偏最小二乘法在回归设计多因变量建模中的应用及其优化

本文利用国际通用统计软件SAS,探讨偏最小二乘法在二次回归旋转设计中多因变量回归建模的技术;同时,应用国际优化大师L ingo软件对多目标进行优化,给出了最优的工艺参数值。     

应用遥感技术进行污染源监测的多元统计方法

本文采用多元统计分析，对地面遥感图象进行主成分分析、聚类分析和主成分回归分析，给出遥感图象对代表的污染源的浓度的半定量化估计结果。本文所提供的方法是对国际通用的污染源监测的林德曼（Ｌｉｎｄｅｍａｎｎ）定性估计方法的改进和精确化．为大气环境质量监测和评价，以及研究污染源排放行为提供了新途径． 本文引入了统计综合评判模型．用来解译遥感信息达到国际水平，应用到实际环保部门取得了一定的社会效益和经济效益．     

二次函数区间最值的类型与解法

中文是世界上人口最多的国家通用的语言文字，是象形文字；英文是国际通用的语言文字，是拼音文字．语言学家在这方面已有较多的比较，特别是近几年中小学甚至幼儿园双语教学的提出，但在抽象的数学语言方面，中英文的差别又有多大呢？此文将介绍一项这方面的研究．该研究是美国纽约城市大学的韩翊教授的博士论文的工作，研究分为两个部分．第一部分比较中英文数学名词的清晰度，第二部分比较这两种语言对学生数学成绩的影响．因该文背景方面的介绍也很有意义，所以本文也将其概括地介绍一下．     

中英文数学名词清晰度比较及其对学生数学表现的影响

中文是世界上人口最多的国家通用的语言文字,是象形文字；英文是国际通用的语言文字,是拼音文字．语言学家在这方面已有较多的比较,特别是近几年中小学甚至幼儿园双     

软件统计测试的比较和改进

针对软件统计测试中随机测试和分域测试的优劣问题，章对这两种测试方法进行了全面的比较，从理论上证明了分域测试优于随机测试。并根据软件验收的实际情况，提出了一种改进的软件测试方法，该方法有较好的测试效率。     

汽车千车故障数的预测与分析

针对原有千车故障数统计方法上的不足,本文从改进统计方法着手,提出一种新的统计方法即重新定义千车故障数,然后利用数据挖掘中的聚类分析方法将具有相同特征的批次综合起来考虑,建立通用的运筹模型.针对缺失数据、近期预测这两个问题,本文对通用模型进行调整,“学习”出同类数据间的不同权值,然后利用加权数据,并通过拟合曲线来求出预测值.由于远期预测中数据的严重缺乏,则是从纯粹统计学的角度出发,计算得到预测值.预测模型通用性强,适用面较广.本文应用了SAS和MATLAB两种软件来求解上述模型,预测结果准确率较高,并且符合实际情况.     

回归模型中有影响变量的检测标准及其灵敏度分析

本文从修正的似然入手，得到了回归模型中自变量影响的一种有效度量，它的表达式简洁易在常见的统计软件上实现．这种影响度量可帮助我们建立一个合适的回归模型，作为特例，它可用来检测回归模型中的异常点或强影响点．利用局部影响分析的思想，我们还研究了这种影响度量的灵敏度，据此可成功地发现对选模有较大影响的观察数据．最后我们给出了一个应用实例．     

IMS-China概率统计国际学术会议在杭州召开

2008年6月11日至13日，由国际数理统计学会（Institute of Mathematical Statistics，简称IMS）举办、浙江大学承办的2008 IMS—China概率统计国际学术会议在浙江大学召开．来自美国、加拿大、瑞士、新加坡、澳大利亚、英国、以色列等国及港台地区和中国大陆高校、科研机构的270余位学者就高维数据分析、随机过程、随机分析、极限理论、生物统计、金融建模、机器学习、非参数统计、回归分析等概率统计的前沿课题进行研讨交流，其中来自海外的代表有100余名．浙江大学副校长朱军出席了会议的开幕式并致辞，浙江大学校长杨卫会见了与会嘉宾．     

