Estimation of the Coefficient of Multiple Determination

Assume that we have iid observations on the random vector X = (X ,...,X ) following a multivariate normal distribution N (,) where both R and (p.d.) are unknown. Let denote the multiple correlation coefficient between X and (X ,...,X ). The parameter = , called the multiple coefficient of determination, indicates the proportion of variability in X explained by its best linear fit based on (X ,..., X ). In this paper we consider the point estimation of under the ordinary squared error loss function. The usual estimators (MLE, UMVUE) have complicated risk expressions and hence it is quite difficult to get exact decision-theoretic results. We therefore follow the asymptotic decision theoretic approach (as done by Ghosh and Sinha (1981, Ann. Statist., 9, 1334-1338)) and study Second Order Admissibility of various estimators including the usual ones.     

Some pairs of adjoint functors involving track homotopy categories

K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH _B over a fixed spaceB ([1]). They have introduced two pairs of adjoint functors:P _B N _B andm _* m ^*, whereP _B :H _B →H ^B , andm _*:H _A →H _B for a fixed mapm:A→B. We have introduced a split fibration of categoriesL:H _b →H _B and provedL J, J L in [2]. This paper first extendsP _B N _B to for any fixed mapb: . Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categoriesH _b andH ^b whereH ^b is the dual ofH _b . One of our results isN _b P _b . This differs fromP _B N _B . Supported by National Natural Science Foundation of China     

Boron segregation control in silicon crystal ingots grown in Czochralski process

Boron-doped silicon single crystals of 207 mm diameter with various growing conditions are grown from a large amount of the melt in the cusp-magnetic Czochralski method, and the effects of growing parameters on dopant concentrations in the crystals are experimentally investigated. Equilibrium distribution coefficient of boron calculated by BPS model is 0.716. With the crystal rotation (ω) of 13 rpm and the crucible rotation of , the effective distribution coefficient (k_e) is 0.751 in zero magnetic strength and increases up to 0.78 in the magnetic strength of 640 G. For , there is no significant influence of ω on k_e. With , k_e is almost unity. The experimental results are compared with theory.     

Existence and multiplicity of positive solutions for the p-Laplacian with nonlocal coefficient

We consider the Dirichlet problem with nonlocal coefficient given by in a bounded, smooth domain Ω⊂Rn (n?2), where Δp is the p-Laplacian, w is a weight function and the nonlinearity f(u) satisfies certain local bounds. In contrast with the hypotheses usually made, no asymptotic behavior is assumed on f. We assume that the nonlocal coefficient (q?1) is defined by a continuous and nondecreasing function satisfying a(t)>0 for t>0 and a(0)?0. A positive solution is obtained by applying the Schauder Fixed Point Theorem. The case a(t)=tγ/q (0<γ<p−1) will be considered as an example where asymptotic conditions on the nonlinearity provide the existence of a sequence of positive solutions for the problem with arbitrarily large sup norm.     

Calorimetric study of molecular superconductor κ-(BEDT-TTF)<Subscript>2</Subscript>Ag(CN)<Subscript>2</Subscript>H<Subscript>2</Subscript>O which contains water in the anion layers

Thermodynamic investigation of an organic superconductor κ-(BEDT-TTF)₂Ag(CN)₂H₂O in which the BEDT-TTF dimers are arranged in the κ-type structure in the donor layers is performed by the relaxation calorimetric technique at low temperatures and under magnetic fields. A thermal anomaly related to the superconductive phase transition was observed at 5 K. The existence of residual γ^* in the superconductive state is about 18% of the normal state γ value, which is larger than those of κ-(BEDT-TTF)₂Cu(NCS)₂, and κ-(BEDT-TTF)₂Cu[N(CN)₂]Br salt. The lattice heat capacity reflected on the β-term in the low-temperature heat capacity was found to be affected by the cooling rate. The disorder produced in the network structure constructed by hydrogen bond in the insulating layer is considered to give low-energy phonon excitations reflected in the heat capacity.     

New cut angle quartz crystal microbalance with low frequency-temperature coefficients in an aqueous phase

In a traditional quartz crystal microbalance (QCM), an AT-cut (cut angle φ = 35.25° in yxl orientation) quartz wafer is employed because it has low frequency–temperature coefficients (dF/dT) at room temperature region. But when a QCM is in contact with a liquid phase, its frequency is also related to the properties of the liquid, which are temperature dependent. The value of dF/dT is about 20 Hz/°C for a 9 MHz AT-cut QCM with one side facing water. In this work, a group of QCMs in new cut angles were prepared. The influence of the cut angle on the frequency–temperature characteristic, response sensitivities to surface mass loading and viscodensity of liquid were investigated. An intrinsically temperature-compensated QCM sensor that possesses low dF/dT values in aqueous solution was reported. When a 9 MHz QCM with φ = 35.65° was contacted with water with one side, its dF/dT value is close to zero at ca. 25 °C and its averaged value of |dF/dT| is only 0.6 Hz/°C in the temperature range of 23–27 °C. The frequency responses to surface mass loading and viscodensity of liquid phase are very close among the QCMs with the cut angles in the range of 35.15–35.7°. The intrinsically temperature-compensated QCM was applied to investigate the alternate adsorption processes of cationic polyelectrolyte and silica nanoparticle.     

微乳电动色谱法的研究进展

微乳电动色谱(MEEKC)是一种以微乳为背景电解质,以电压为驱动力的分离技术。本文对MEEKC中的各调节参数进行了概述,重点归纳了MEEKC法在正辛醇-水分配系数测定、中药和手性化合物分离方面的应用,以及在操作技术上的新进展,如多路进样技术以及在线联用质谱检测技术等,并通过对相关文献的分析,对一直存有争议的MEEKC与胶束电动色谱(MEKC)的联系与区别进行了讨论,最后提出了MEEKC法未来的发展空间。     

非血红素配合物[FeⅣ(O)(TMC)(NCMe)]2+与[FeⅣ(O)(TMCS)]+的几何结构、电子结构、成键性和反应活性比较

采用密度泛函理论计算了[FeⅣ(O)(TMC)(NCMe)]2+ 和[FeⅣ(O)(TMCS)]+的电子结构、反应活性和Fe—O的成键性. 几何构型的优化采用非限制性的B3LYP混合密度泛函方法, 重原子Fe的优化采用是LanL2dZ基组, C, H, O, N和S的优化采用TZV基组, 理论计算结果与实验结果相符. 通过对轨道系数和键级的分析发现, TMC配位基对Fe—O的π键几乎没有影响. 由于竖直方向的硫甲基配位基的轨道与Fe的3d轨道具有较强的重迭, 而乙腈配位基作为轴向配体时, 这种重迭则小得多, 导致了两种配合物在电子结构和反应活性上存在一定的差别.