Local polynomial fitting under association

We consider the estimation of multivariate regression functions r(x₁,…,x_d) and their partial derivatives up to a total order p1 using high-order local polynomial fitting. The processes {Y_i,X_i} are assumed to be (jointly) associated. Joint asymptotic normality is established for the estimates of the regression function r and all its partial derivatives up to the total order p. Expressions for the bias and variance/covariance matrix (of the asymptotic distribution) are given.     

图书采购流程中资金分配模型研究

本应用现代经济理论的择优分配原理，在图书产出效益函数的性质探讨的基础上，将效益函数的约束条件转化为对资金变量的约束条件，从而简化了资金分配方案的求解。提出了资金在各类别图书中的分配模型，指导图书馆图书采购工作。     

一种基于多目标约束的互连线宽和线间距优化模型

优化线宽和线间距已经成为改善系统芯片性能的关键技术.本文基于互连线线宽和线间距对互连延时、功耗、面积和带宽的影响,提出了基于多目标优化方法实现优化线宽和线间距的思路,并利用曲线拟合方法得到了多目标约束的解析模型.Hspice验证结果显示,该解析模型精度较高,平均误差不超过5%,算法简单,能有效弥补应用品质因数方法的缺陷,可以应用于纳米级互补金属氧化物半导体系统芯片的计算机辅助设计.     

光谱辐射照度标准灯的数据插值与曲线拟合方法研究

介绍了多种插值方法与曲线拟合方法,对光谱辐射照度标准灯在所需波长间隔上的照度值进行内插运算,包括这些方法的模型建立、参数计算及误差分析过程。得到了效果较好的插值方法及分段普朗克曲线拟合模型,其中拟合模型较好地体现了光谱辐射照度标准灯的灯丝发射率及灯壳的光谱透射比。最终结果的相对偏差接近国家级计量院提供标准灯的最佳不确定度0.2%。     

Analytical Dielectric Spectrum Formula Based on Representative Frequencies

基于电介质复折射率的实验数据,采用最小二乘法结合选取的代表频率拟合得到了电介质的介电谱解析表达式,可以得到电介质在全频段的光频常数和介电常数. 研究了三个典型液态电介质,水、乙醇和甲苯的介电谱. 在实验数据可以获取的频率范围内,采用解析表达式得到的光频常数与采用Kramers-Kronig转换得到的折射率实部和实验得到的折射率虚部吻合得很好. 基于介电谱解析表达式可以预测目前实验无法测量的区域的介电谱.     

New open modified Newton Cotes type formulae as multilayer symplectic integrators

New modified open Newton Cotes integrators are introduced in this paper. For the new proposed integrators the connection between these new algorithms, differential methods and symplectic integrators is studied. Much research has been done on one step symplectic integrators and several of them have obtained based on symplectic geometry. However, the research on multistep symplectic integrators is very poor. Zhu et al. [1] studied the well known open Newton Cotes differential methods and they presented them as multilayer symplectic integrators. Chiou and Wu [2] studied the development of multistep symplectic integrators based on the open Newton Cotes integration methods. In this paper we introduce a new open modified numerical method of Newton Cotes type and we present it as symplectic multilayer structure. The new obtained symplectic schemes are applied for the solution of Hamilton’s equations of motion which are linear in position and momentum. An important remark is that the Hamiltonian energy of the system remains almost constant as integration proceeds. We have applied also efficiently the new proposed method to a nonlinear orbital problem and an almost periodic orbital problem.     

基于改进非线性拟合的核磁共振T2谱多指数反演

核磁共振T₂谱多指数反演算法是开展复杂体系样品核磁共振(NMR)弛豫研究最重要的数学工具. 常用的T₂谱多指数反演算法一般都是事先给出弛豫时间T₂分布的布点, 然后转化为线性拟合问题进行求解. 在求解的T₂谱较为分散的时候, 反演得到的T₂谱精确度不高, 分辨率较低. 非线性拟合是解决这个问题的有效办法. 本文针对分散T₂谱反演利用非线性拟合时遇到的初值依赖及运算复杂问题, 利用线性回归最小二乘方法, 改进了其中的带非负约束非线性优化模型, 将搜索的反演参数从T₂, f 减少为T₂, 加快了收敛速度, 减少了对初值的依赖, 提高了反演精度, 使算法更加稳健. 通过用改进的Levenberg-Marquardt算法和差分进化算法进行计算机模拟反演及实验数据反演, 验证了改进方法在核磁共振T₂ 谱反演中的有效性.     

A density functional theory study on parameters fitting of ultra long armchair （n, n） single walled boron nitride nanotubes

Armchair(n,n) single walled boron nitride nanotubes with n = 2-17 are studied by the density functional theory at the B3LYP/3-21G(d) level combined with the periodic boundary conditions for simulating the ultra long model.The results show that the structure parameters and the formation energies bear a strong relationship to n.The fitted analytical equations are developed with correlation coefficients larger than 0.999.The energy gaps of(2,2) and(3,3) tubes are indirect gaps,and the larger tubes(n = 4-17) have direct energy gaps.Results show that the armchair boron nitride nanotubes(n = 2-17) are insulators with wide energy gaps of between 5.93 eV and 6.23 eV.     

小样本定数截尾场合下威布尔和对数正态分布的拟合检验

本文给出了小样本定数截尾场合下两参数威布尔分布和对数正态分布的拟合检验方法,该方法还适用于一般的位置-刻度参数族分布,论文还通过实际算例说明方法的可行性。     

舰船目标红外图像特性研究

针对成像型反舰导弹所获红外图像的特点,分析了舰船目标和海天背景的红外辐射特性,得知舰船目标红外图像有一重要特征-海天线,它可以确定目标的所在区域。为了舰船目标的跟踪定位,对舰船目标红外图像中的海天线特征进行研究,提出一种基于预处理和直线拟合法提取海天线特征的算法,首先对图像进行边缘检测得到梯度图像,进而二值化并细化,最后利用Hough变换提取海天线。结果表明,在低对比度和有云团干扰的情况下,该算法与改进的直线拟合法相比,能够有效地、准确地提取舰船目标红外图像中海天线特征。