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.     

Vibrational energies for the X1A1, A1B1, and B1A1 states of SiH2/SiD2 and related transition probabilities based on global potential energy surfaces

Transition probabilities were evaluated for the X(1)A(1)-A(1)B(1) and A(1)B(1)-B(1)A(1) systems of SiH(2) and SiD(2) to analyze the X-->A-->B photoexcitation. The Franck-Condon factors (FCFs) and Einstein's B coefficients were computed by quantum vibrational calculations using the three-dimensional potential energy surfaces (PESs) of the SiH(2)(X(1)A(1),A(1)B(1),B(1)A(1)) electronic states and the electronic transition moments for the X-A, X-B, and A-B system. The global PESs were determined by the multireference configuration interaction calculations with the Davidson correction and the interpolant moving least-squares method combined with the Shepard interpolation. The obtained FCFs for the X-A and A-B systems exhibit that the bending mode is strongly enhanced in the excitation since the equilibrium bond angle greatly varies with the three states; the barrier to linearity is evaluated to be 21,900 cm(-1) for the X state, 6400 cm(-1) for the A state, and 230-240 cm(-1) for the B state. The theoretical lifetimes for the pure bending levels of the A and B states were calculated from the fluorescence decay rates for the A-X, B-A, and B-X emissions.     

Improvement of some pharmaceutical properties of nocloprost by β- and γ-Cyclodextrin Complexation

Inclusion complexation of nocloprost, a potent antiulcer prostaglandin derivative, with -, -, and -cyclodextrins (CyDs) in aqueous solutions has been studied by the solubility method and¹³C-NMR spectroscopy. The steric requirement of host-guest interaction was reflected in the magnitude of the stability constants and the thermodynamic parameters of the inclusion complexes. Solid complexes of nocloprost with - and -CyDs in a molar ratio of 1 : 2 were obtained on the basis of aBs-type phase solubility diagram. The X-ray diffraction data suggested that nocloprost is included in the cylindrical channel formed by coaxial alignment of -CyD molecules to give a channel type structure. Release and thermal behavior of the solid complexes was examined and compared with nocloprost itself. The results indicated that the -CyD complex may have great utility among the three CyDs, being a rapid dissolving form of nocloprost with improved thermal stability.     

Anticoagulant activity of immobilized thrombomodulin

Bovine lung thrombomodulin was partially purified, and immobilized on agarose gel (Sepharose 4B). Immobilized thrombomodulin inhibited the procoagulant activity of thrombin, and enhanced the thrombin-catalyzed protein C activation. The plasma recalcification time test showed that immobilized thrombomodulin prolonged plasma clotting time. It is suggested that the immobilization of thrombomodulin will provide an antithrombogenic biomaterial able to convert thrombin from a procoagulant to an anticoagulant enzyme.