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     

Magnetic-field-induced valence transition in EuNi2(Si1−x Gex)2 in fields up to 500 T

The critical fields of the valence transition induced by a magnetic field in the EuNi₂(Si_1?x Ge_x)₂ (x=0.5–0.75) compound in an intermediate valence state are measured. The magnetic-field-induced valence transition is observed in the low-concentration range down to x=0.5. It is demonstrated that the critical field increases linearly with a decrease in the germanium concentration.     

Exponential decay rate of survival probability in a disastrous random environment

Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf; ^d in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0. Received: 21 May 1996 / In revised form: 2 February 1997     

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.     

The economical parameter survey program for long-term transient temperature distribution and stress analysis around the sodium level of the liquid metal fast breeder reactor

The thermal stress around the sodium level of the LMFBR reactor vessel, caused by the axial temperature distribution during heat-up and cool-down transient conditions, is one of the most important problems for a reactor vessel designer, especially in a conceptual design stage. Key parameters relating to plant operating transient conditions and reactor vessel main configuration should be settled carefully, thermal stresses not being allowed to exceed design stress limits. In order to examine the sodium level thermal stress easily and economically, a simple computer program for parameter survey has been developed. This program uses a one-dimensional Fourier series solution in transient temperature distribution analysis, and an analytical stress solution based on shell theory in stress value estimation. This paper presents a simplified and economical calculation method for the axial temperature distribution and stress value in the LMFBR operating transient conditions, and analysis examples obtained with this computer program.

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Zusammenfassung Der durch die axiale Temperaturverteilung während der Übergangsphase von Aufheizen und Abkühlen verursachte thermische Streß rund um den Natriumfüllstand des LMFBR-Reaktorkessels ist für den Reaktorkesselkonstrukteur, besonders im Entwurfstadiuni eines der wichtigsten Probleme. Die mit den transienten Operationsbedingungen der Anlage und der Gestaltung des Reaktorkessels in Beziehung stehenden Grundparameter müssen sorgfältig ermittelt werden, um zu verhindern, daß der thermische Streß die geplanten Streßgrenzen nicht überschreitet. Um den thermischen Streß um den Natriumfüllstand, leicht und ökonomisch zu bestimmen, wurde ein Komputerprogramm für die Parameterübersicht aufgestellt. In diesem Programm wird von einer eindimensionalen Fourrierreihe zur Analyse der transienten Temperaturverteilung und einer auf der Schalentheorie von Streßwertbestimmungen basierende analytische Lösung Gebrauch gemacht. Im vorliegenden Artikel werden eine vereinfachte und wirtschaftliche Berechnungsmethode für die axiale Temperaturverteilung und Streßwerte bei transienten Arbeitsbedingungen mitgeteilt und mit diesem Komputerprogramm ausgeführte Analysenbeispiele angegeben.

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Paper presented at the World Conference on Thermal Analysis, Madeira (Portugal) 1986.     

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.     

Practical asymmetric synthesis of (S)-MA20565, a wide-spectrum agricultural fungicide

A practical asymmetric synthesis of a wide-spectrum agricultural fungicide, (S)-MA20565 (1), is described. The convergent synthesis was achieved starting from commercially available 3-(trifluoromethyl)aniline (7) in 44% overall yield through five steps and 2-bromobenzaldehyde (9) in 48% overall yield through four steps, respectively. (S)-O-[1-(3-Trifluoromethylphenyl)ethyl]hydroxylamine (2), a key intermediate of 1, was prepared via ruthenium(II)-catalyzed asymmetric transfer hydrogenation of 1-(3-trifluoromethylphenyl)ethanone (6) followed by chlorination using methanesulfonyl chloride and oxyamination using potassium acetohydroxamate with high level of stereocontrol.