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.     

Ni-catalyzed alkylative dimerization of vinyl grignard reagents using alkyl fluorides

Alkyl halides underwent unique cross-coupling reaction with vinylmagnesium chloride in the presence of Ni catalyst to give 2-alkyl-3-butenyl Grignard reagent (1) in high yields. This reaction proceeded efficiently at 25 degrees C in THF using primary and secondary alkyl fluorides. On the other hand, PhCH=CHMgBr gave double alkylative vinyl coupling product 4 in good yield as the sole coupling product. Alkyl fluorides react as the most suitable alkylating reagent in comparison to the corresponding chlorides, bromides, and iodides.