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1.
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 相似文献
2.
Shigeyuki Toki Igors Sics Benjamin S. Hsiao Syozo Murakami Masatoshi Tosaka Sirilux Poompradub Shinzo Kohjiya Yuko Ikeda 《Journal of Polymer Science.Polymer Physics》2004,42(6):956-964
The molecular orientation and strain‐induced crystallization of synthetic rubbers—polyisoprene rubber, polybutadiene rubber, and butyl rubber [poly(isobutylene isoprene)]—during uniaxial deformation were studied with in situ synchrotron wide‐angle X‐ray diffraction. The high intensity of the synchrotron X‐rays and the new data analysis method made it possible to estimate the mass fractions of the strain‐induced crystals and amorphous chain segments in both the oriented and unoriented states. Contrary to the conventional concept, the majority of the molecules (50–75%) remained in an unoriented amorphous state at high strains. Each synthetic rubber showed a different behavior of strain‐induced crystallization and molecular orientation during extension and retraction. Our results confirmed the occurence of strain‐induced networks in the synthetic rubbers due to the inhomogeneity of the crosslink distribution. The strain‐induced networks containing microfibrillar crystals and oriented amorphous tie chains were responsible for the ultimate mechanical properties. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 956–964, 2004 相似文献
3.
4.
It is an important challenge to analyze a three-dimensional thermal flow field in engineering, science, and agriculture. For such an analysis, it is essential to measure physical quantities such as temperature and velocity over the entire thermal flow field. This paper presents a measurement system based on color image processing for temperature and velocity vector distributions in a three-dimensional thermal flow field. Flow visualization is accomplished by the use of thermo-sensitive liquid crystal tracers. An algorithm for the color-to-temperature transformation using a multi-layer feed-forward neural network is applied to three-dimensional natural convection in a rotating cylindrical cell. Two-dimensional temperature distributions in a slit plane are obtained by using the algorithm. A three-dimensional temperature distribution is consequently constructed by interpolating the two-dimensional distributions using the B-spline function. In addition, the Spatio-Temporal correlation method is applied to the natural convection to obtain a three-dimensional velocity vector distribution. 相似文献
5.
Terahertz time-domain spectroscopy (THz-TDS) is used to study the intra- and intermolecular vibrational modes of aromatic carboxylic acids, for example, o-phthalic acid, benzoic acid, and salicylic acid, which form either intra- or intermolecular hydrogen bond(s) in different ways. Incorporating the target molecules in nano-sized spaces in mesoporous silicate (SBA-16) is found to be effective for the separate detection of intramolecular hydrogen bonding modes and intermolecular modes. The results are supported by an analysis of the differences in the peak shifts, which depend on temperature, caused by the different nature of the THz absorption. Raman spectra revealed that incorporating the molecules in the nano-sized pores of SBA-16 slightly changes the molecular structures. In the future, THz-TDS using nanoporous materials will be used to analyze the intra- and intermolecular vibrational modes of molecules with larger hydrogen bonding networks such as proteins or DNA. 相似文献
6.
Kai Kamada Shintaro Udo Shuichi Yamashita Yuko Tsutsumi Yasumichi Matsumoto 《Solid State Ionics》2003,160(3-4):389-394
Quantitative analysis of metal cation doping by solid oxide electrochemical doping (SOED) has been performed under galvanostatic doping conditions. A M–β″-Al2O3 (M=Ag, Na) microelectrode (contact radius: about 10 μm) was used as cation source to attain a homogeneous solid–solid contact between the β″-Al2O3 and doping target. In Ag doping into alkali borate glass, the measured dopant amount closely matched the theoretical value. High Faraday efficiencies of above 90% were obtained. This suggests that the dopant amount can be precisely controlled on a micromole scale by the electric charge during electrolysis. On the other hand, current efficiencies of Na doping into Bi2Sr2CaCu2Oy (BSCCO) ceramics depended on the applied constant current. Efficiencies of above 80% were achieved at a constant current of 10 μA (1.6 A cm−2). The relatively low efficiencies were explained by the saturation of BSCCO grain boundaries with Na. By contrast, excess Na was detected on the anodic surface of ceramics at a constant current of 100 μA (16 A cm−2). In the present study, we demonstrate that SOED enables micromole-scale control over dopant amount. 相似文献
7.
Miyuki Harada Yutaka Watanabe Yuko Tanaka Mitsukazu Ochi 《Journal of Polymer Science.Polymer Physics》2006,44(17):2486-2494
A mesogenic‐type curing agent was synthesized to introduce a mesogenic group not only into epoxy resin backbones but also into the crosslink units. In the mesogenic curing agent system, the domain size became larger, and the network arrangement in each domain existed to a greater extent than that in a system cured with the ordinary diamine curing system according to the evidence from polarized optical micrographs and polarized Fourier transform infrared mapping measurements. Moreover, the fracture toughness of the system was considerably improved. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2486–2494, 2006 相似文献
8.
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. 相似文献
9.