SO_2和NO_2在γ-Al_2O_3(110)表面吸附的第一性原理计算

采用基于平面波基组的Vienna Ab-initio Simulations Package (VASP)程序研究了SO_2和NO_2在γ-Al_2O_3(110)表面和羟基化γ-Al_2O_3(110)表面的吸附,获得了SO_2和NO_2吸附的不同构型和结构参数.对吸附能,电荷转移,差分电荷密度和投影态密度等进行分析和讨论.对比发现,在γ-Al_2O_3(110)表面SO_2的吸附能力强于NO_2.SO_2或NO_2在非羟基化γ-Al_2O_3(110)表面吸附时O原子的2p轨道和Al原子的3s3p轨道作用形成O-Al键,且SO_2吸附时键结强度高于NO_2.NO_2吸附时费米能级以下有部分反键态,削弱了与γ-Al_2O_3(110)表面相互作用.在羟基化γ-Al_2O_3(110)表面SO_2或NO_2的吸附能力会低于非羟基化表面,但是SO_2的吸附能力依旧强于NO_2.计算结果说明SO_2与γ-Al_2O_3(110)表面的相互作用强于NO_2.以上研究,将有助于理解SO_2和NO_2在γ-Al_2O_3的反应性,为进一步研究它们的非均相转化和在灰霾形成中的促进作用奠定基础.     

金属和非金属原子间协同效应调控气体小分子的吸附特性研究

采用基于密度泛函理论方法系统地研究了单个NO和CO小分子在非金属(B和N)与金属Ni原子共掺杂石墨烯(Bx-Ny-gra-Ni,x+y=0,1,2,3)表面的吸附特性,分析了吸附气体小分子的几何结构,吸附能,电荷转移量以及引起体系磁性变化等情况.研究结果表明：NO和CO倾向于吸附在Ni原子的顶位,B和N掺杂原子的数量和比例能够有效地调制小分子的吸附强度;与吸附的CO分子相比,Bx-Ny-gra-Ni表面吸附的NO分子能获得较多的电荷,进而表现出高的稳定性.此外,利用吸附的气体小分子与衬底间相互作用强度和灵敏性的差异、以及引起反应衬底的磁性变化将为设计石墨烯基气敏、催化和电子器件提供重要参考.     

硅和锗纳米线的原子排布和电荷分布的密度泛函紧束缚方法研究

低维硅锗材料是制备纳米电子器件的重要候选材料,是研发高效率、低能耗和超高速新一代纳米电子器件的基础材料之一,有着潜在的应用价值。采用密度泛函紧束缚方法分别对厚度相同、宽度在0.272 nm~0.554 nm之间的硅纳米线和宽度在0.283 nm~0.567 nm之间的锗纳米线的原子排布和电荷分布进行了计算研究。硅、锗纳米线宽度的改变使原子排布,纳米线的原子间键长和键角发生明显改变。纳米线表层结构的改变对各层内的电荷分布产生重要影响。纳米线中各原子的电荷转移量与该原子在表层内的位置相关。纳米线的尺寸和表层内原子排列结构对体系的稳定性产生重要影响。     

基于数学形态学的表面原子熔融相的 STM图像识别算法

高温扫描隧道显微镜(HT-STM)可以实时原位地捕捉到表面原子的熔化相变过程.在这一原位变温实验中,快速可靠地识别出每帧STM图像中的熔融相十分关键.传统的手工统计方法存在效率低下、随意性大等问题.我们发展出一套基于数学形态学的算法,来自动快速地识别.与人工方法相比,该算法消除了人为主观误差,使确定的边界更加准确、光滑,处理效率提高了266倍.     

Cr、Mn、Co、Ni掺杂对Al13Fe4相稳定性和力学性能影响的第一性原理研

采用基于密度泛函理论的第一性原理计算方法,系统地研究了不同掺杂浓度下过渡族元素Cr、Mn、Co、Ni在Al13Fe4相中的占位情况、结构稳定性和机械性能. 计算得到所有的Al13(Fe24-xMx) (M=Cr、Mn、Co、Ni;X=1,2,4)相都具有良好的热力学稳定性和机械稳定性. 相同掺杂浓度化合物的形成焓按如下顺序减小：Al78(Fe24-xCrx) > Al78(Fe24-xMnx) > Al13Fe4 > Al78(Fe24-xNix) > Al78(Fe24-xCox).形成焓的降低增加了Al13Fe4相成核驱动力,Co和Ni有利于促进Al-Fe合金中Al13Fe4相形核,细化Al13Fe4相. 过渡族元素可以改善金属间化合物的脆性,增强塑性变形能力. 并且随着掺杂浓度的增加,过渡族元素的加入对脆性的改善呈先增大后减小的趋势.     

Convergence rate of the best-r-point-average estimator for the maximizer of a nonparametric regression function

The best-r-point-average (BRPA) estimator of the maximizer of a regression function, proposed in Changchien (in: M.T. Chao, P.E. Cheng (Eds.), Proceedings of the 1990 Taipei Symposium in Statistics, June 28–30, 1990, pp. 63–78) has certain merits over the estimators derived through the estimation of the regression function. Some of the properties of the BRPA estimator have been studied in Chen et al. (J. Multivariate Anal. 57 (1996) 191) and Bai and Huang (Sankhya: Indian J. Statist. Ser. A. 61 (Pt. 2) (1999) 208–217). In this article, we further study the properties of the BRPA estimator and give its convergence rate under some quite general conditions. Simulation results are presented for the illustration of the convergence rate. Some comparisons with existing estimators such as the Müller estimator are provided.     

一类广义Lanchester模型的数值解及若干结论

本讨论了一类广义的Lanchester模型在一些限制条件下的近似解，并给出了若干结论。     

Duality Theory in Fuzzy Linear Programming Problems with Fuzzy Coefficients

The concept of fuzzy scalar (inner) product that will be used in the fuzzy objective and inequality constraints of the fuzzy primal and dual linear programming problems with fuzzy coefficients is proposed in this paper. We also introduce a solution concept that is essentially similar to the notion of Pareto optimal solution in the multiobjective programming problems by imposing a partial ordering on the set of all fuzzy numbers. We then prove the weak and strong duality theorems for fuzzy linear programming problems with fuzzy coefficients.     

A NOTE OF THE SPECTRUM OF HOMOGENEOUS COMPACT OPERATORS

In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.     

Comparison of MINQUE and Simple Estimate of the Error Variance in the General Linear Models

Comparison is made between the MINQUE and simple estimate of the error variance in the normal linear model under the nean square errors criterion,where the model matrix need not have full rank and the dispersion matrix can be singular.Our results show that any one of both estimates cannot be always superior to the other.Some sufficient criteria for any one of them to be better than the other are established.Some interesting relations between these two estimates are also given.