Algorithms of common solutions to quasi variational inclusion and fixed point problems

The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with multivalued maximal monotone mapping and inverse-strongly monotone mappings and the set of fixed points of nonexpansive mappings in Hilbert space.Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper not only improve and extend the main results in Korpelevich（Ekonomika i Matematicheskie Metody,1976,12（4）：747-756）,but also extend and replenish the corresponding results obtained by Iiduka and Takahashi（Nonlinear Anal TMA,2005,61（3）：341-350）,Takahashi and Toyoda（J Optim Theory Appl,2003, 118（2）：417-428）,Nadezhkina and Takahashi（J Optim Theory Appl,2006,128（1）：191- 201）,and Zeng and Yao（Taiwanese Journal of Mathematics,2006,10（5）：1293-1303）.     

ANALYSIS OF NANOBRIDGE TESTS

This paper analyzes nanobridge tests with consideration of adhesive contact deformation, which occurs between a probe tip and a tested nanobeam, and deformation of a substrate or template that supports the tested nanobeam.Analytical displacement-load relation, including adhesive contact deformation and substrate deformation, is presented here for small deformation of bending.The analytic results are confirmed by finite element analysis.If adhesive contact deformation and substrate deformation are not considered in the analysis of nanobridge test data, they might lead to lower values of Young＇s modulus of tested nanobeams.     

The onset of Görtler vortices in laminar boundary layer flow over a slightly concave wall

The onset of convective instability in the laminar boundary layer over the slightly curved wall is analyzed theoretically and compared with the existing experimental data. A new set of stability equations are derived by the propagation theory considering the relative instability under the linear stability theory. In this analysis the disturbances are assumed to have the form of longitudinal vortices and also to grow themselves in streamwise direction. The critical position to mark the onset of Görtler instability is obtained as a function of the Görtler number, where disturbances at the critical state are mainly confined to the hydrodynamic boundary layer. Comparing the theoretical predictions with available experimental and other theoretical results, the present predictions follow experimental trends fairly well with slightly higher critical Görtler numbers than those from the local stability theory. The propagation theory commanding the local eigenvalue analysis is successful to obtain stability conditions reasonably in Görtler vortex problems, relaxing the limitations by the conventional analyses.     

PEPT study of particle motion for different riser exit geometries

Laboratory and industrial risers are equipped with exits of many different layouts, and numerous publications discuss the influence of riser exit geometry on local and overall solids hydrodynamics in the riser. The present paper reviews literature findings--mostly based upon indirect experimental techniques and often somewhat contradictory, Direct measurement of particle velocity and particle occupancy near and in the riser exit provide a better indication of the effect of riser exit geometry. Positron Emission Particle Tracking （PEPT） was used in this work for the first time to investigate the exit region of the riser, An abrupt or sharp exit causes particles to be knocked out of the gas flow, so forming a recirculation or reflux region in the upper part of the riser. This is much less pronounced with a curved or gradual exit.     

磁性聚苯胺纳米微球的合成与表征

报道了具有核壳结构的Fe3O4-聚苯胺磁性纳米微球的合成方法和表征结果.微球同时具有导电性和磁性能.在优化的实验条件下,可得到饱和磁化强度Ms为55.4 emu/g,矫顽力Hc为62 Oe的磁性微球.微球的导电性随着微球中Fe含量的增加而下降.微球的磁性能则随着Fe含量的增加而增大.Fe3O4磁流体的粒径和磁性聚苯胺微球的粒径均在纳米量级.纳米Fe3O4粒子能够提高复合物的热性能.实验表明,磁流体和聚苯胺之间可能存在着一定的相互作用,但这种相互作用较为复杂,难于研究     

