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61.
Nakao?HayashiEmail author Pavel?I.?Naumkin 《Communications in Mathematical Physics》2006,267(2):477-492
We study the final problem for the nonlinear Schrödinger equation where\(\lambda \in{\bf R},n=1,2,3\). If the final data\(u_{+}\in {\bf H}^{0,\alpha }=\left\{ \phi \in {\bf L}^{2}:\left( 1+\left\vert x\right\vert \right) ^{\alpha }\phi \in {\bf L}^{2}\right\} \) with\(\frac{ n}{2} < \alpha < \min \left( n,2,1+\frac{2}{n}\right) \) and the norm\(\Vert \widehat{u_{+}}\Vert _{{\bf L}^{\infty }}\) is sufficiently small, then we prove the existence of the wave operator in L 2. We also construct the modified scattering operator from H 0,α to H 0,δ with\(\frac{n}{2} < \delta < \alpha\).
相似文献
$i{\partial }_{t}u+\frac{1}{2}\Delta u=\lambda|u|^{\frac{2}{n}}u,\quad (t,x)\in {\mathbf{R}}\times \mathbf{R}^{n},$
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63.
H. Fuchigami Y. Nakao S. Tanimura Y. Uehara T. Kurata S. Tsunoda H. Niino A. Yabe 《Applied Physics A: Materials Science & Processing》1998,67(3):277-282
Received: 12 March 1998/Accepted: 15 March 1998 相似文献
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65.
Dan He Susana Behar Nakao Nomura Shigeru Sassa Henry W. Lim 《Photochemistry and photobiology》1995,61(6):656-661
To study porphyrin biosynthesis in human microvascular endothelial cells, HMEC-1 cells, a transformed human microvascular endothelial cell line, were incubated with 5-aminolevulinic acid (ALA), the precursor of endogenous porphyrins, and porphyrin accumulation was measured spectro-fluorometrically. The HMEC-1 cells accumulated porphyrin in a concentration-related and a time-dependent fashion. Protoporphyrin was the predominant porphyrin accumulated in the cells. The effect of light on protoporphyrin accumulation was evaluated by exposing the ALA-loaded HMEC-1 cells to ultraviolet-A (UVA) and blue light, followed by another incubation with ALA for 2–24 h. Enhancement of protoporphyrin accumulation in irradiated HMEC-1 cells was observed 2–24 h after irradiation, which was associated with a decrease in ferrochelatase protein and activity. Porphyrin accumulation from ALA after irradiation was significantly decreased when catalase (750–3000 U/mL, 29.3–44.3% suppression) or superoxide dismutase (270 U/mL, 36.4% suppression) was present during irradiation. These data demonstrate that HMEC-1 cells were capable of porphyrin biosynthesis, and that exposure of protoporphyrin-containing HMEC-1 cells to UVA and blue light, which includes the Soret band spectrum, decreased the ferrochelatase activity and its protein. These changes were mediated, at least in part, by reactive oxygen species. 相似文献
66.
An apparatus and the procedure for cellulose acetate isoelectric focusing were refined and optimized for routine use in clinical laboratories. The space in the electrophoretic chamber was minimized to maintain high humidity during the run. The water content of the thin cellulose acetate membranes in the chamber was well controlled during isoelectric focusing and the effect of atmospheric carbon dioxide was also excluded. The temperature of the membranes was kept below 2 degrees C, even under conditions of high electric field strength for faster isoelectric focusing of high-molecular-weight proteins. No special training was required for technicians in clinical laboratories to obtain reproducible isoelectric profiles of human serum proteins. 相似文献
67.
Hayashi Nakao; Kaikina Elena I.; Naumkin Pavel I. 《Journal London Mathematical Society》2005,72(3):663-688
The Cauchy problem is studied for the nonlinear equations withfractional power of the negative Laplacian
where (0,2), with critical = /n and sub-critical (0,/n)powers of the nonlinearity. Let u0 L1,a L C, u0(x) 0 in Rn, = . The case of not small initial data is of interest. It is proved that the Cauchy problemhas a unique global solution u C([0,); L L1,a C) and the largetime asymptotics are obtained. 相似文献
68.
Nakao Hayashi Elena I. Kaikina Pavel I. Naumkin 《Mathematical Methods in the Applied Sciences》2005,28(3):275-308
We study the Cauchy problem for non‐linear dissipative evolution equations (1) where ?? is the linear pseudodifferential operator and the non‐linearity is a quadratic pseudodifferential operator (2) û ≡ ?x→ξ u is the Fourier transformation. We consider non‐convective type non‐linearity, that is we suppose that a(t,0,y) ≠ 0. Let the initial data , are sufficiently small and have a non‐zero total mass , where is the weighted Sobolev space. Then we give the main term of the large time asymptotics of solutions in the sub critical case. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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A new method to evaluate the weights of resonance structures from molecular orbital wave function is proposed, which is based on the second quantization of singlet-coupling. The present method is useful to analyze molecules of which the electronic structures are well localizable. The evaluation is carried out through localization of molecular orbitals followed by algebraic calculation of density matrices. This method is applied to H(2)O, H(3)O(+), and BH(3). The calculated weights of covalent and ionic structures are in excellent agreement with those of the previous works and our chemical intuition. 相似文献