An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

Hamilton cycles in line graphs of 3-hypergraphs

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.     

一些稀疏图的强边染色（英文）

图G的强边染色是指对图G进行正常边染色使得任意长度为3的路的三条边染不同的颜色.图G的强边色数,记为χ’_s(G),是使得图G是强k边着色的最小正整数kk.2015年,Zang [arXiv:1510.00785]证明了:最大度△(G)=5的图G,χ’_s(G)≤37.本文证明了:最大度△(G)=5且最大平均度小于8/3(或者14/5)的图G,χ’_s(G)≤13 (或者14).另外,本文证明了:最大度△(G)≥3的不含K_2,3-图子式的图G,χ’_s(G)≤4△(G)-6,这个界是紧的.     

Orientation control of perovskite thin films on glass substrates by the application of a seed layer prepared from oxide nanosheets

Orientation control of perovskite compounds was investigated by the application of a seed layer prepared from oxide nanosheets. An aqueous suspension of oxide nanosheets was prepared by the exfoliation of a layered compound of KCa₂Nb₃O₁₀ oxide grains. A seed layer composed of (TBA)Ca₂Nb₃O₁₀ nanosheets (TBA = tetrabutylammonium) was formed on a glass substrate by simply dip coating it in the suspension. Two kinds of perovskite compounds, LaNiO₃ (LNO) and Pb(Zr,Ti)O₃ (PZT) with a preferred orientation of (00l) were successfully grown on this seeded glass substrate. In this study, the relation between lattice mismatch and electrical properties is investigated. A large, oriented PZT film with a size of 5 ×4 cm shows an improved P-E hysteresis behavior by use of this orientation control.     

可调谐钛宝石双波长激光在β－BaB2O4晶体中和频

本文用矩阵光学推导出了相位共轭腔的热稳条件。     

A genetic algorithm for the automated generation of molecules within constraints

Summary A genetic algorithm has been designed which generates molecular structures within constraints. The constraints may be any useful function, for example an enzyme active site, a pharmacophore or molecular properties from pattern recognition or rule-induction analyses. The starting point may be random or may utilise known molecules. These are modified to grow into families of structures which, using the evolutionary operators of selection, crossover and mutation evolve to better fit the constraints. The basis of the algorithm is described together with some applications in lead generation, 3D database construction and drug design. Genetic algorithms of this type may have wider applications in chemistry, for example in the design and optimisation of new polymers, materials (e.g. superconducting materials) or synthetic enzymes.     

Preparation and characterization of theβ-cyclodextrin inclusion complex with sulfafurazole

The 1 : 1 inclusion complex involving sulfafurazole (SF) and-cyclodextrin (-CD) is prepared by the freeze-drying method and characterized on the basis of its chemical analysis, thermal behavior, infrared spectrum, X-ray powder pattern and¹³C NMR spectrum in DMSO-d₆ solution. The stability constant of the inclusion complex was determined by the solubility method. The effect of cyclodextrin on the UV absorption spectrum of sulfafurazole was also observed.     

Synthesis of esters ofpara-hydroxy substituted α-trifluoromethylmandelic acids

Methyl trifluoropiruvate in trifluoroacetic acid at 20 °C rapidly C-hydroxyalkylates various phenols at thepara-positions to afford the corresponding esters ofpara-hydroxy substituted -trifluoromethylmandelic acids.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 528–530, March, 1995.The present study was carried out with the financial support of the Russian Foundation for Basic Research (Project code 93-03-22696).     

掺钕单模光纤激光器的调Q实验研究

采用连续运转Ar+激光器5145 Å输出波长光作为泵浦源,采取端泵浦的平凹光学谐振腔结构,用光学斩波器作为Q开关,建立了掺钕单模光纤激光器的调Q实验装置,对这种激光器的调Q特性进行了实验研究和讨论。     

Non-abelian electrodynamics and the vacuumB (3)

By using an 0(3) gauge group, a non-Abelian theory of vacuum electrodynamics is developed in which the newly discovered longitudinal vacuum fieldsB ⁽³⁾ andi E ⁽³⁾ appear self-consistently with the usual plane wavesB ⁽¹⁾,B ⁽²⁾,E ⁽¹⁾, andE ⁽²⁾ in the circular basis (1), (2), (3), a complex representation of space. Using the charge quantization condition the vacuum Maxwell equations are given in the non-Abelian representation.