统计模拟中的数论方法

受现实生活的一个案例形成的随机覆盖问题之启发,我们在本文中讨论并比较了统计模拟中的几种方法,包括ELP网、NT网与其他网．我们给出的一些结果对统计模拟是有用的．     

二次回归正交组合设计回归计算与统计检验软件设计

本文用ＢＡＳＩＣ语言编制了在ＩＢＭ—ＰＣ及其兼容机上运行的二次回归正交组合设计试验的回归计算及统计检验软件．运行本软件时，只需输入试验因素个数，中心试验点重复试验次数和每个试验点的试验结果，就能迅速得到所有回归系数和统计检验的各种参数值，解决了这一优良的试验设计方法所存在的计算繁冗和容易出错的问题．     

Formulation of linear problems and solution by a universal machine

Using the predicate language for ordered fields a class of problems referred to aslinear problems is defined. This class contains, for example, all systems of linear equations and inequalities, all linear programming problems, all integer programming problems with bounded variables, all linear complementarity problems, the testing of whether sets that are defined by linear inequalities are semilattices, all satisfiability problems in sentenial logic, the rank-computation of matrices, the computation of row-reduced echelon forms of matrices, and all quadratic programming problems with bounded variables. A single, one, algorithm, to which we refer as theUniversal Linear Machine, is described. It solves any instance of any linear problem. The Universal Linear Machine runs in two phases. Given a linear problem, in the first phase a Compiler running on a Turing Machine generates alinear algorithm for the problem. Then, given an instance of the linear problem, in the second phase the linear algorithm solves the particular instance of the linear problem. The linear algorithm is finite, deterministic, loopless and executes only the five ordered field operations — additions, multiplications, subtractions, divisions and comparisons. Conversely, we show that for each linear algorithm there is a linear problem which the linear algorithm solves uniquely. Finally, it is shown that with a linear algorithm for a linear problem, one can solve certain parametric instances of the linear problem.Research was supported in part by the National Science Foundation Grant DMS 92-07409, by the Department of Energy Grant DE-FG03-87-ER-25028, by the United States—Israel Binational Science Foundation Grant 90-00434 and by ONR Grant N00014-92-J1142.Corresponding author.     

A double-stage piecewise recursive filter for real-time applications

This paper examines the basic problem of estimating the state of a system described by a set of dynamical equations. The state estimation is performed by means of optimal filtering techniques in which the state observation is given by a set of nonlinear equations.The basic issue encountered in most engineering problems is the availability of more observable information than the processor can effectively process in real-time, while performing full optimal filtering on all available observable data. To alleviate this deficiency, an algorithm is developed in which the rate of information processing is kept at a high value, while the system statistics are evaluated at a much slower rate.The method utilizes a combination of fast and slow filtering loops, in which the observable data are processed at a high rate during the fast loop, while the system error covariance, gain computations, and all other system statistics are processed at a lower rate in the slow loop. Methods are provided to resolve any incompatibility in the system statistics resulting from this fast-loop/slow-loop processing combination.Applications describing problems pertaining to aircraft navigation are presented. Specifically, applications to aircraft navigation through a satellite network are studied. Appropriate simulation results from the above studies are shown.This work was performed under contract with the Department of the Air Force, Space and Missile Organization (SAMSO), Los Angeles, California, Contract No. F04-701-75-C-0180.The authors are indebted to Dr. C. Johnson, GPS System Engineer, Mr. G. Consolver, GPS Software Manager, and Mr. W. Riley, Communications/Navigation Department, Texas Instruments for their continuous encouragement in the course of this work. Also, they are indebted to Major M. Birnbaum, SAMSO, for his constructive criticism on the conceptual design of this work, and to Mr. A. Bierman, Aerospace Corporation, for kindly providing simulation data of aircraft trajectories. Finally, the authors would like to express their gratitude to Dr. N. Carlson, Intermetrics, for valuable consultation during the progress of this work.Portions of this paper were presented by the senior author at the GSP Conference, Plan 76, IEEE Position, Location, and Navigation Symposium, San Diego, California, 1976.     

