensation reactions. Following the reactions, the desired product was effectively separated from the fluorous pyridone by-product using a simple fluorous solid phase extraction.     

A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self‐similar solutions to nonlinear wave equations are proved on up to five space dimensions. © 2006 Wiley Periodicals, Inc.     

Complexation of a hydrophobic thiazorylazophenol with Ni2+ at sodium dodecylsulfate micellar surface

Complexation of thiazorylazododecylphenol (TADP) with Ni2+ at the surface of sodium dodecylsulfate (SDS) micelles has been spectrophotometrically studied. Complicated spectral changes are analyzed by a factor and multivariate analysis, which implies the formation of [TDAP(OH-)Ni]0 as well as a simple 1:1 complex of Ni2+ with TDAP at the micellar interface. All of the equilibrium constants required to describe this system are substantially affected by electrolyte concentrations. Coexistent electrolytes vary the surface potential of the micelle, and in turn influence the equilibria taking place on the micellar surface. The electrostatic potential estimated based on the equilibrium shifts is more negative than that calculated according to Poisson-Boltzmann theory, which simply involves electrostatic effects. This disagreement is possibly caused by different aqueous environments around the micelle from bulk solution, which also facilitate the formation of unusual complex such as [TDAP(OH-)Ni]0.     

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.     

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.     

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.