Probabilistic and Average Linear Widths of Sobolev Space with Gaussian Measure in L \infty-Norm

In this paper we investigate the probabilistic linear $(n,\delta)$-widths and $p$-average linear $n$-widths of the Sobolev space $W^r_2$ equipped with the Gaussian measure $\mu$ in the $L_{\infty}$-norm, and determine the asymptotic equalities \begin{eqnarray*} \lambda_{n,\delta}(W^r_2,\mu,L_{\infty}) &\asymp&\frac{\sqrt{\ln (n/\delta)}}{n^{r+(s-1)/2}},\\[3pt] \lambda^{(a)}_n(W^r_2,\mu,L_{\infty})_p &\asymp&\frac{\sqrt{\ln n}}{n^{r+(s-1)/2}}, \qquad 0 < p < \infty. \end{eqnarray*}     

高斯光束照射下的圆盘夫琅禾费衍射

推导了高斯光束照射圆孔或圆盘的衍射场普遍表达式，计算了半波带数接近于零的情况下上述衍射场的数据，进而分析了圆盘衍射场在艾里斑中增加一个暗环的原因。     

Synthesis and characterization of norbornene–ethylene–styrene terpolymers with a substituted ansa‐fluorenylamidodimethyltitanium‐based catalyst

This article reports a synthetic method for a norbornene–ethylene–styrene (N‐E‐S) terpolymer, which has not been well investigated so far, via incorporation of styrene (S) into vinyl‐type norbornene–ethylene (N‐E) copolymers catalyzed by a substituted ansa‐fluorenylamidodimethyltitanium [Me₂Si(3,6‐tBu₂Flu)(tBuN)]TiMe₂ catalyst ( I ) activated with a [Ph₃C][B(C₆F₅)₄]/Al(iBu)₃ cocatalyst at room temperature in toluene. The resulting terpolymerization product contained the targeted N‐E‐S terpolymer and the contaminated homopolymers, which were then able to be completely removed by solvent fractionation techniques. While homopolystyrene was easily extracted by fractionation with methylethylketone as a soluble part, homopolyethylene and a trace amount of homopolynorbornene could be perfectly separated by fractionation with chloroform as insoluble parts. The detail characterizations of a chloroform‐soluble polymer with gel permeation chromatography, nuclear magnetic resonance, and differential scanning calorimetry analyses proved that it contained a true N‐E‐S terpolymer with long N‐E sequences incorporated with isolated or short styrene sequences. The homogeneity of the morphology together with a single glass transition temperature that proportionally decreased with the increase of the styrene contents indicated that the N‐E‐S terpolymer obtained in this work is a random polymer with an amorphous structure. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2765–2773, 2007     

利用谱线宽度测人发中的微量元素

通过实验证明了可以利用谱线宽度做永久工作曲线用于光谱定量分析。给出了用于测量人发中微量元素Ｃｕ，Ｚｎ，Ｆｅ和Ｃａ的永久工作曲线，利用这些工作曲线对实际样品进行了测定，所得结果与用ＩＣＰ－ＡＥＳ测得的结果相吻合。     

群青颜料呈色机理的电子顺磁共振研究

研究了阿富汗青金石矿石、敦煌石窟青金石颜料、合成群青的呈色机理。实验表明三者均有ｇ＝２．０２９峰，前两者多一个ｇ＝２．０４７峰，４００℃时，ｇ＝２．０４７峰变平，６００℃时消失。ｇ＝２．０２９峰随温度升高而增强，８００℃时增强放慢，颜色也随温度变深。在Ｍ０Ｏ３／ＳｉＯ２和Ｍ０Ｏ３／Ａｌ２Ｏ３表面上，Ｓ２＾－的ＥＰＲ有ｇ１＝２．０４７，ｇ２＝２．２０８，ｇ３＝１．９９８三个分量。因此，群青、青金石和     

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.     

单分散纳米InVO4(正交相)的低温合成

InVO₄ is a new developed visible light responding photocatalyst for water decomposition, which is obtained by a solid-state reaction at high temperature traditionally. In this paper, pure InVO₄ nano-crystalline powder has been prepared by a hydrothermal process at low temperature and was characterized by TEM, IR, and X-ray diffraction. Many factors such as pH value, reaction time and temperature have been investigated. It is found that the optimal conditions for the preparation is: n_InCl3∶n_NaVO3=1∶2; temperature : 150 ℃; Reaction time: 4～8 h; pH=7.9～8.0. And the experimental result shows that it is a convenient way to get single dispersing InVO₄ nano-crystalline powder by flux in alkyl alcohol.     

Phosphorescence lifetime of naphthalene and phenanthrene in aggregated aromatic molecule-β-cyclodextrin-precipitant complexes

Aggregated aromatic molecule--cyclodextrin-precipitant complexes exhibit long-lived phosphorescence at room temperature in water after the chemical binding of oxygen. The temperature dependences of the phosphorescence lifetimes of naphthalene-h₈, naphthalene-de, and phenanthrene in the aggregates were measured. For example, the phosphorescence lifetimes of naphthalene-d₈ aggregated with -cyclodextrin and cyclohexane are equal to 25.1, 17.6, and 6.8 s at 77, 276, and 347 K, respectively, and that of phenanthrene aggregated with isooctane and -cyclodextrin are 3.24, 3.06, and 1.26 s at 268, 274, and 335 K, respectively. The temperature dependences of the phosphorescence lifetimes at room temperature are determined by the rate constants of the radiative and nonradiative transitions from the triplet state of an aromatic molecule.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 2225–2228, September, 1996.     

Characterization of high-temperature superconductors by electron microprobe analysis

In order to optimize the physical properties of HTSC small single crystals grown from a melt for basic studies of their physical properties the influence of the environment on their impurity content was investigated by EPMA. This requires quantitative analysis of all elements being present in the crystals. The accuracy of results was affected by problems with the choice and quality of standards, by contamination but also by malfunction of microprobe electronics. The HTSC materials were found to react with mills, milling balls, crucibles and the atmosphere. These problems are being discussed and some reactions being studied for Y₁Ba₂Cu₃O_6+x (0 < x < 1) HTSC in A1₂O₃ and ZrO₂ crucibles. The crystals grown contain reproducible amounts of impurities depending on boundary conditions and exhibit a zone structure in composition particularly for Y and Ba within their range of homogeneity.     

Capacity factors and peak widths in the gradient elution reversed phase separation of high molar mass polystyrenes

Summary A simplex method for determining the constantsS andk _o from the equation lnk’=lnk _o−S ϕ (was developed and applied to the reversed phase separation of high molar mass polystyrenes using gradients of any curvature. Experimental retention times described using the equation had a standard deviation of 1.1%. The inclusion of a quadratic term in the equation was found to be unwarranted. BothS and lnk _o varied linearly with ln molar mass. The logarithm of peak width of an eluting polystyrene peak was found to be a linear function of the mobile phase composition at elution. The slope was equal toS.