混合位级正交试验设计的极差分析方法

本文指出，在混合位级的正交试验设计中，以往的极差分析方法存在着不足。本文给出了极差的修正方法，并用大量实例做了数值验证，说明这个修正确实很有效     

Estimating Sampling Errors in REA Survey: A Model Approach for the Synthetic Presentation of Results for Main Variables Involved in Economic Analysis

A new sample business survey for agriculture, the REA survey, and a project of integration with the FADN network (RICA in Italy) have significantly changed the production of statistical information nowadays available with reference to the agricultural sector. On the basis of this relevant information, new economic analyses are being developed on farms’ performance, agricultural households’ income and the Common Agricultural Policy (CAP). In this paper the authors estimate the relationship between the levels of variables of interest and their sampling errors using models in order to improve the accessibility of the information on estimates accuracy to the final users (agricultural analysts, policy makers). The paper is the result of a joint research of the three authors. Sections 1–3 and 6 by Pizzoli, Sects. 4 and 5 by Rondinelli, Sect. 7 by Filiberti, conclusions joint to the three authors.     

The Exact Hausdorff Measure Function of the Level Sets of Multi-parameter Symmetric Stable Process

In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф（r） = r^N-d/α （log log l/r）d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general （N, d, α） strictly stable processes.     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Artinian level modules and cancellable sequences

In order to use dualization to study Hilbert functions of artinian level algebras we extend the notion of level sequences and cancellable sequences, introduced by Geramita and Lorenzini, to include Hilbert functions of certain artinian modules. As in the case of algebras a level sequence is cancellable, but now by dualization its reverse is also cancellable which gives a new condition on level sequences. We also give a characterization of the cancellable sequences involving Macaulay representations.     

Sample path analysis of level crossings for the workload process

We examine level crossings of sample paths of queueing processes and investigate the conditions under which the limiting empirical distribution for the workload process exists and is absolutely continuous. The connection between the density of the workload distribution and the rate of downcrossings is established as a sample path result that does not depend on any stochastic assumptions. As a corollary, we obtain the sample path version of the Takács formula connecting the time and customer stationary distributions in a queue. Defective limiting empirical distributions are considered and an expression for the mass at infinity is derived.This research has been supported in part by NSF Grants ECS-8811003 and DDM-8905638.     

Variable resolution triangulations

A comprehensive study of multiresolution decompositions of planar domains into triangles is given. A general model is introduced, called a Multi-Triangulation (MT), which is based on a collection of fragments of triangulations arranged into a directed acyclic graph. Different decompositions of a domain can be obtained by combining different fragments of the model. Theoretical results on the expressive power of the MT are given. An efficient algorithm is proposed that can extract a triangulation from the MT, whose level of detail is variable over the domain according to a given threshold function. The algorithm works in linear time, and the extracted representation has minimum size among all possible triangulations that can be built from triangles in the MT, and that satisfy the given level of detail. Major applications of these results are in real-time rendering of complex surfaces, such as topographic surfaces in flight simulation.     

Electron energy level crossings in the time-dependent Born-Oppenheimer approximation

Summary We summarize the results of a mathematical study of the time-dependent Born-Oppenheimer approximation near crossings of two non-degenerate electron energy surfaces. We illustrate our techniques by relatively simple examples that contain the essential ingredients of the general cases. We discuss all generic types of crossings of two non-degenerate electron energy surfaces.Supported in part by the National Science Foundation under Grant number DMS-8801360     

An Ensemble Kalman Filter Approach Based on Level Set Parameterization for Acoustic Source Identification Using Multiple Frequency Information

In this paper, a reconstruction problem of the spatial dependent acoustic source from multiple frequency data is discussed. Suppose that the source function is supported on a bounded domain and the piecewise constant intensities of the source are known on the support. We characterize unknown domain by the level set technique. And the level set function can be modeled by a Hamilton-Jacobi system. We use the ensemble Kalman filter approach to analyze the system state. This method can avoid to deal with the nonlinearity directly and reduce the computation complexity. In addition, the algorithm can achieve the stable state quickly with the Hamilton-Jacobi system. From some numerical examples, we show these advantages and verify the feasibility and effectiveness.     

LIBS中药材石斛等级识别研究

石斛是一种常用的中药材,经常使用新鲜的或干燥的茎条入药,有益胃生津、滋阴清热的效果。近年来,药理学研究探索出石斛具有抗白内障、抗氧化、抗肿瘤、提高免疫力的作用,其在许多病例中疗效显著,引起了国内外学者的关注,然而不同时间采集的石斛中氨基酸、微量元素等含量各不同,其对应药用价值,价格也不同,因此石斛价格等级分辨的研究具有重要意义。为快速鉴别不同价格、不同药效的石斛,研究了随机森林分类模型结合激光诱导击穿光谱技术(LIBS)对石斛价格等级进行分析建模。选取5个等级的石斛样品进行建模,为了对样品进行精确稳定分析,所有石斛样品均通过粉碎压片减小实验误差。采用1 064 nm波长的Nd∶YAG脉冲激光器作为激发光源,设置激光脉冲能量50 mJ,探测延时1μs,采集五个等级石斛样本的光谱数据,每个等级的样本采集40组光谱,共200组数据,并采用归一化处理,使所有的光谱数据转换到-1~1之间。采用归一化处理后的光谱数据进行主成分分析,通过主成分分析获得前7个主成分的得分矩阵,其累计解释95.24%的光谱信息。将选取的7个主成分作为输入,建立波段为220~880 nm的随机森林鉴别模型。并将石斛样本编号打乱,任意选取50%的光谱数据作为训练集,剩下50%的光谱数据作为测试集,默认决策树个数ntree为500,分裂属性集中属性个数mtry为5,建立模型对不同等级的石斛进行分类。等级一、二、三、四、五的识别率分别为95.45%, 100%, 78.26%, 94.12%和85%,平均识别率为90.57%。为提高识别率,研究了不同的ntree和mtry对分类模型的影响,利用袋外数据误差率估计对随机森林的两个参数进行了优化。选择ntree为300,mtry为1,等级一、二、三、四、五的识别率分别为100%, 100%, 92.31%, 100%和90%,平均识别率为96.46%,识别率提高了5.89%。综上所述,采用LIBS技术结合优化后的随机森林模型鉴别石斛等级具有一定的可行性,为未来快速鉴定不同价格的石斛等级分类提供了可行性的判别系统。