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.     

Photodimerization of benzene -photochromism of layered dithiacyclophane-

A novel cage compound was obtained by irradiation of a quadruple-layered dithiacyclophane and showed thermally reverse reaction.     

Constituents of holothuroidea.9. Isolation and structure of a new ganglioside molecular species from the sea cucumber Holothuria pervicax

A new ganglioside molecular species, HPG-7 (1) was obtained from the polar fraction of the chloroform/methanol extract of the sea cucumber, Holothuria pervicax. On the basis of chemical and spectroscopic evidence, the structure of 1 was determined, and the major component was 1-O-[alpha-L-fucopyranosyl-(1-->4)-(N-acetyl-alpha-D-neuraminosyl) - (2-->11)-(N-glycolyl-alpha-D-neuraminosyl)-(2-->4)-(N-acetyl -alpha-D- neuraminosyl)-(2-->6)-beta-D-glucopyranosyl]-(2S,3S,4R)-2-[(2R)-2- hydroxytetracosanoylamino]-14-methyl-hexadecane-1,3,4-triol. This is the first report on the isolation and structure elucidation of trisialo-ganglioside from sea cucumber. 1 showed neuritogenic activity toward the rat pheochromocytoma cell line, PC-12 cell.     

Three-way-output response system by electric potential: UV-vis, CD, and fluorescence spectral changes upon electrolysis of the chiral ester of tetracyanoanthraquinodimethane

The newly prepared tetracyanoanthraquinodimethane (TCNAQ) derivatives 1a,b with a chiral auxiliary are good electron acceptors and exhibit weak circular dichroism (CD) based on the absorption of TCNAQ. The twin-type electron acceptor 1c with two TCNAQ units shows larger ellipticity by exciton coupling. UV-vis, CD, and fluorescence spectra were changed drastically upon electrochemical reduction of 1c, which demonstrates the unprecedented three-way-output response system.     

Ab initio calculations of isomerization reaction of diphosphene 1-sulfide to thiadiphosphirane

Ab initio Calculations of the isomerization reaction of diphosphene 1-sulfide (2′) to thiadiphosphirane (3′) suggest that the energy barrier of the reaction in the ground state is 25 kcal/mol and that 2′ lies 21 kcal/mol above 3′, while the calculations show that there exists one local minimum on the lowest triplet energy surface.     

Importance of the Debye interaction in organic solutions: Henry's law constants for polar liquids in nonpolar solvents and vice versa

Henry's law constants have been determined for -butyrolactone (BL), ethyl acetate (EA), and 2-methyl-3-pentanol (MEP) in mixtures of iso-octane (ISO) and toluene (TOL), for BL, EA, TOL, and ISO in cinnamaldehyde (CIN) and for TOL and ISO in each other and in BL. From these data and published vapor pressures, the activity coefficients at infinite dilution and the standard molar Gibbs free energy of transfer, G ₂ ⁰ of the solutes from dilute solution in ISO to dilute solution in each solvent medium have been calculated. The different behavior patterns of BL and EA are attributed to differences in their abilities to exist in different conformations possessing different dipole moments. For polar solutes, G ₂ ⁰ decreases with increasing polarizability of the solvent and with increasing dipole moment of the solute, suggesting increased contributions from dipole-induced dipole (Debye) interactions. The sigmoidal plot of G ₂ ⁰ against the change in pair potential energy calculated from the classical expressions suggests that G ₂ ⁰ seriously underestimates the strength of the Debye interactions in comparison with the London interactions.     

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