Estimation of a smooth quantile function under the proportional hazards model

The problem of estimating a smooth quantile function, Q(·), at a fixed point p, 0 < p < 1, is treated under a nonparametric smoothness condition on Q. The asymptotic relative deficiency of the sample quantile based on the maximum likelihood estimate of the survival function under the proportional hazards model with respect to kernel type estimators of the quantile is evaluated. The comparison is based on the mean square errors of the estimators. It is shown that the relative deficiency tends to infinity as the sample size, n, tends to infinity.     

Adaptive nonparametric estimation of a multivariate regression function

We consider the kernel estimation of a multivariate regression function at a point. Theoretical choices of the bandwidth are possible for attaining minimum mean squared error or for local scaling, in the sense of asymptotic distribution. However, these choices are not available in practice. We follow the approach of Krieger and Pickands (Ann. Statist.9 (1981) 1066–1078) and Abramson (J. Multivariate Anal.12 (1982), 562–567) in constructing adaptive estimates after demonstrating the weak convergence of some error process. As consequences, efficient data-driven consistent estimation is feasible, and data-driven local scaling is also feasible. In the latter instance, nearest-neighbor-type estimates and variance-stabilizing estimates are obtained as special cases.     

一维无限深势阱中粒子运动的路径积分解法

用路径积分的分析方法求得了一维无限深势阱中粒子的传播函数,并由传播函数导出了粒子的波函数和能量,展示了路径积分与传统方法的等价性,同时还介绍了一种有用的数学函数——雅可比θ_3函数．     

最小二乘法在液体粘滞系数实验中的应用

本文用多管落球法测得原始实验数据,运用最小二乘法进行处理,求得无限广延液体粘滞系数,并与直接作图法进行比较。     

局部偏最小二乘回归建模参数对近红外检测结果的影响研究

报道了在局部加权(LWR)回归方法基础上,自主改进的更简单、实用的局部偏最小二乘回归(LPLS)的原理和方法。并以云南优质烤烟为实验材料,在国产光栅漫反射型近红外仪器上,研究了主成分数以及局部建模样品数对检测结果的影响。结果表明：应用交叉验证方法推荐的尼古丁组分模型主成分数并不是最优,通过适当降低主成分数可提高检测效果;局部建模样品数为30～50个时总糖、总氮、尼古丁预测准确度的提高幅度可分别达7%,14%,10%以上。该方法能有效提高近红外数学模型的预测准确度,是建立具有高度适应性近红外数学模型的有效方法。     

基于光谱技术的杨梅汁品种快速鉴别方法的研究

为了实现杨梅汁品种的快速无损鉴别,提出了一种用可见和近红外光谱技术快速鉴别杨梅汁品种的新方法。首先采用偏最小二乘法进行模式特征分析,经过交互验证法判别,确定最佳主成分数为9。完成特征提取后,将这9个主成分作为神经网络的输入变量,建立了三层BP神经网络,实现类别预测的同时也完成了数学建模与优化分析工作。3个品种的杨梅汁样本数均为20,共计60个样本。在神经网络学习中,将其分成训练集样本51个和预测集样本9个。对9个未知样本进行预测,准确率为100％。说明本文提出的基于光谱技术和模式识别的方法具有很好的分类和鉴别能力。     

From C58 to C62 and back: Stability,structural similarity,and ring current

An increasing number of observations show that non‐classical isomers may play an important role in the formation of fullerenes and their exo‐ and endo‐derivatives. A quantum‐mechanical study of all classical isomers of C₅₈, C₆₀, and C₆₂, and all non‐classical isomers with at most one square or heptagonal face, was carried out. Calculations at the B3LYP/6‐31G* level show that the favored isomers of C₅₈, C₆₀, and C₆₂ have closely related structures and suggest plausible inter‐conversion and growth pathways among low‐energy isomers. Similarity of the favored structures is reinforced by comparison of calculated ring currents induced on faces of these polyhedral cages by radial external magnetic fields, implying patterns of magnetic response similar to those of the stable, isolated‐pentagon C₆₀ molecule. © 2016 Wiley Periodicals, Inc.     

纳米粒子在方管中传输与沉降的研究

采用有限体积法离散并应用Simple方法对方截面弯曲管道内的纳米粒子传输和沉降进行了数值计算,结果表明Reynolds数和Schmidt数是影响纳米粒子传输和沉降的重要参数。粒子较小时,弯管中轴向速度较大的区域就是粒子的高浓度区域,沉降增强因子最大值出现在外弯侧的中心位置;粒子较大时,截面浓度的梯度值降低,沉降增强因子趋于平均,此时整个截面的粒子平均沉降。弯曲作用对于粒子较大且Dean数也较大时的影响更加明显。     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.     

Antiferromagnetic Potts Models on the Square Lattice: A High-Precision Monte Carlo Study

We study the antiferromagnetic q-state Potts model on the square lattice for q=3 and q=4, using the Wang–Swendsen–Kotecký (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length 5000; the data are consistent with ()=Ae ^{2 p} (1+a ₁ e ^– + ...) as , with p1. The staggered susceptibility behaves as _stagg ^5/3. For q=4 the model is disordered (2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.