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Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$begin{alignedat}{2} - Mbiggl(iint_{mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y),d x,d ybiggr)mathscr... 相似文献
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D. T. Luyen 《Mathematical Notes》2017,101(5-6):815-823
In this paper, we study the existence of multiple solutions for the boundary-value problem where Ω is a bounded domain with smooth boundary in R N (N ≥ 2) and Δ γ is the subelliptic operator of the type We use the three critical point theorem.
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$${\Delta _\gamma }u + f\left( {x,u} \right) = 0in\Omega ,u = 0on\partial \Omega ,$$
$${\Delta _\gamma }u = \sum\limits_{j = 1}^N {{\partial _{{x_j}}}\left( {\gamma _j^2{\partial _{{x_j}}}u} \right)} ,{\partial _{{x_j}}}u = \frac{{\partial u}}{{\partial {x_j}}},\gamma = \left( {{\gamma _1},{\gamma _2}, \ldots ,{\gamma _N}} \right).$$
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Pham Khac Hung Fumiya Noritake Luyen Thi San To Ba Van Le The Vinh 《The European Physical Journal B - Condensed Matter and Complex Systems》2017,90(10):185
A systematic analysis on sodium-silicate melt with various silica contents was carried out. The simulation revealed two diffusion mechanisms occurred in the melt: the bond-breaking and hopping between sites. The local structure was analyzed through T-simplexes. It was revealed that T-clusters have a non-spherical shape and represent the diffusion channel, in which Na atoms are dominant, but no any O atoms are located. The SiO2-poor melt acquires a long channel. In contrast, the SiO2-rich melt consists of unconnected short channels. The simulation also revealed the immobile and mobile regions which differ in local structure and constituent composition. We propose a new CL-function to characterizing the spatial distribution of different atom component. The spatial distribution of mobile and immobile atoms is found quite different. In particular, the immobile atoms are concentrated in high-density regions possessing very large density of immobile atoms. The spatial distribution of mobile atoms in contrast is more homogeneous. 相似文献
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A new series of thermotropic liquid crystalline polymers has been synthesized. Mesogenic elements are separated by flexible spacers —(CH2)n— in the backbone. The thermal properties of these polymers are analogous to liquid crystals. 相似文献
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Analysis of a TE011 mode composite sapphire-rutile dielectric resonator has been carried out to study the temperature variation of resonance
frequency, close to the Cs atomic clock hyperfine frequency of 9.192 GHz. The complementary behavior of dielectric permittivity
with temperature of the composite has been exploited to obtain the desired turning point in the resonant frequency. The frequency
of the composite structure is found to be independent of the shield diameter beyond four times the puck diameter. 相似文献
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Ukrainian Mathematical Journal - We prove a nonlinear analog of Picone’s identity for the ?γ -Laplace operator. As an application, we give a Hardy-type inequality and the Sturmian... 相似文献
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Phi Hung Tran Thi Ha Do Thi Luyen Nguyen Phuong Thao Nguyen Trong Thong Nguyen 《Natural product research》2019,33(5):695-700
One new and three known compounds were isolated from the ethanol extract of Psychotria prainii aerial parts. By means of spectroscopic methods, their structures were elucidated to be deacetylasperulosidic acid 6-ethyl ether (1), asperulosidic acid (2), asperuloside (3) and obtucarbamates C (4). The isolated compounds were evaluated for their inhibitory effect on NO production in LPS-stimulated RAW264.7 cells. Among them, compounds 2 and 4 exhibited strong effect with the IC50 values of 5.75 ± 0.85 and 6.92 ± 0.43 μM, respectively. This is the first report for the chemical composition and biological activity of P. prainii. 相似文献
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The structure of a mesomorphic polyester, studied by X-ray diffraction in the anisotropic phase, is very similar to a typical nematic. Orientation of the nematic phase by a magnetic field (0.3 T) is preserved during solidification of the polymer which then appears as a very homogeneous fibre. 相似文献