A Study of the Equivalence of the BLUEs between a Partitioned Singular Linear Model and Its Reduced Singular Linear Models

Abstract Consider the partitioned linear regression model and its four reduced linear models, where y is an n × 1 observable random vector with E(y) = Xβ and dispersion matrix Var(y) = σ² V, where σ² is an unknown positive scalar, V is an n × n known symmetric nonnegative definite matrix, X = (X ₁ : X ₂) is an n×(p+q) known design matrix with rank(X) = r ≤ (p+q), and β = (β′ ₁: β′₂ )′ with β₁ and β₂ being p×1 and q×1 vectors of unknown parameters, respectively. In this article the formulae for the differences between the best linear unbiased estimators of M ₂ X ₁β₁under the model and its best linear unbiased estimators under the reduced linear models of are given, where M ₂ = I -X ₂ X ₂ ⁺ . Furthermore, the necessary and sufficient conditions for the equalities between the best linear unbiased estimators of M ₂ X ₁β₁ under the model and those under its reduced linear models are established. Lastly, we also study the connections between the model and its linear transformation model. *This work is supported by the National Natural Science Foundation of China, Tian Yuan Special Foundation (No. 10226024), Postdoctoral Foundation of China and Lab. of Math. for Nonlinear Sciences at Fudan University. This research is supported in part by The International Organizing Committee and The Local Organizing Committee at the University of Tampere for this Workshop **The work is supported in part by an NSF grant of China. Results in this paper were presented by the first author at The Eighth International Workshop on Matrices and Statistics: Tampere, Finland, August 1999     

Distillation protocols: output entanglement and local mutual information

A complementary behavior between local mutual information and average output entanglement is derived for arbitrary bipartite ensembles. This leads to bounds on the yield of entanglement in distillation protocols that involve disinguishing. This bound is saturated in the hashing protocol for distillation, for Bell-diagonal states.     

二环己基(三甲基硅基亚甲基)锡芳香酸酯的合成及结构表征

合成了二环己基(三甲基硅基亚甲基)溴化锡及9个二环己基(三甲基硅基亚甲基)锡芳香酸酯,并通过IR1、H NMR及13C NMR的测定确定了它们的分子结构。结果显示,二环己基(三甲基硅基亚甲基)锡芳香酸酯为中心锡原子四配位的单体结构。     

吸引子的强稳定性与Ω-极限集的性质

本文讨论紧Ｈａｕｓｄｏｒｆｆ拓扑空间上流的吸引子在小扰动下的坚持性和强稳定性,以及Ω－极限集的一些性质．     

A r -Weighted Poincaré-Type Inequalities for Differential Forms in Some Domains

We prove local weighted integral inequalities for differential forms. Then byusing the local results, we prove global weighted integral inequalities for differential forms in L _s (μ)-averaging domains and in John domains, respectively, which can be considered as generalizations of the classical Poincaré-type inequality.     

Tortuosity measurement and the effects of finite pulse widths on xenon gas diffusion NMR studies of porous media.

We have extended the utility of NMR as a technique to probe porous media structure over length scales of approximately 100-2000 microm by using the spin 1/2 noble gas 129Xe imbibed into the system's pore space. Such length scales are much greater than can be probed with NMR diffusion studies of water-saturated porous media. We utilized Pulsed Gradient Spin Echo NMR measurements of the time-dependent diffusion coefficient, D(t), of the xenon gas filling the pore space to study further the measurements of both the pore surface-area-to-volume ratio, S/V(p), and the tortuosity (pore connectivity) of the medium. In uniform-size glass bead packs, we observed D(t) decreasing with increasing t, reaching an observed asymptote of approximately 0.62-0.65D(0), that could be measured over diffusion distances extending over multiple bead diameters. Measurements of D(t)/D(0) at differing gas pressures showed this tortuosity limit was not affected by changing the characteristic diffusion length of the spins during the diffusion encoding gradient pulse. This was not the case at the short time limit, where D(t)/D(0) was noticeably affected by the gas pressure in the sample. Increasing the gas pressure, and hence reducing D(0) and the diffusion during the gradient pulse served to reduce the previously observed deviation of D(t)/D(0) from the S/V(p) relation. The Pade approximation is used to interpolate between the long and short time limits in D(t). While the short time D(t) points lay above the interpolation line in the case of small beads, due to diffusion during the gradient pulse on the order of the pore size, it was also noted that the experimental D(t) data fell below the Pade line in the case of large beads, most likely due to finite size effects.     

