Efficient robust estimation of parameter in the random censorship model

For an open set Θ of ^k, let \s{P_θ: θ Θ\s} be a parametric family of probabilities modeling the distribution of i.i.d. random variables X₁,…, X_n. Suppose X_i's are subject to right censoring and one is only able to observe the pairs (min(X_i, Y_i), [X_i Y_i]), i = 1,…, n, where [A] denotes the indicator function of the event A, Y₁,…, Y_n are independent of X₁,…, X_n and i.i.d. with unknown distribution Q₀. This paper investigates estimation of the value θ that gives a fitted member of the parametric family when the distributions of X₁ and Y₁ are subject to contamination. The constructed estimators are adaptive under the semi-parametric model and robust against small contaminations: they achieve a lower bound for the local asymptotic minimax risk over Hellinger neighborhoods, in the Hájel—Le Cam sense. The work relies on Beran (1981). The construction employs some results on product-limit estimators.     

基于改进U-Net的量子点STM图像分割

为提升量子点图像分割精度,降低特征识别误差,提出一种基于改进U-Net的量子点图像分割方法.首先,在预处理阶段,设计了以色彩通道为权值的灰度化算法,以提升后续分割效果.其次,在STM图像分割部分,在原始U-Net结构上引入中间过渡层以均衡网络各层特征.而后,建立数据集,并通过实验对比不同分割算法的精确度、召回率、F-measure.最后,将分割算法应用于量子点的特征识别,并测试了不同分割方式对应用的影响.实验结果显示,改进灰度化方法保留细节信息丰富,明显提升了量子点分割精度;改进U-Net的平均精确率、召回率、F-measure相较原始网络分别提升了13.83%、2.16%、8.13%.同时,实验数据表明由于分割精度的提升,量子点数量、纵横比等特征参数的识别更加精确.     

团簇Aun+1-1、AunCr-1 (n=1-10)吸附CO的密度泛函理论研究

采用密度泛函理论对CO在阴离子团簇Aun+1-1、AunCr-1(n=1-10))表面的吸附做了系统研究.结果表明,团簇Aun+1CO-1、AunCrCO-1的基态结构是在团簇Aun+1-1、AunCr-1最低能量结构的基础上吸附CO形成; 吸附后的CO键长变长,振动频率减小,表明CO分子被活化;取值相同时,AunCrCO-1的平均结合能高,表明团簇Aun+1CO-1掺杂Cr后稳定性升高.HOMO-LOMO能隙结果表明Aun+1CO-1替代掺杂Cr原子后团簇的化学活性得到了提升,AunCrCO-1、Aun+1CO-1团簇能隙具有奇偶振荡的现象;轨道电荷分析表明CO与团簇相互作用实质是C原子与成键Au原子或Cr原子间转移电荷,CO在与团簇相互作用过程中O原子轨道电荷分布几乎没有发生变化.     

On the Exceptional Zeros of Rankin–Selberg L-Functions

The main objects of study in this article are two classes of Rankin–Selberg L-functions, namely L(s,f×g) and L(s, sym²(g)× sym²(g)), where f,g are newforms, holomorphic or of Maass type, on the upper half plane, and sym²(g) denotes the symmetric square lift of g to GL(3). We prove that in general, i.e., when these L-functions are not divisible by L-functions of quadratic characters (such divisibility happening rarely), they do not admit any LandauSiegel zeros. Such zeros, which are real and close to s=1, are highly mysterious and are not expected to occur. There are corollaries of our result, one of them being a strong lower bound for special value at s=1, which is of interest both geometrically and analytically. One also gets this way a good bound onthe norm of sym²(g).     

具无限时滞的周期系统的持久性与正周期解

本文利用比较定理,控制收敛定理和积分平均的方法,讨论一类具有无限时滞的非自治,非卷积的捕食者-食饵系统的一致持久性和正周期解。     

Testing Lack-of-fit for a Polynomial Errors-in-variables Model

When a regression model is applied as an approximation of underlying model of data, the model checking is important and relevant. In this paper, we investigate the lack-of-fit test for a polynomial error-in-variables model. As the ordinary residuals are biased when there exist measurement errors in covariables,we correct them and then construct a residual-based test of score type. The constructed test is asymptotically chi-squared under null hypotheses. Simulation study shows that the test can maintain the significance level well.The choice of weight functions involved in the test statistic and the related power study are also investigated.The application to two examples is illustrated. The approach can be readily extended to handle more general models.     

Drift transforms and Green function estimates for discontinuous processes

In this paper, we consider Girsanov transforms of pure jump type for discontinuous Markov processes. We show that, under some quite natural conditions, the Green functions of the Girsanov transformed process are comparable to those of the original process. As an application of the general results, the drift transform of symmetric stable processes is studied in detail. In particular, we show that the relativistic α-stable process in a bounded C^1,1-smooth open set D can be obtained from symmetric α-stable process in D through a combination of a pure jump Girsanov transform and a Feynman-Kac transform. From this, we deduce that the Green functions for these two processes in D are comparable.     

Studies on self-pumped phase conjugation in Cu-doped (K0.5Na0.5)0.2(Sr0.61Ba0.39)0.9Nb2O6 crystals

The use of Cu-doped (K_0.5Na_0.5)_0.2(Sr_0.61Ba_0.39)_0.9Nb₂O₆ as self-pumped phase conjugators using internal reflection is reported. Reflectivities as high as 63% at 5145.5 nm and 60% at 632.8 nm were realized. It was found that the photorefractive response changes significantly at different doping concentration. The responses of the crystals to the laser wavelength, incident angle and dopant concentration are studied.     

自适应光学中的非等晕性

本文讨论了自适应光学中非等晕域对补偿效果的影响,提出了一种减小非等晕性误差的新方法—位相梯度法。分析结果表明,该方法可显著增大有效校正的角范围,使非等晕性误差的影响大大减小。我们预期位相梯度法有望解决自适应光学中信标的非等晕性问题。     

Coupling Constant in High Temperature QCD and Deconfinement Phase Transition

Finite temperature renormalization group equation is employed to investigate the effective coupling constant of QCD with respect to temperature.At high temperature,it is very small over the entire region of momentum,this leads to the property of deconfinement of QCD.