Derivatives of (modified) Fredholm determinants and stability of standing and traveling waves

Continuing a line of investigation initiated in [F. Gesztesy, Y. Latushkin, K.A. Makarov, Evans functions, Jost functions, and Fredholm determinants, Arch. Rat. Mech. Anal. 186 (2007) 361–421] exploring the connections between Jost and Evans functions and (modified) Fredholm determinants of Birman–Schwinger type integral operators, we here examine the stability index, or sign of the first nonvanishing derivative at frequency zero of the characteristic determinant, an object that has found considerable use in the study by Evans function techniques of stability of standing and traveling wave solutions of partial differential equations (PDE) in one dimension. This leads us to the derivation of general perturbation expansions for analytically-varying modified Fredholm determinants of abstract operators. Our main conclusion, similarly in the analysis of the determinant itself, is that the derivative of the characteristic Fredholm determinant may be efficiently computed from first principles for integral operators with semi-separable integral kernels, which include in particular the general one-dimensional case, and for sums thereof, which appears to offer applications in the multi-dimensional case.A second main result is to show that the multi-dimensional characteristic Fredholm determinant is the renormalized limit of a sequence of Evans functions defined in [G.J. Lord, D. Peterhof, B. Sandstede, A. Scheel, Numerical computation of solitary waves in infinite cylindrical domains, SIAM J. Numer. Anal. 37 (2000) 1420–1454] on successive Galerkin subspaces, giving a natural extension of the one-dimensional results of [F. Gesztesy, Y. Latushkin, K.A. Makarov, Evans functions, Jost functions, and Fredholm determinants, Arch. Rat. Mech. Anal. 186 (2007) 361–421] and answering a question of [J. Niesen, Evans function calculations for a two-dimensional system, presented talk, SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, USA, May 2007] whether this sequence might possibly converge (in general, no, but with renormalization, yes). Convergence is useful in practice for numerical error control and acceleration.     

Representation of the solution to a model problem in semiconductor physics

We study a mixed type problem for the Poisson equation arising in the modeling of charge transport in semiconductor devices [V. Romano, 2D simulation of a silicon MESFET with a non-parabolic hydrodynamical model based on the maximum entropy principle, J. Comput. Phys. 176 (2002) 70-92; A.M. Blokhin, R.S. Bushmanov, A.S. Rudometova, V. Romano, Linear asymptotic stability of the equilibrium state for the 2D MEP hydrodynamical model of charge transport in semiconductors, Nonlinear Anal. 65 (2006) 1018-1038]. Unlike well-studied elliptic boundary-value problems in domains with smooth boundaries (see, for example, [O.A. Ladyzhenskaya, N.N. Uralceva, Linear and Quasilinear Elliptic Equations, Nauka, Moscow, 1973; D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983]), our problem has two significant features: firstly, the boundary is not a smooth curve and, secondly, the type of boundary conditions is mixed (the Dirichlet condition is satisfied on the one part of the boundary whereas the Neumann condition on the other part). The well-posedness of the problem in Hölder and Sobolev spaces is proved. The representation of the solution to the problem is obtained in an explicit form.     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

Critical time of a long multilayer viscoelastic shell

The buckling in stability of a long multilayer linearly viscoelastic shell, composed of different materials and loaded with a uniformly distributed external pressure of given intensity, is investigated. By neglecting the influence of fastening of its end faces, the initial problem is reduced to an analysis of the loss of load-carrying capacity of a ring of unit width separated from the shell. The new problem is solved by using a mixed-type variational method, allowing for the geometric nonlinearity, together with the Rayleigh-Ritz method. The creep kernels are taken exponential with equal indices of creep. As an example, a three-layer ring with a structure symmetric about its midsurface is considered, and the effect of its physicomechanical and geometrical parameters, as well as of wave formation, on the critical time of buckling in stability of the ring is determined. It is found that, by selecting appropriate materials, more efficient multilayer shell-type structural members can be created. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 617–628, September–October, 2007.     