催化过硫酸钾氧化银-邻二氮菲-荧光黄离子缔合物褪色光度法测定痕量铋(Ⅲ)

基于 p H=5.50弱酸性介质中 ,铋 ( )催化 K2 S2 O8氧化 [Ag(phen) 2 ]+ · [FIn]-离子缔合物的褪色反应 ,建立了一种催化褪色光度法测定痕量铋 ( )的新方法。该方法线性范围为 0 .0 4— 0 .4 mg/ L,检出限为 6 .0× 10 -11g/ m L。用于发样及水样中 Bi( )的测定 ,获得了令人满意的结果 ,并对反应的机理进行了探讨。     

Time evolution of emission by carbon nanoparticles generated with a laser furnace technique

Time evolution of emission by carbon nanoparticles generated with a laser furnace technique was investigated with a high-speed video camera. Assuming blackbody radiation formula for small spherical particle, the internal temperature of these carbon nanoparticles was determined as a function of time delay (Δt) after laser vaporization. It was found that the internal temperature of them drastically decreased at Δt < 400μs through collision with the surrounding rare gas inside the furnace. On the other hand, in particular laser vaporization condition where yields of C₆₀ and other higher fullerenes in the soot were found to be high, an increase in the blackbody emission intensity could be recognized for longer wavelength ( 660 < λ < 830 nm) at Δt > 400μs. This finding suggests that a certain exothermic process related to the formation of C₆₀ and other higher fullerenes should occur at Δt > 400μs inside the furnace.     

Influence of doping on OH absorption in LiNbO3 crystals

Undoped, Cr doped and Mg, Cr codoped LiNbO₃ crystals were grown by conventional Czochralski technique. Comparative study was carried out using Fourier transform infrared (FTIR) and UV‐Visible spectroscopy. Infrared optical absorption for OH^– ion has been used to study the effect of dopants on the crystals. The peak position of OH^– shift to 3535 cm^‐1 for Mg, Cr codoped crystals compared to 3484 cm^‐1 for undoped and Cr doped crystals. Prominent absorption bands are found in the visible region centered at 480 nm (20833 cm^‐1) and 653 nm (15313 cm^‐1) in Cr doped crystals. Whereas in Mg, Cr codoped crystals these broad absorption bands are red shifted to 517 nm (19342 cm^‐1) and 678 nm (14749 cm^‐1). UV cutoff in Cr doped crystals shift towards higher wavelength compared to undoped LiNbO₃ crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

玻璃表面的无钯活化化学镀镍

在非金属基体上化学镀镍 ,一般要先在基体上形成一层化学镀的催化剂 ,传统工艺是采用PdCl2 SnCl2 活化 敏化法[1 ] 。该工艺处理过程复杂 ,而且使用有毒的PdCl2 ,其价格昂贵。因此无钯活化法将带来巨大的经济效益和社会效益。我们曾在这方面进行了有益的尝试 ,如将玻璃表面经喷雾热解形成ZnO ,然后吸附银盐 ,活化还原 ,再化学镀[2 ] 。李兵等[3] 研究了非金属材料无钯催化活化工艺。研究了活化时间及温度对覆盖度的影响 ,但未给出具体活化液配方。本文提出了玻璃表面的一种无钯活化镀镍液配方 ,该配方由醋酸镍、甲醇、柠檬酸钠和氨组…