$2$-Primal环的Ore扩张中的极小素理想和单位元

Let R be an(α,δ)-compatible ring.It is proved that R is a 2-primal ring if and only if for every minimal prime ideal P in R[x;α,δ] there exists a minimal prime ideal P in R such that P = P [x;α,δ],and that f(x) ∈ R[x;α,δ] is a unit if and only if its constant term is a unit and other coefficients are nilpotent.     

Theoretical studies on the electronic structures and spectra of single silicon-doped SWCNTs

The equilibrium geometries and electronic structures of a series of SWCNTs doped with a silicon atom were studied by using density function theory (DFT). The most stable doping site of silicon predicted at B3LYP/6-31G(d,p) level was located near the boundary of the SWCNTs. The energy gaps of (3,3) C₄₈, (3,3) C₆₀ and (3,3) C₇₂ were respectively decreased by 0.43, 0.25 and 0.14 eV after doping. Based on the B3LYP/6-31G(d) optimized geometries, the electronic spectra of the doped SWCNTs were computed using the INDO/CIS method. The first UV absorption at 973.9 nm of (5,5)-Si(L) (C₅₉Si) compared with that at 937.5 nm of (5,5) (C₆₀) was red-shifted. The ¹³C NMR spectra and nuclear independent chemical shifts (NICS) of the doped SWCNTs were investigated at B3LYP/6-31G(d) level. The chemical shift at 119.4 of the carbon atom bonded with the silicon atom in (3,3)-Si(L) (C₅₉Si) in comparison with that at 144.1 of the same carbon atom in (3,3) (C₆₀) moved upfield. The tendency of the aromaticity (NICS = −0.1) for (3,3)-Si(H) (C₄₇Si) with respect to that of the anti-aromaticity (NICS = 6.0) for (3,3) (C₄₈) was predicted.      

Preparation, characterization, and analytical applications of a novel polymer stationary phase with embedded or grafted carbon fibers

A polymer-based chromatographic stationary phase with embedded or grafted multi-walled carbon nanotubes (MWCNTs) has been developed. Three different synthetic methods were utilized to combine the nano-fibers with the substrate of polystyrene-divinylbenzene (PS-DVB). After optimizing the synthetic conditions, this novel polystyrene-divinylbenzene-carbon nanotube (PS-DVB-CNT) stationary phase was characterized by scanning electron microscopy, Raman spectroscopy, thermogravimetric analysis, chemical adsorption and desorption measurement, and mechanical stability test. Compared to PS-DVB particles, PS-DVB-CNT particles have certain improvement in physical and chromatographic performances because the addition of MWCNTs has altered the structures of the particles. The novel stationary phase owns satisfactory resolution, wide pH endurance, and long lifetime, which can be used as an extent to normal HPLC.     

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or the variance parameter of the normal distribution with a normal-inverse-gamma prior, we analytically calculate the Bayes posterior estimator with respect to a conjugate normal-inverse-gamma prior distribution under Stein's loss function. This estimator minimizes the Posterior Expected Stein's Loss (PESL). We also analytically calculate the Bayes posterior estimator and the PESL under the squared error loss function. The numerical simulations exemplify our theoretical studies that the PESLs do not depend on the sample, and that the Bayes posterior estimator and the PESL under the squared error loss function are unanimously larger than those under Stein's loss function. Finally, we calculate the Bayes posterior estimators and the PESLs of the monthly simple returns of the SSE Composite Index.     

具有正态逆伽玛先验的正态分布中的方差参数在Stein损失下的贝叶斯后验估计量（英文）

对于先验分布为正态逆伽玛分布的正态分布的方差参数,我们解析地计算了具有共轭的正态逆伽玛先验分布的在Stein损失函数下的贝叶斯后验估计量.这个估计量最小化后验期望Stein损失.我们还解析地计算了在平方误差损失函数下的贝叶斯后验估计量和后验期望Stein损失.数值模拟的结果例证了我们的如下理论研究:后验期望Stein损失不依赖于样本;在平方误差损失函数下的贝叶斯后验估计量和后验期望Stein损失要一致地大于在Stein损失函数下的对应的量.最后,我们计算了上证综指的月度的简单回报的贝叶斯后验估计量和后验期望Stein损失.     

Kirkendall-effect-based growth of dendrite-shaped CuO hollow micro/nanostructures for lithium-ion battery anodes

Three-dimensional (3D) dendrite-shaped CuO hollow micro/nanostructures have been prepared via a Kirkendall-effect-based approach for the first time and have been demonstrated as a high-performance anode material for lithium-ion batteries. The as-prepared hollow structures were investigated by scanning electron microscopy, transmission electron microscopy, X-ray diffraction, and electrochemical properties. A CuO hollow structure composed of nanocubes outside and a dense film inside was selected as a typical example of the optimized design; it exhibited significantly improved cyclability at a current rate of 0.5 C, with the average Coulombic efficiency of ∼97.0% and 57.9% retention of the discharge capacity of the second cycle after 50 cycles. The correlation between the structure features of the hollow CuO and their electrochemical behavior was discussed in detail. Smaller size of primary structure and larger internal space of electrode materials are crucial to better electrochemical performance. This work represents that Kirkendall effect is a promising method to fabricate excellent hollow electrode materials for Li-ion batteries.     

Synthesis of new amphiphilic diblock copolymers containing poly(ethylene oxide) and poly(α‐olefin)

This article discusses an effective route to prepare amphiphilic diblock copolymers containing a poly(ethylene oxide) block and a polyolefin block that includes semicrystalline thermoplastics, such as polyethylene and syndiotactic polystyrene (s‐PS), and elastomers, such as poly(ethylene‐co‐1‐octene) and poly(ethylene‐co‐styrene) random copolymers. The broad choice of polyolefin blocks provides the amphiphilic copolymers with a wide range of thermal properties from high melting temperature ～270 °C to low glass‐transition temperature ～?60 °C. The chemistry involves two reaction steps, including the preparation of a borane group‐terminated polyolefin by the combination of a metallocene catalyst and a borane chain‐transfer agent as well as the interconversion of a borane terminal group to an anionic (? O^?K⁺) terminal group for the subsequent ring‐opening polymerization of ethylene oxide. The overall reaction process resembles a transformation from the metallocene polymerization of α‐olefins to the ring‐opening polymerization of ethylene oxide. The well‐defined reaction mechanisms in both steps provide the diblock copolymer with controlled molecular structure in terms of composition, molecular weight, moderate molecular weight distribution (M_w/M_n < 2.5), and absence of homopolymer. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3416–3425, 2002     

Study on the polymerizations of methyl methacrylate and styrene initiated with chlorotrimethylsilane and CuCl/N,N,N′,N″,N″-pentamethyldiethyltriamine

Methyl methacrylate (MMA) and styrene (St) have been radically polymerized in the presence of chlorotrimethylsilane and CuCl/N,N,N′,N″,N″-pentamethyldiethyltriamine (Me₃SiCl/CuCl/PMDETA). An analysis of the resultant polymers by ¹H NMR discloses terminal silyl group and chlorine atom in all the obtained polymers. Kinetics studies have been carried out by measuring monomer conversions and polymer molecular weights against polymerization time. The results indicate that, for both MMA and St polymerizations, the monomer conversions exhibit a quasi-linear relationship with polymerization time, and the polymer number-average molecular weight (M_n) also increases with monomer conversion. The molecular weights of both PS and PMMA exceed one hundred thousand. Regardless of molecular weight, all the polymers show narrow molecular distributions (M_w/M_n = 1.2-1.5). These polymerization reactions are speculated to follow a mechanism similar to that of atom transfer radical polymerization (ATRP).