L~p INEQUALITIES AND ADMISSIBLE OPERATOR FOR POLYNOMIALS

Let p(z) be a polynomial of degree at most n. In this paper we obtain some new results about the dependence of p(Rz)-βp(rz) + α (R+1/r+1)n-|β | p(rz) s on p(z) s for every α, β∈ C with |α|≤ 1, |β | ≤ 1, R > r 1, and s > 0. Our results not only generalize some well known inequalities, but also are variety of interesting results deduced from them by a fairly uniform procedure.     

Stereoisomeric Tris-BINOL-Menthol Bulky Monophosphites: Synthesis,Characterisation and Application in Rhodium-Catalysed Hydroformylation

Four stereoisomeric monoether derivatives, based on axially chiral (R)- or (S)-BINOL bearing a chiral (+)- or (−)-neomenthyloxy group were synthesised and fully characterised by NMR spectroscopy and X-ray crystallography. The respective tris-monophosphites were thereof prepared and fully characterised. The coordination ability of the new bulky phosphites with Rh(CO)₂(acac), was attested by ³¹P NMR, which presented a doublet in the range of δ = 120 ppm, with a ¹J(¹⁰³Rh-³¹P) coupling constant of 290 Hz. The new tris-binaphthyl phosphite ligands were further characterised by DFT computational methods, which allowed us to calculate an electronic (CEP) parameter of 2083.2 cm⁻¹ and an extremely large cone angle of 345°, decreasing to 265° upon coordination with a metal atom. Furthermore, the monophosphites were applied as ligands in rhodium-catalysed hydroformylation of styrene, leading to complete conversions in 4 h, 100% chemoselectivity for aldehydes and up to 98% iso-regioselectivity. The Rh(I)/phosphite catalytic system was also highly active and selective in the hydroformylation of disubstituted olefins, including (E)-prop-1-en-1-ylbenzene and prop-1-en-2-ylbenzene.     

Using Taguchi Method to Determine the Optimum Conditions for Synthesizing Parapyruvate

The synthesis of parapyruvate is important for the analysis of the content in the pyruvate supplements and the study of aging-related neurodegenerative diseases. However, the pure parapyruvate crystal is not, as yet, commercially available. In this study, we applied the Taguchi’s L9 orthogonal array to investigate the optimal conditions for the preparation of the pure parapyruvate by the alkaline treatment of the pyruvic acid and then followed it with the solvent crystallization steps. We were also interested in revealing the major factors that affect the yield for the synthesized pure parapyruvate crystals. In addition, the parapyruvate-inhibited enzyme kinetic of α-ketoglutarate dehydrogenase complex (KGDHC) was also investigated. We found that the pure parapyruvate could be obtained in combination with an alkaline treatment and two solvent crystallization steps. The main factors affecting the yield of the pure parapyruvate were the concentration of the pyruvic acid (the reactant), the pH of the alkali treatment, the type of solvent used for the crystallization and the volume ratio of solvent used for crystallization. Finally, the optimal conditions could prepare parapyruvate crystals with a high purity of 99.8% and a high yield of 72.8%. In addition, the results demonstrate that parapyruvate is a reversibly competitive inhibitor for KGDHC.     

Electrical properties of highly (111)-oriented lead zirconate thin films

Antiferroelectric PbZrO₃ thin films were grown on Pt/Ti/SiO₂/Si substrates with predominant (111) orientation using a sol-gel process. The Pt/PbZrO₃/Pt film capacitor showed well-saturated hysteresis loops at an applied voltage of 5 V with remanent polarisation (P_r) and coercive electric field (E_c) values of 8.97 μC/cm² and 162 kV/cm, respectively. The leakage current density of the highly (111)-oriented PbZrO₃ film was less than 1.0×10⁻⁷ A/cm² over electric field ranges from 0 to 105 kV/cm. The conduction current depended on the voltage polarity. The PbZrO₃/Pt interface forms a Schottky barrier at electric fields from 20 to 160 kV/cm. The dielectric relaxation current behaviour of Pt/PbZrO₃/Pt capacitor obeys the well-known Curie-Von Schweidler law at electric field of 20-80 kV/cm, the currents have contributions of both dielectric relaxation current and leakage current.     

光学平面绝对检验方法的研究

应用两种方法对三个高精度平面进行了测试。第一种方法是Fritz的三面互检法,它利用Zernike多项式的特性拟合三个面四次组合测量得到的干涉图,然后求出三个面的Zernike多项式系数,从而得到三个面的面形偏差。第二种方法是奇偶函数法,根据函数的奇偶性,把平面的面形函数分解为四类:偶奇、奇偶、偶偶和奇奇函数,分别求出各分量,从而得到三个面的三维面形偏差。对两种方法都编制了理论模拟和实测程序,并进行了实验,实现了无参考面的高精度平面面形测试。     

Critical phenomena in FINEMET alloy

The Fe_73.5Cu₁Nb₃Si_13.5B₉ FINEMET alloy has been prepared by the rapid solidification technique. The critical behaviour of this alloy in the amorphous as well as in its nanocrystalline states has been studied near their respective Curie temperatures. From the values of the critical exponents one can conclude that the alloy behaves like a 3D Heisenberg ferromagnet in the amorphous and nanocrystalline states. But there exists a slight increase in the value of β for the alloy annealed at 823 K (the nanocrystalline state) as observed in most of the amorphous alloys.     

Cu(1 1 1) and Cu(0 0 1) surface electronic states. Comparison between theory and experiment

Recent advances in both the experimental resolution and in the computational capabilities motivate new studies of surface properties. In particular, a detailed comparison between theoretical and experimental data is expected to provide a better insight into surface and image states. In this work we present a joint effort analyzing such features of the Cu(1 1 1) and Cu(0 0 1) surfaces. The experiments are performed by using both linear and non-linear angle-resolved photoemission. From the theoretical point of view, we make use of the Green function embedding technique within density functional theory. We are able to account for the image states by suitably modifying the effective potential in the Kohn-Sham equation and the generalized boundary conditions on the Green function. Comprehensive theoretical and experimental results on the effective mass and the binding energy of the Shockley state and the first image states are reported.     

Accurate and analytical strain mapping at the surface of Ge/Si(0 0 1) islands by an improved flat-island approximation

We propose an extension of the well-known flat-island approximation in (1 + 1) dimensions which, while keeping simple analytical relations, allows one to better describe the strain field on the facets of steeper islands, and on the wetting layer between them. The results of atomistic molecular dynamics simulations using the Tersoff potential are used as a benchmark. The simple continuum approach is also shown to predict the correct trend of the strain gradients characterizing closely-spaced interacting islands, which has been recently observed to produce lateral motion of large Ge dots on Si(0 0 1).     

水平层状介质中电磁场并矢Green函数的一种快速新算法

本文利用提取直射波并结合自适应数字滤波等技术提出一种计算水平层状介质中电磁场并矢Green函数的快速算法. 首先将谱域Green函数中表征均匀介质作用的直射波提取出来并对其积分进行解析计算,这种处理降低了谱域Green函数的奇异性,可在很大程度上缩短其积分收敛区间. 然后在将谱域Green函数剩余部分对应积分转化为三个快速下降积分的基础上,引入一种自适应数字滤波算法对其进行快速求解. 最后通过具体算例验证了本文所述算法的有效性. 关键词： 并矢Green函数 快速算法 水平层状介质     

密立根油滴实验数据处理的一种方法

以在重力场和静电场中运动的带电油滴为研究对象,提出了一种数据处理的方法,快速、准确地求解出基本电荷的电量,验证电荷的不连续性。