L-对甲苯磺酰乳酸乙酯合成物产率的化学分析法

建立了采用 K2 Cr O4 - K2 Cr2 O7混合指示剂测定 L-对甲苯磺酰乳酸乙酯合成物产率的化学分析方法 ,K2 Cr O4 - K2 Cr2 O7的最佳配比为 K2 Cr O4 ∶ K2 Cr2 O7=6∶ 1 (m/m) ,体系的最佳酸度为 p H5.8,测得 L-乳酸乙酯与甲苯磺酰氯反应制备的 L-对甲苯磺酰乳酸乙酯的产率为 94.0 %。     

l—对甲苯磺酰乳酸乙酯合成中产率分析方法的研究

报道了实验室可行、工业生产实用的l－对甲苯磺酸乳酸乙酯产率的分析方法,采用K2CrO4-K2Cr2O7混合指示剂,其最佳配比为K2CrO4:K2Cr2O7=6:1（质量比）,体系的最佳pH为5．8,测得l-乳酸乙酯与对甲苯碘酰氯反应制备和的l-对甲苯磺酰乳酸乙酯的产率为94．0％。     

Synthesis of 1‐Methyl‐3‐aryl‐substituted Titanocene and Zirconocene Dichlorides and Crystal Structure of Bis[η5‐1‐methyl‐3‐(α, α‐dimethylbenzyl) cyclopentadienyl] titanium Dichloride

The syntheses of a series of l‐methyl‐3‐aryl‐substituted titanocene and zirconocene dichlorides are reported. These complexes are synthesized by the reaction of 2‐ and 3‐methyl‐6, 6‐dimethylfulvenes (1:4) with aryllithium, followed by the reaction with TiCl₄·2THF, ZrCl₄ and (CpTiCl₂)₂O respectively, to give complexes 1–5. The complex [η⁵‐1‐methyl‐3‐(α, α‐dimethylbenzyl) cyclopentadienyl] titanium dichloride has been studied by X‐ray diffraction. The red crystal of this complex is monoclinic, space group P2_t/C with unit cell parameters: a =6.973(6) × 10^?1 nm, b =36.91(2) × 10^?1 nm, c = 10.063(4) × 10^?1 nm, α=β= γ = 93.35(5)°, V = 2584(5) × 10^?3 nm³ and Z = 4. Refinement for 1004 observed reflections gives the final R of 0.088. There are four independent molecules per unit cell.     

Enantioselective Allylic Oxidation of Olefins Using Chiral Quinolinyl‐oxazoline Copper Complex Catalysts

Copper complexes of chiral quinolinyl‐oxazoline have been studied as the catalysts for enantioselective allylic oxidation of cycloalkenes with tert‐butyl perbenzoate. Using 5 mol% of these chiral catalysts, optical active allylic benzoates were obtained in moderate enantiomeric excesses. CuOTf prepared in situ, CuClO₄ and CuPF₆ were found to be good precatalysts in acetone.     

Density functional theory studies on the dissociation energies of metallic salts: relationship between lattice and dissociation energies

The formation and physicochemical properties of polymer electrolytes strongly depend on the lattice energy of metal salts. An indirect but efficient way to estimate the lattice energy through the relationship between the heterolytic bond dissociation and lattice energies is proposed in this work. The heterolytic bond dissociation energies for alkali metal compounds were calculated theoretically using the Density Functional Theory (DFT) of B3LYP level with 6‐311+G(d,p) and 6‐311+G(2df,p) basis sets. For transition metal compounds, the same method was employed except for using the effective core potential (ECP) of LANL2DZ and SDD on transition metals for 6‐311+G(d,p) and 6‐311+G(2df,p) calculations, respectively. The dissociation energies calculated by 6‐311+G(2df,p) basis set combined with SDD basis set were better correlated with the experimental values with average error of ca. ±1.0% than those by 6‐311+G* combined with the LANL2DZ basis set. The relationship between dissociation and lattice energies was found to be fairly linear (r>0.98). Thus, this method can be used to estimate the lattice energy of an unknown ionic compound with reasonably high accuracy. We also found that the dissociation energies of transition metal salts were relatively larger than those of alkaline metal salts for comparable ionic radii. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 827–834, 2001