A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

First-principles study on the origin of optical transitions to be associated with F colour centers for PbWO4 crystals

The electronic structures of PbWO₄ crystals containing F type color centers with the lattice structure optimized are studied within the framework of the fully relativistic self-consistent Direc–Slater theory, using a numerically discrete variational (DV-Xα) method. The calculated results show that F and F⁺ centers have donor energy level in forbidden band. Their optical transition energy are 1.84 eV, 2.21 eV, respectively, which corresponds to the 680 nm, 550 nm absorption bands. It predicts that the 680 nm, 550 nm absorption bands originate form the F and F⁺ centers in PbWO₄ crystals.     

Characterization of iron surface modified by 2-mercaptobenzothiazole self-assembled monolayers

A self-assembled monolayer of 2-mercaptobenzothiazole (MBT) adsorbed on the iron surface was prepared. The films were characterized by electrochemical impedance spectroscopy (EIS), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared reflection spectroscopy (FT-IR) and scanning electron microscopy (SEM). Besides, the microcalorimetry method was utilized to study the self-assembled process on iron surface and the adsorption mechanism was discussed from the power-time curve. The results indicated that MBT was able to form a film spontaneously on iron surface and the presence of it could protect iron from corrosion effectively. However, the assembling time and the concentration influence the protection efficiency. Quantum chemical calculations, according to which adsorption mechanism was discussed, could explain the experimental results to some extent.     

北京自由电子激光最近进展──实现饱和振荡

北京自由电子激光(BFEL)装置于1993年底在10.68μm处实现了饱和振荡.输出激光能量为3mJ,饱和平顶宽度2μs.对应饱和振荡平均功率为210kW(宏脉冲),峰值功率约为20MW,比自发辐射高8个量级,单程小讯号净增益为24%,转换效率为0.45%,与理论预期结果相符.光束质量接近衍射极限.目前装置可工作于9-11μm.     

广义风险过程中渐近方差的非参数估计

本文对广义风险过程中的渐近方差作了非参数估计,得出并证明了两个定理,为广义风险过程中破产概率的区间估计作了理论准备．     

3,3,6,6-四甲基-9-邻氯苯基-1,8-二氧代-3,4,5,6,7,9-六氧化氧杂蒽的合成和晶体结构

标题化合物C23H25对O3Cl是由邻氯苯甲醛与5，5-二甲基1，3-环己二酮在N，N-二甲基甲酸腹中反应而得。结构通过单晶X-射线衍射法确定，其晶体属于单科晶系，空间群=1632。晶体结构用直接法解出，使用全矩阵最小二乘法对原子参数进行修正，最后的偏离因子为R=0．054，Rw一0．063。在晶体结构中，吡喃环与苯环之间的两面角为92．43°。     

Selective dimerization of α-methylstyrene catalyzed by a solid acid

A novel solid acid prepared from concentrated sulfuric, boric and phosphoric acid is a highly selective catalyst for the dimerization of α-methylstyrene at room temperature to generate 4-methyl-2,4-diphenyl-1-pentene.     

Geometry,stability and aromaticity of β-diketiminate-coordinated alkaline-earth compounds

Alkaline-earth (Ae) metals have attracted a wealth of interdependent research from synthetic chemists. In Ae-catalyzed organometallic reactions, β-diketiminate is a typical ligand used to stabilize Ae catalysts by forming six-membered rings comprising Ae metals. Herein, studies focusing on the configuration of β-diketiminate-coordinated Ae compounds observed that the CC and CN bonds are homogeneous and unchanged. Furthermore, energetic studies observed that the formation of the Ae-incorporated six-membered rings results in enhanced stability of >20 kcal/mol. The nucleus-independent chemical shifts, anisotropy of the induced current density, and molecular orbital analyses demonstrated the non-aromaticity of the β-diketiminate-coordinated Ae compounds. The improved stability of these compounds can be explained by the delocalization of the π electrons derived from the β-diketiminate moiety.     

Total Synthesis of Several 8, 8",-Biflavones

8,8"-Biflavonoidsareantw0rtantclass0fbiflavonoids.Asasystematicresearchofthe8,8"-biflav0noids,wehavepreviouslyreportedthestudyonthereactionof2'-hydroxychaloneswithl2-H2SO4-DMSOsystem.'InthispaPer,thesynthesisof5,5",7,7',-tetTameth0xy-8,8"-biflavonela2,4,4",7,7"-tetramethoxy-8,8"-biflavone1b',4',4",,5,5,',7,7"-hexamethoxy-8,8"-biflav0ne1c4and4,4"-dibenZyl0xy-5,5",7,7"-tetramothoxy-8,8"-biflavoneldisreported.ThesyntheticmethodisshownintheSchemebelow.2-Hydroxyacet0phenonescondensedwithsubsti…     

The formation of mesoporous TiO2 spheres via a facile chemical process

The mesoporous TiO(2) solid and hollow spheres have been synthesized via a controllable and simple chemical route. Structural characterization indicates that these TiO(2) mesoporous spheres after calcined at 500 degrees C have an obvious mesoporous structure with the diameters of 200-300 nm for solid spheres and 200-500 nm for hollow spheres. The average pore sizes and BET surface areas of the mesoporous TiO(2) solid and hollow spheres are 6.8, 7.0 nm and 162, 90 m(2)/g, respectively. Optical adsorption investigation shows that TiO(2) solid and hollow spheres possess a direct band gap structure with the optical band gap of 3.68 and 3.75 eV, respectively. A possible formation mechanism for TiO(2) solid and hollow spheres is discussed.