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     

Two-mass models of the vocal cords for natural sounding voice synthesis

Three new two-mass models of the vocal cords are treated. First, the features, structure, and differential equations of motion are described for each of the new models and compared with those of previous models. Second, performances of the models are discussed in terms of glottal volume flow, glottal area, radiated sound pressure, trajectories of mass movement, running spectra of the output sound pressure, and perceptual naturalness of the output sound. Finally, the major effects of glottal source-vocal tract interaction including skewing, truncation, and superposition are investigated, using one of the simplest types of two-mass models and two types of load representing the vocal tract.     

A compact optical heterodyne interferometer by optical integration and its application

A compact high-resolution optical heterodyne interferometer combining a two-frequency light module and a minute optical system is described. The light module, which generates two independent frequencies of light, is fabricated by proton exchange method on LiNbO₃ substrate. We report an experiment evaluating measurement accuracy using a micro-displacement measurement system which incorporates this interferometer. Results of the experiment with a standard thickness sample show high thermal stability with maximum measurement error of 1.8 nm at a temperature from 19°C to 33°C. The system was used to measure the hysteresis of a piezoelectric element for displacements of several nm, thereby making it possible to analyze the system quantitatively in practice.     

Spherical dye-doped silica particles

Organic dyes such as water soluble porphyrins were incorporated into monodispersed SiO₂ particles using the sol-gel technique (the Stober synthesis) and their monomeric and dimeric properties were investigated by aiming at the microcavity effect. Doping efficiencies of dyes into SiO₂ particles depended on dye's hydrophilic properties. The doping efficiency of a porphyrin, TTMAPP, decreased with increasing the nominal content in the starting solution and the doping content showed the maximum value of 1.6×10^–5 mol/g SiO₂. With increasing the TTMAPP content, spectra of doped particles were changed from dimeric to monomeric nature; the absorption peak due to dimers disappeared and halfwidth of absorption at Soret band decreased. This unusual change was caused by the decrease of particle sizes by dye doping. The TTMAPP-doped sample having monomeric spectrum showed the fluorescence life time of 8.5 nsec and photochemical hole burning at about 5 K.     

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.     

Effect of pressure on the solubilities ofo-,m- andp-xylene in water

The solubilities of o-, m- and p-xylene in water were measured at 25.0°C up to 250, 385, and 50 MPa, respectively. The solubility increased with increasing pressure up to 120 MPa (50 MPa for p-xylene) and then decreased. The reaction volumes, V^o accompanying the dissolution at 0.1 MPa were estimated as –3.6±0.5, –3.4±0.5, and –4.1±0.5 cm³-mol^–1 for o-, m-, and p-xylene, respectively, from the pressure dependences of the solubilities. The limiting partial molar volumes, of p- and o-xylene in water under high pressure were estimated from V^o and the molar volume of the xylene. The partial molar volumes decreased with increasing pressure. The reaction volume for the formation of intra-molecular pairwise hydrophobic interaction between the methyl groups, as proposed by Ben-Naim, is discussed for the V^o of p- and o-xylene at 0.1 MPa.     

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