无偏的岭回归迭代算法

本文探讨线性模型的无偏的岭回归迭代算法,这种算法保持最小二乘法的性质,当存在较为严重的共线性时,它能给出较为精确的参数及其协差阵的估计值;当存在严格的共线性时,给出参数及其协差阵的无穷多解中的一个,这个解由初值决定。文章还给出了算法的收敛性及一些其它性质的证明。     

Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

AN ALTERNATIVE SPECIFICATION FOR MODELING GROUNDWATER DYNAMICS

This research extends previous work with dynamic models to manage groundwater quality by using the consumptive nitrate use rate instead of the nitrate application rate. The analysis indicates that misspecification results in overestimation of economic benefits, and supra-optimum nitrogen fertilizer application rates and groundwater nitrate stocks at a steady state.     

The Potts model representation and a Robinson–Schensted correspondence for the partition algebra

We construct a correspondence between the set of partitions of a finite set M and the set of pairs of walks to the same vertex on a graph giving the Bratteli diagram of the partition algebra on M. This is the precise analogue of the correspondence between the set of permutations of a finite set and the set of pairs of Young tableaux of the same shape, called the Robinson–Schensted correspondence.     

泛Loeb可测集的S-饱和性

在 K-饱和的非标准模型中,研究了泛 Loeb 可测集 m(A),pns(~*X),cpt(~*X),fin(~*X),ns(~*X)的 S-饱和性.当 A 是紧致 Hausdorff 空间 X 的子集时,得到了 st~(-1)(A)是标准集的充分条件.     

掺杂离子导体的粒子交叠广义晶格模型及其电导的粒子尺度效应

提出了一种掺杂离子导体（ＤＩＣ）的粒子交叠广义晶格模型，由此模型，推导随机－电阻－网络（ＲＲＮ）理论中３种导电键各自组分的几率，并采用有效介质近似（ＥＭＡ）计算了ＤＩＣ系统的电导及其粒子尺度效应。     

模型优适度辨识含水层补给进口的原理、方法和应用

本文阐述了一种新的研究成果——用模型优适度寻找含水层主进水口位置的原理、方法和应用。模型优适度作为衡量地下水模型场势与原型(矿区)场势相似拟合程度的量度,它凭借含水层地下水场势对源点的响应差异,判别模型源点位置与原型源点位置是否一致、接近或偏离。本文给出了模型优适度的计算公式和用统计分析方法对动态矩阵施行标准化的公式推演过程。通过多次模拟试验,绘出优适度的等值线图,为华北某矿圈定含水层补给范围,进行注浆堵水,大大地降低了矿井涌水量,在实践应用中获得初步成功。     

对西方数学直观的评析

本文从数学方法论的角度,具体论述和评析了西方数学直观随数学发展的不同阶段所表现出的特点和演变方式。     

精密镗削头振动模态的实验研究

通过对国产与进Ｄ的同类型精密镗削头振动模态实验研究，找出了这两种精密镗削头的固有振动频率，给出了它们的各阶动画振型图．从这一侧面解释了国产精密镗削头回转精度偏低的原因。     

L3 L~＋L~－γγ事例的一种可能解释

本文用ＴＣ（Ｔｅｃｈｎｉｃｏｌｏｒ）模型，解释了Ｌ３Ｌ￣＋Ｌ￣－γγ事例，具体分析发现四个Ｌ３事例可以由过程ｚ→ρ°ρ°→Ｌ￣＋Ｌ￣－Ｐ°（γγ）产生。