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.     

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.     

The study of the lipophilicity of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimidobutyramides using chromatographic and computational methods

The lipophilicity of the series of alpha-(4-phenylpiperazin-1-yl)-gamma-phthalimido-butyramides (1-8) has been investigated. Several methods, like reversed-phase thin-layer chromatography and high-performance liquid chromatography using reversed-phase RP18 and IAM.DD2 columns, were applied to determine RMO, log k0 and log k(0IAM) factors. The RP-TLC investigations were performed in mixtures of acetone-water and acetonitrile-water. For RP-HPLC method mixtures of acetonitrile, water and 0.01% TFA were used as the mobile phases while for IAM.DD2 investigations mixtures of acetonitrile and water were applied. The partition coefficients of compounds (1-8) were also calculated with the Pallas and CAChe programs. All the obtained data, both from experimental methods and computational calculations, were compared and a suitable conclusion was reached.     

(Liquid + liquid) equilibria for ternary mixtures of (ethylene glycol + toluene + n-octane)

Tie-line data for ternary systems of (ethylene glycol + toluene + n-octane) at three temperatures (295.15, 301.15, and 307.15) K are reported. The compositions of liquid phases at equilibrium were determined and the results were correlated with the UNIQUAC and NRTL activity coefficient models. The partition coefficients and the selectivity factor of ethylene glycol are calculated and compared to suggest which ethylene glycol is more suitable for extracting of toluene from n-octane. The phase diagrams for the studied ternary mixtures including both the experimental and correlated tie lines are presented. From the phase diagrams and the selectivity factors, it is concluded that ethylene glycol may be used as a suitable solvent in extraction of toluene from n-octane mixtures.     

High-temperature transport properties, thermal expansion and cathodic performance of Ni-substituted LaSr2Mn2O7−δ

The substitution of manganese with nickel in LaSr₂Mn₂O_7−δ, where the solubility limit corresponds to approximately 25% Mn sites, enhances the Ruddlesden-Popper phase stability at elevated temperatures and atmospheric oxygen pressure. The total conductivity of LaSr₂Mn_2−yNi_yO_7−δ (y=0-0.4) decreases with nickel additions, whilst the average thermal expansion coefficients calculated from dilatometric data in the temperature range 300-1370 K increase from (11.4-13.7)×10⁻⁶ K⁻¹ at y=0 up to (12.5-14.4)×10⁻⁶ K⁻¹ at y=0.4. The conductivity and Seebeck coefficient of LaSr₂Mn_1.6Ni_0.4O_7−δ, analyzed in the oxygen partial pressure range 10⁻¹⁵-0.3 atm at 600-1270 K, display that the electronic transport is n-type and occurs via a small polaron mechanism. Reductive decomposition is observed at the oxygen pressures close to Ni/NiO boundary, namely ∼2.3×10⁻¹¹ atm at 1223 K. Within the phase stability domain, the electronic transport properties are essentially p(O₂)-independent. The steady-state oxygen permeability of dense LaSr₂Mn_1.6Ni_0.4O_7−δ membranes is higher than that of (La,Sr)MnO_3−δ, but lower if compared to perovskite-like (Sr,Ce)MnO_3−δ. Porous LaSr₂Mn_1.6Ni_0.4O_7−δ cathodes in contact with apatite-type La₁₀Si₅AlO_26.5 solid electrolyte exhibit, however, a relatively poor electrochemical performance, partly associated with strong cation interdiffusion between the materials.