Profile empirical likelihood for parametric and semiparametric models

This paper introduces a profile empirical likelihood and a profile conditionally empirical likelihood to estimate the parameter of interest in the presence of nuisance parameters respectively for the parametric and semiparametric models. It is proven that these methods propose some efficient estimators of parameters of interest in the sense of least-favorable efficiency. Particularly, for the decomposable semiparametric models, an explicit representation for the estimator of parameter of interest is derived from the proposed nonparametric method. These new estimations are different from and more efficient than the existing estimations. Some examples and simulation studies are given to illustrate the theoretical results. The first author is supported by NNSF projects (10371059 and 10171051) of China. The second author is supported by a grant from The Research Grants Council of the Hong Kong Special Administrative Region, China (#HKU7060/04P). The third author is supported by the University Research Committee of the University of Hong Kong and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU7323/01M).     

Metric discrepancy results for subsequences of {θ k x}

We determine the set of possible constants appearing in the law of the iterated logarithm for discrepancies of subsequences of {?? ^k x}. We prove that the set coincides with the interval [?1/2, ?? _?? ?], where ?? _?? is the constant for {?? ^k x}. It implies that the discrepancies decrease if we take a subsequence of {?? ^k x}.     

Stability analysis for stochastic jump systems with time-varying delay

This paper deals with the mean-square asymptotic stability of stochastic Markovian jump systems with time-varying delay. Based on a new stochastic inequality and convex analysis property, some novel stability conditions are presented. In the derivation, the information of the time-varying delay is retained and the estimation of it by the worst-case enlargement is not involved. Some special cases of the systems under consideration are also investigated. Illustrative examples are given to show the effectiveness of the proposed approach.     

Stylized facts of price gaps in limit order books

Price gap, defined as the logarithmic price difference between the first two occupied price levels on the same side of a limit order book (LOB), is a key determinant of market depth, which is one of the dimensions of liquidity. However, the properties of price gaps have not been thoroughly studied due to the less availability of ultrahigh frequency data. In the paper, we rebuild the LOB dynamics based on the order flow data of 26 A-share stocks traded on the Shenzhen Stock Exchange in 2003. Three key empirical statistical properties of price gaps are investigated. We find that the distribution of price gaps has a power-law tail for all stocks with an average tail exponent close to 3.2. Applying modern statistical methods, we confirm that the gap time series are long-range correlated and possess multifractal nature. These three features appear to be different in the measures across stocks, but they are similar for the buy and sell LOBs within each stock. Furthermore, we also unveil buy–sell asymmetry phenomena in the properties of price gaps on the buy and sell sides of the LOBs for individual stocks. These findings deepen our understanding of the dynamics of liquidity of common stocks and can be used to calibrate agent-based computational financial models.     

Theoretical and experimental IR spectra of binary rare earth tellurite glasses—1

The binary rare earth tellurite glasses (A_nO_m)_x-(TeO₂)_1−x, where x = 0.1 and A = Sm, Ce, La, were prepared by melting the oxides at 800°C for 1 h and quenched rapidly. The IR spectra has been measured in the frequency region 4000-200 cm⁻¹. The main absorption bands in these glasses related to the characteristics of TeO₂. The detected shift in these bands are found to be sensitive to the glass structure. The A-O bond vibration in the glasses has been calculated. The results were interpreted on the basis of stretching force constant of each bond.     

正电子冲击下氦电离三重微分截面的理论计算

我们发展了一种正电子碰撞原子电离的畸变波Born近似方法, 在这个方法中,正负电子偶素通道通过一个ab initio的光学势附加到入射粒子和靶的相互作用势上,且通道对电离作用被第一次被考虑在正电子碰撞原子电离的过程中. 应用这个方法计算了在50 eV入射能量范围氦的电离的三重微分截面,计算结果和实验数据很好的符合.     

Mathematical modeling and simulation for the flow of magneto-Powell-Eyring fluid in an annulus with concentric rotating cylinders

The rheological fluid flows through concentric rotating cylinders have wide range of applications in many machinary parts such as axles and shafts to spinning projectiles. Whenever, the rotating motion connected with the discs, the proximity of a surface may be remarkably change the structure of the flow. The main purpose of this study is to discuss the motion of Powell-Eyring fluid between two concentric rotating cylinders. We formulated the problem in cylindrical coordinate system with suitable boundary conditions. The existence and uniqueness of the solution for the equation governing the flow is provided with the help of Schauder’s fixed point theorem. The velocity distribution is obtained by Mathematica software. The numerical results are presented for the sundry parameters through graphical representations. It is depicted from our analysis that, the velocity is an increasing function of rotation parameter and Powell-Eyring fluid parameter. The present analysis has wide range of applications in engineering sciences.     

Globalexponential stability of an epidemic model with saturated and periodic incidence rate

This paper is concerned with a SIR model with saturated and periodic incidence rate and saturated treatment function. By using differential inequality technique, we employ a novel argument to show that the disease‐free equilibrium is globally exponentially stable. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

N,Fe, La三掺杂锐钛矿型TiO2能带调节的理论与实验研究

采用基于密度泛函理论(DFT)的平面波超软赝势方法(PWPP), 利用Material studio 计算N, Fe, La三种元素掺杂引起的锐钛矿TiO₂晶体结构、能带结构和态密度变化. 并通过溶胶-凝胶法制得锐钛矿型本征TiO₂, N, Fe共掺杂TiO₂和N, Fe, La共掺杂TiO₂; 用X射线衍射和扫描电镜表征结构; 紫外-可见分光光度计检测TiO₂对甲基橙的降解效率变化. 计算结果表明, 由于N, Fe, La三掺杂TiO₂的晶格体积、键长等发生变化, 导致晶体对称性下降, 光生电子-空穴对有效分离, 同时在导带底和价带顶形成杂质能级, TiO₂禁带宽度由1.78 eV变为1.35 eV, 减小25%, 光吸收带边红移, 态密度数增加, 电子跃迁概率提升, 光催化能力增加. 实验结果表明: 离子掺杂使颗粒变小, 粒径大小: 本征TiO₂>N/Fe_TiO₂>N/Fe/La_TiO₂, 并测得N/Fe/La_TiO₂发光峰425 nm, 能隙减小, 光催化能力比N/Fe_TiO₂强, 增强原因是杂质能级和电子态数量增加引起.