Infinitely Many Solutions of Nonlocal Kirchhoff-Type Equations via Perturbation Methods

Mathematical Notes - We study the multiplicity of weak solutions to the boundary-value problem $$\begin{alignedat}{2} - M\biggl(\iint_{\mathbb R^{2N}}|u(x)-u(y)|^2 K(x-y)\,d x\,d y\biggr)\mathscr...     

Two nontrivial solutions of boundary-value problems for semilinear Δ<Subscript><Emphasis Type="Italic">γ</Emphasis></Subscript>-differential equations

In this paper, we study the existence of multiple solutions for the boundary-value problem

$${\Delta _\gamma }u + f\left( {x,u} \right) = 0in\Omega ,u = 0on\partial \Omega ,$$

where Ω is a bounded domain with smooth boundary in R ^N (N ≥ 2) and Δ _γ is the subelliptic operator of the type

$${\Delta _\gamma }u = \sum\limits_{j = 1}^N {{\partial _{{x_j}}}\left( {\gamma _j^2{\partial _{{x_j}}}u} \right)} ,{\partial _{{x_j}}}u = \frac{{\partial u}}{{\partial {x_j}}},\gamma = \left( {{\gamma _1},{\gamma _2}, \ldots ,{\gamma _N}} \right).$$

We use the three critical point theorem.

     

含油岩心显微荧光成像光谱研究

发展了一种显微荧光光谱成像技术,并将其应用于天然岩心进行显微荧光成像光谱研究。利用这种技术同时采集含油岩心表面的荧光光谱信息和空间信息．并对获得的光谱图像给予光谱学和地质学解释。结果表明,不但能显示岩心形貌和组分的大致趋势,而且能揭示其精细细节．为石油地质研究提供了一种新方法,为今后的石油勘探开发工作提供了一种先进的指导手段。     

Study of diffusion and local structure of sodium-silicate liquid: the molecular dynamic simulation

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.     

Influence de la structure sur les proprietes mesomorphes des polyesters—I

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.     

Analysis of a shielded TE011 mode composite dielectric resonator for stable frequency reference

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.     

Picone’s Identity For ∆γ -Laplace Operator and its Applications

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...     

Anti-inflammatory constituents from Psychotria prainii H. Lév

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.     

Etude structurale aux rayons-x d'un polyester nematique thermotrope

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.