Accurate finite element method for atomic calculations based on density functional theory and Hartree–Fock method

An accurate finite element method is developed for atomic calculations based on density functional theory (DFT) within local density approximation (LDA) and Hartree–Fock (HF) method. The radial wave functions are expanded by cubic Hermite spline functions on a uniform mesh for , and all the associated integrals are analytically evaluated in conjunction with fitting procedures of the Hartree and the exchange–correlation potentials to the same cubic Hermite spline functions using a set of recurrence formulas. The total energy of atoms systematically converges from above, and the error algebraically decays as the mesh spacing decreases. When the mesh spacing d is taken to be , the total energy for an atom of atomic number Z can be calculated within error of ¹⁰−7 hartree for both the LDA and HF methods. The equal applicability of the method to DFT and the HF method with a similar degree of high accuracy enables the method to be a reliable platform for development of new functionals in DFT such as hybrid functionals.     

一种多约束的密度聚类算法的研究

针对传统的密度聚类算法不能处理带有多约束条件的问题,在现有的密度聚类算法的基础上,提出了一个带有多约束条件限制的密度聚类算法。该算法将多约束条件引入到密度聚类分析中,并分析了多约束条件对聚类结果的影响。实验表明该算法在多约束条件下,可有效完成对数据点的聚类并且效果较好,为现实情况中处理多约束聚类提供了良好的理论支持。     

On the complexity of binary samples

Consider a class of binary functions h: X→{ − 1, + 1} on an interval . Define the sample width of h on a finite subset (a sample) S ⊂ X as ω _S (h) =  min _x ∈ S |ω _h (x)| where ω _h (x) = h(x) max {a ≥ 0: h(z) = h(x), x − a ≤ z ≤ x + a}. Let be the space of all samples in X of cardinality ℓ and consider sets of wide samples, i.e., hypersets which are defined as Through an application of the Sauer-Shelah result on the density of sets an upper estimate is obtained on the growth function (or trace) of the class , β > 0, i.e., on the number of possible dichotomies obtained by intersecting all hypersets with a fixed collection of samples of cardinality m. The estimate is .      

An Artificial Neural Network Classifier Design Based-on Variable Kernel and Non-Parametric Density Estimation

This paper proposes a probabilistic variant of the SOM-kMER (Self Organising Map-kernel-based Maximum Entropy learning Rule) model for data classification. The classifier, known as pSOM-kMER (probabilistic SOM-kMER), is able to operate in a probabilistic environment and to implement the principles of statistical decision theory in undertaking classification problems. A distinctive feature of pSOM-kMER is its ability in revealing the underlying structure of data. In addition, the Receptive Field (RF) regions generated can be used for variable kernel and non-parametric density estimation. Empirical evaluation using benchmark datasets shows that pSOM-kMER is able to achieve good performance as compared with those from a number of machine learning systems. The applicability of the proposed model as a useful data classifier is also demonstrated with a real-world medical data classification problem.     

一种面向并行实现的全局光照算法

提出了种适合于并行实现的全局光照算法。对真实感图象的实时生成和交互式性运行进行了有益的探索,算法主要由两个模块组成;粒子跟踪过程,网格优化与密度估计过程,在此进行了详细介绍。另外,给出算法实际运行得到的具有高度真实感的生成图象。     

一种基于密度树的网格快速聚类算法的研究

聚类算法是数据挖掘领域中一个非常重要的研究方向。人们已经提出了许多适用于大规模的、高维的数据库的聚类算法。基于密度的聚类算法是其中一个比较典型的研究方向。该文以CABDET算法为基础，提出了一种基于密度树的网格快速聚类算法，该算法将网格的原理运用到基于密度树的聚类算法中，有效地提高了聚类的效率，降低了I/O的开销。     

科氏质量流量计在外输原油自动计量中的应用

科氏质量流量计是一种多功能仪表,在液体计量方面有着广泛的应用前景。本文从其工作原理出发,建立了科氏质量流量计的直接测量参数与间接测量参数之间的关系模型,分析了其间接测量的不确定度,提出了采用科氏质量流量计和低含水分析仪构成原油外输动态油量自动计量系统。计算表明,该自动计量系统具有较高的测量精度,可满足原油外输计量精度的要求,为外输原油自动计量方式的正确、合理选择提供了理论依据。     

含氟化镁电解质体系的性质探讨和生产对策

针对电解铝生产中出现的含镁电解质体系性质进行了探讨。对生产中出现的操作问题,系统的分析了原因,并结合生产实际找出了应对措施。     

密度估计函数的收敛速度及重对数率

设ｆＦ为（－∞，∞）上的一族概率密度，ｘ１，ｘ２，…，ｘｎ为取自ｆ的样本。记Ｊｎｉ＝（（ｉ－１）ｈｎ，ｉｈｎ），ｈｎ∞（ｎ→∞），又记Ｒｉ＝＃｛ｔ：ｔ＝１，２，…，ｎ｝，当ｘＪｎｉ时，讨论了ｆ（ｘ）的密度估计函数。并且在Ｌｉｐｓｈｉｔｚ条件下研究了密度估计函数ｆｎ（ｘ）的渐近正态性，最佳可能收敛速度和一致收敛的重对数率。当０＜α＜１，β＜１－α２时，ｆｎ（ｘ）－ｆ（ｘ）＝Ｏ（ｌｎｎｎ－β）ａ．ｓ．；当－１４＜α＜１２时，ｓｕｐｘ｜ｆｎ（ｘ）－ｆ（ｘ）｜＝Ｏ（ｎα－１２ｌｎｌｎｎ）ａ．ｓ等．     

InSb(110)弛豫表面电子态的计算

利用形式散射理论方法，采用最近邻的紧束缚模型计算了ＩｎＳｂ（１１０）弛豫表面的电子结构，给出了总体、局域、分波态密度和表面投影能带。通过分析其表面态的变化指出了表面发生弛豫的原因主要是阴阳离子的ｐ态电子的相互作用加强所产生的。