一个关于线性模型结构变化预测的推断

利用统计诊断的一些思想，从Bayes预测理论的角度分析线性模型中的结构变化．考察两相回归模型其中诸yi是观察值，凡是回归变量的已知向量（p×1）,Oj（j＝1，2）是未知参数向县（p×1），是未知参数，诸εi是相互独立的．m是未知参数称为变点．我们主要对m感兴趣．实际上，在模型（1．1）中的统计推断之前，我们不知道哪个参数变化．本文结合统计诊断的一些思想和Dayes观点，利用基于条件预测奇异诊断（以下简记为CPDD）和Kullback-Leibler散度两种方法，来研究线性模型的结构变化．这些方法不限于任何条件，且能找出哪些参数变化；哪…     

应用诊断识别模型评估高考数学试卷难度（三）──评估结果

应用诊断识别模型评估高考数学试卷难度（三）──评估结果任子朝，于福生（国家教委考试中心，北京师范大学数学系）１通用诊断识别问题专家系统开发工具诊断识别问题数学模型具备很广的应用领域．把上述模型编写成为一个专家系统开发工具是很有意义的工作．该开发工具用...     

基于T—S模糊模型的非线性不确定系统奇偶方程鲁棒故障诊断

针对T-S模糊模型描述的具有外部干扰的非线性不确定系统，构造了相应的测量冗余方程和奇偶方程，给出并证明了对特定传感器和执行器故障敏感的最优奇偶向量的存在条件和求解定理．采用奇偶方程故障检测与诊断方法，研究了非线性不确定系统的鲁棒故障检测和诊断．最后，通过仿真示例说明了本文所提出的方法是有效的．     

糖尿病Ⅰ、Ⅱ型的判别分析

本文根据一组糖尿病患者所测的数据，应用逐步Ｂｅｙｅｓ判别法及逐步Ｆｉｓｈｅｒ判别法建立判断糖尿病分型的判别方程，选入判别方程中的因子都与医学理论及临床相符．用所建立的判别方程对原数据的糖尿病患者进行回代诊断，其国代正确率分别为 ９３．７５％及９０％．诊断正确率较高，应用方便，可在基层医院等单位推广使用．     

数学教学诊断的理论与方法

数学教学诊断的理论与方法奚家成（江苏省南通市跃龙中学）在同一教学要求和进度下，由于教学对象个别差异和客观性，学生在理解知识、掌握技能和方法等方面往往存在“缺陷”．这就需要通过诊断．从可能出现的“症状”中精确地找到“症结”所在．进而制定矫正对策，以便对...     

“‘利用数形结合解决数学问题’教学设计”的评析

新课程改革倡导的教育理念认为：学校教育的根本任务是在以往教会学生知识的基础上，帮助和指导他们养成良好的学习习惯，学会如何学习、如何实践、如何与他人合作，形成学习能力．优秀的教学设计是课堂教学成功的前提，教学设计的实施是教学效果的保证，而教师的教学诊断与反思是提高教师的专业水平的有效途径之一．笔者以“利用数形结合解决数学问题”教学设计这一案例，进行评价与诊断．     

半参数广义线性模型的影响分析与异常点检验

统计诊断就是对统计推断方法解决问题的全过程进行诊断，而影响分析是统计诊断中十分重要的分支．本文针对半参数广义线性模型，证明了数据删除模型和均值漂移模型的等价性定理，给出了诸如广义Cook距离等诊断统计量并研究了异常点的Score检验统计量，最后通过实例验证了本文给出的诊断方法的有效性。     

多组判别分析法在恶性卵巢肿瘤B超评分诊断中的应用

为了妇科恶性肿瘤的早期诊断，对病人进行Ｂ型超声波的检查和Ｂ超评分，并把Ｂ超评分数作为初始条件，利用多组判别分析法，将它们划分为良性、过渡性或畸胎瘤和恶性等三类，是利用多元统计分析对妇科恶性肿瘤早期诊断的一种尝试．     

一类数列不等式问题的研讨

笔者多次参与乌鲁木齐市高三年级诊断性测验的命题工作，在乌鲁木齐地区2010年高三年级诊断性测验数学试卷命题过程中，觉得其中数列那道题的编制和推敲过程很有典型性，下面我们把这道题的命题思路及其渊源整理出来，对学生的学习会有一定的教育价值．     

