有限群的s-条件置换子群

如果对群G的任意Sylow子群T,存在一个元素x∈G,使得HT~x=T~xH,那么称群G的子群H在G中s-条件置换．利用s-条件置换子群给出了一些群的性质和结构．     

Empirical likelihood ratio tests for multivariate regression models

This paper proposes some diagnostic tools for checking the adequacy of multivariate regression models including classical regression and time series autoregression. In statistical inference, the empirical likelihood ratio method has been well known to be a powerful tool for constructing test and confidence region. For model checking, however, the naive empirical likelihood (EL) based tests are not of Wilks’ phenomenon. Hence, we make use of bias correction to construct the EL-based score tests and derive a nonparametric version of Wilks’ theorem. Moreover, by the advantages of both the EL and score test method, the EL-based score tests share many desirable features as follows: They are self-scale invariant and can detect the alternatives that converge to the null at rate n ^−1/2, the possibly fastest rate for lack-of-fit testing; they involve weight functions, which provides us with the flexibility to choose scores for improving power performance, especially under directional alternatives. Furthermore, when the alternatives are not directional, we construct asymptotically distribution-free maximin tests for a large class of possible alternatives. A simulation study is carried out and an application for a real dataset is analyzed.      

Study on a broad-area laser diode with external cavity feedback

The external cavity feedback of a broad-area laser diode is investigated. In Fourier optic methods, the inserted prism in an external cavity can be interpreted as a spatial filter in the Fourier plane of the laser diode. The transverse mode can be selected by changing the position of the filter. As the result of a self-consistency theoretical analysis, the output beam of the external cavity has a single-lobed far-field profile. It agrees well with the experiment result. The beam times-diffraction-limit-factor M² is measured to be 1.16.     

平衡线性混合模型方差分量几种估计的优良性

对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计.同时证明了在此条件下,似然方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子.     

Template in situ inducing dispersion of nickel on SBA-15 for methane reforming with carbon dioxide

Highly dispersed Ni/SBA-15 catalysts were prepared via template extraction with varying different extraction times (Ni/S-x, x = 0.5, 3.5, 6.5 h) for methane reforming with carbon dioxide. Based on the various characterization results and initial activity evaluation, Ni/S-3.5 h catalyst showed the best catalytic performance. Compared with the catalyst prepared via template calcination (Ni-S), Ni/S-3.5 h catalyst held steady with CH₄ and CO₂ conversions while those of the Ni-S catalyst respectively decreased by 15 and 11% during the long-term stability test at 700 °C for 50 h. As TEM and TG–DSC results confirmed, Ni particles in spent Ni/S-3.5 h catalyst stayed well-dispersed with size slightly increasing from an initial 3.9–4.1 nm and nearly no carbon deposition was observed. On the contrary, Ni-S catalyst was subjected to sintered metal particles (increased from 11.6 to 18 nm) and formed carbon fibers. The prominent resistance to sintering and coking over stable Ni/S-3.5 h catalyst was attributed to the high dispersion and strengthened metal-support interaction induced via the residual in situ templates.     

Developments in high‐speed countercurrent chromatography and its applications in the separation of terpenoids and saponins

High‐speed countercurrent chromatography is a liquid–liquid separation chromatographic technique, which has the unique feature of eliminating irreversible adsorption using liquid support medium, and is widely used in research and development of traditional Chinese medicine, biochemistry, food, environment analysis, and so on. In this review, some new developments of countercurrent chromatography, for instance cross‐axis countercurrent chromatography, dual countercurrent chromatography, foam countercurrent chromatography, and pH‐zone‐refining countercurrent chromatography are presented. Furthermore, the research and progress in high‐speed countercurrent chromatography techniques and its application in the separation and purification of terpenoids and saponins are reviewed.     

Double Soliton Solutions of Belinsky–Zakharov Equation Related to the Self-Dual SU(N) Gauge Fields

The Belinsky–Zakharov inverse scatteringmethod is extended to a double high-dimension form. Itis associated with the self-dual SU(N) gauge fields.With the harmonic function method, some scattering wave functions can be directly obtained. Theone-soliton solution and general n-soliton solution aregiven.     

Study of electrochemical performances of multi-doped spinel Li1.1Mn1.85Co0.075Ni0.075O4 at 4.3 and 5 V

Li_1.1Mn_2???2x Co _x Ni _x O₄ (x?=?0, 0.075) spinel powders were successfully synthesized using a liquid stirred tank reactor method. The electrochemical performances of the undoped and doped spinels at 4.3 and 5 V were investigated by X-ray diffraction, field-emission scanning electron microscopy, and electrochemical impedance spectroscopy. The capacity of Li_1.1Mn_2???2x Co _x Ni _x O₄ could be divided into two parts, with 4.3 V as the dividing line in the 3–5 V charge–discharge range. Low capacity and good cyclic performance were obtained when cycled in the 3–4.3 V range for the multi-doped Li_1.1Mn_2???2x Co _x Ni _x O₄ spinel. In comparison with multi-doped spinel at 4.3 V, the results of the cyclic performance worsened at 5 V because the structure underwent further shrinkage, the charge transfer resistance rose and the electrolyte decomposed.     

Control of Hopf bifurcations of nonlinear infinite-dimensional systems: application to axial flow engine compressor

We study the local feedback stabilization of Hopf bifurcations for nonlinear systems of infinite dimensions in the case where the linearized vector field has a pair of simple nonzero imaginary eigenvalues and all its other eigenvalues lie strictly in the left half-plane. Discussing the normal form of nonlinear systems obtained by making use of the integral averaging method, we obtain sufficient and necessary condition for controlling the stability of the systems even if the critical modes are uncontrollable. As an application, we apply the obtained results to the control of axial flow engine compressor.     

BBO晶体四倍频全固态小功率紫外激光器

 利用KTP晶体和BBO晶体,进行了激光二极管泵浦的Nd:YVO₄声光调Q激光脉冲四倍频实验。在不同绿光功率入射时,获得光束的束腰半径和紫外转换效率的依赖关系:当绿光功率为1.10 W,束腰半径为12.4 μm时,得到了210 mW的准连续266 nm紫外脉冲输出,四倍频转换效率为19.1%。实验还对紫外远场光斑分别在o光振动面和e光振动面内进行分析,指出了BBO晶体在该两平面内不同的倍频接受角是造成椭圆形紫外光斑和主光斑附近明暗条纹的主要原因。