Wave parameter identification problem for ocean test structure data,part 2, discrete formulation

This paper deals with the solution of the wave parameter identification problem for ocean test structure data. A discrete formulation is assumed. An ocean test structure is considered, and wave elevation and velocities are assumed to be measured with a number of sensors. Within the frame of linear wave theory, a Fourier series model is chosen for the wave elevation and velocities. Then, the following problem is posed: Find the amplitudes of the various wave components of specified frequency and direction, so that the assumed model of wave elevation and velocities provides the best fit to the measured data. Here, the term best fit is employed in the least-square sense over a given time interval.At each time instant, the wave representation involves four indexes (frequency, direction, instrument, time); hence, four-dimensional arrays are required. This formal difficulty can be avoided by switching to an alternative representation involving only two indexes (frequency-direction, instrument-time); hence, standard vector-matrix notation can be used. Within this frame, optimality conditions are derived for the amplitudes of the assumed wave model.A characteristic of the wave parameter identification problem is that the condition number of the system matrix can be large. Therefore, the numerical solution is not an easy task and special procedures must be employed. Specifically, Gaussian elimination is avoided and advantageous use is made of the Householder transformation, in the light of the least-square nature of the problem and the discretized approach to the problem.Numerical results are presented. The effect of various system parameters (number of frequencies, number of directions, sampling time, number of sensors, and location of sensors) is investigated in connection with global or strong accuracy, local or weak accuracy, integral accuracy, and condition number of the system matrix.From the numerical experiments, it appears that the wave parameter identification problem has a unique solution if the number of directions is smaller than or equal to the number of sensors; it has an infinite number of solutions otherwise. In the case where a unique solution exists, the condition number of the system matrix increases as the size of the system increases, and this has a detrimental effect on the accuracy. However, the accuracy can be improved by proper selection of the sampling time and by proper choice of the number and location of the sensors.Generally speaking, the computations done for the discrete case exhibit better accuracy than the computations done for the continuous case (Ref. 5). This improved accuracy is a direct consequence of having used advantageously the Householder transformation and is obtained at the expense of increased memory requirements and increased CPU time.This work was supported by Exxon Production Research Company, Houston, Texas. This paper is based partly on Refs. 1–4.     

From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions

In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated.     

Personae at play. ‘Men of Mathematics’ in commentary

Mathematical writers, above all, Euclid, tend to present their theorems as decontextualized, abstract propositions, which has become the standard modus of textual presentation in theoretical mathematics. Mathematical commentators, however, provide their readers with personal names and historical facts in order to elucidate problems, provide contexts of discovery, or construct doxographies, among other things. Modern readers have used such information for the construction of histories of science. When we look at these passages, however, we see that personal names and information about mathematicians of the past can serve quite a range of different objectives, such as the strategic self-positioning of the commentator vis-à-vis the past or present of mathematics, the education of the reader, mathematical or moral, the construction of the history of the field, etc. Not only does the commentator present a persona of himself to the reader, he can also turn colleagues and predecessors into personae. This paper attempts to elucidate the practice, by offering four examples of such plays of and with personae, in Pappus, Eutocius, al-Nayrīzī, and Proclus.     

Rheological properties of microcrystalline chitosan gels

The procedure of thermocatalic processing of chitosan developed allows one to decrease its degree of polymerization to the so-called leveling-off degree and, after the precipitation from a solution and washing, to obtain hydrogels of microcrystalline chitosan (MCC.) The flow curves of the MCC gels showed that a spatial structure was formed in the gels even at low their concentrations. The measurements of vicoelastic properties of the dispersions verified the existence of such a structure. It is shown that, at MCC concentrations above 3%, a transition from the isotropic phase to a liquid-crystalline one occurs. For comparison, the flow properties of chitosan solutions in acetic acid were studied too. The measurements showed that, at the solution concentrations considered, they did not exhibit liquid-crystalline rheological properties. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 385–398, May–June, 2007.