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     

Synthesis of endogenous sperm-activating and attracting factor isolated from ascidian Ciona intestinalis

A chemoattractant candidate named sperm-activating and attracting factor (SAAF) from the eggs of ascidian Ciona intestinalis, was synthesized from chenodeoxycholic acid in 16 steps. The present synthesis led to the unambiguous structure determination of SAAF to be (3R,4R,7R,25S)-3,4,7,26-tetrahydroxycholestane-3,26-disulfate. The synthetic pure specimen was also used to confirm the dual sperm-activating and attracting activity.     

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.     

Tumor cell detection method using complement-mediated cytolytic reaction and imaging sensor system

A novel tumor-detection system consisting of complementmediated cytolytic reaction and an image processing system was developed for the simple and rapid determination of tumor cells. The present system consists of a CCD image sensor, image memory board, personal computer, and microscope. When monoclonal antibody 3C4, which is specific to the guinea pig hepatoma L-10, was added to cell suspension, only L-10 cytolysis occurred. Cytolysis caused a decrease in brightness of the cells observed by phase-contrast microscopy. The phase contrast image of the cells before cytolysis was converted to a digitalized signal and stored in computer memory. After cytolysis, a brightness threshold above that of lysed cells was subtracted from the digitalized signal and compared to the signal stored before reaction. L-10 cells in mixed cell suspension were determined specifically by the system. Measurement time was only 2 sec and overall time, including reaction time, was approximately 30 min. Since this method does not require a cell washing process, automation of the whole system is possible.     

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.     

Stereochemistry of nucleophilic addition reactions 13 : Kinetically controlled nucleophilic addition reactions to methyl 4,6-0-benzylidene-2,3- dideoxy-2-nitro-β-D-erythro-hex-2-enopyranoside: an important role of a(1,3) strain

An improved synthesis of methyl 4,6-0-benzylidene-2,3-dideoxy-2-nitro-β-D-erythro-hex-2-enopyranoside and its reactions with various nucleophiles are described; all the nucleophiles were found to approach exclusively or predominantly from the equatorial side of the molecule, giving the β-D-glucopyranoside derivatives as the major or exclusive product. The stereochemical course of approach of a nucleophile observed in the present reactions and in the literature are discussed.