胃癌早期诊断数学方法初探

运用数学方法，根据Ｂａｙｅｓ＇递推公式，建立一种胃癌逐步门诊的数学模型，用以辅助鉴别诊断胃癌．用此方法回顾性诊断随机抽取的５０例胃癌和１００例非胃癌上消化道疾病，其结果与胃镜加活检或手术加病检比较，符合率８５％，敏感性９０％，特异性８２％，阳性预测值７１％，阴性预测值９４％，误诊断（假阴性率）２９％，漏诊率（假阴性率）６％。     

探讨线性代数的核心

本文从关于线性代数基本结构的各种不同看法出发，探讨线性代数在整个数学学习中的基本问题，并根据线性代数基本问题讨论线性代数的结构安排.     

On the stability of linear systems with an exact constraint set

This paper deals with the stability of the intersection of a given set with the solution, , of a given linear system whose coefficients can be arbitrarily perturbed. In the optimization context, the fixed constraint set X can be the solution set of the (possibly nonlinear) system formed by all the exact constraints (e.g., the sign constraints), a discrete subset of (as or { 0,1} ⁿ , as it happens in integer or Boolean programming) as well as the intersection of both kind of sets. Conditions are given for the intersection to remain nonempty (or empty) under sufficiently small perturbations of the data. Research supported by Fondecyt Grant 1020(7020)-646. Research supported by DGES and FEDER, Grant BFM2002-04114-C02-01     

A Characterization of Partially Ordered Sets with Linear Discrepancy Equal to 2

The linear discrepancy of a poset P is the least k such that there is a linear extension L of P such that if x and y are incomparable in P, then |h _L (x)–h _L (y)|≤k, where h _L (x) is the height of x in L. Tanenbaum, Trenk, and Fishburn characterized the posets of linear discrepancy 1 as the semiorders of width 2 and posed the problem of characterizing the posets of linear discrepancy 2. We show that this problem is equivalent to finding the posets with linear discrepancy equal to 3 having the property that the deletion of any point results in a reduction in the linear discrepancy. Howard determined that there are infinitely many such posets of width 2. We complete the forbidden subposet characterization of posets with linear discrepancy equal to 2 by finding the minimal posets of width 3 with linear discrepancy equal to 3. We do so by showing that, with a small number of exceptions, they can all be derived from the list for width 2 by the removal of specific comparisons. The first and second authors were supported during this research by National Science Foundation VIGRE grant DMS-0135290.     

A note on an open problem in linear complementarity

LetK be the class ofn × n matricesM such that for everyn-vectorq for which the linear complementarity problem (q, M) is feasible, then the problem (q, M) has a solution. Recently, a characterization ofK has been obtained by Mangasarian [5] in his study of solving linear complementarity problems as linear programs. This note proves a result which improves on such a characterization.Research sponsored by the United States Army under Contract No. DAAG29-75-C-0024 and the National Science Foundation under Grant No. MCS75-17385.     

A remark on linear permutation polynomials

We give an explicit representation of the class of linear permutation polynomials. By the representation, the number of them can be computed easily.     

An index formula for the product of linear relations

Let , and be linear spaces and let A and B be linear relations from to and from to , respectively. The main result of this note is a formula which relates the nullities and the defects of the relations A and B with those of the product relation BA.     

Average relational distance in linear extensions of posets

We consider a natural analogue of the graph linear arrangement problem for posets. Let P=(X,?) be a poset that is not an antichain, and let λ:X→[n] be an order-preserving bijection, that is, a linear extension of P. For any relation a?b of P, the distance between a and b in λ is λ(b)−λ(a). The average relational distance of λ, denoted , is the average of these distances over all relations in P. We show that we can find a linear extension of P that maximises in polynomial time. Furthermore, we show that this maximum is at least , and this bound is extremal.     

An algorithm for computing equilibria in a linear monetary economy

An algorithm is presented for computing equilibria in a linear monetary economy, that is, an exchange economy in which all individuals have linear utility functions and in which goods are bought and sold only in exchange for money. The algorithm computes the equilibrium prices by solving a finite sequence of linear programming problems.