危机应对术

回忆去年的情况，用一段比较流行的话来说，基本上眼睛一闭一睁，发现世界变了，箭头的方向变了，指标的颜色变了，公司的形势变了，经营业绩变了。     

本期知识整合与能力提升

同学们，朋友们，通过本期的学习，我们认识了数的又一次扩展，理解了坐标的意义及函数关系，会进一步整理数据，知道了相似三角形的特征与识别方法，明确了直角三角形的边角关系，掌握了解决一些简单实际问题的方法，收获可真不小。     

新课程理念下数学教师能力的重新诠释

在新课程实施中，一切都在发生着显著的变化；培养目标发生了变化，课程理念发生了变化，教学内容发生了变化，教学形式发生了变化，评价导向发生了变化，学生生活发生了变化，……．但是，所有这些变革与发展都需要一线教师以及相关人员的积极参与，教师自身的理论素养和实践     

营造文化数学氛围建构数学教育新观念

在日常数学教学活动中，愈来愈多的学生对数学学习的动力不是来自数学本身，而主要来自于考试的压力，学生被动的数学学习观念，不仅阻止了他们的主动性与探索性，扼杀了数学的魅力，而且不利于数学学科的发展，不利于学生创新思维能力及个人综合能力的形成．也就是说，学生学到了数学的壳，却丢掉了数学的核；学到了数学的形式，却扔掉了数学的美；学到了数学的方法，却抛弃了数学的灵魂．新一轮的数学课程改革提出了数学的应用性、文化性两个新观念，以通过课程、课堂及课外的途径，改变过去重结论轻过程、重理论轻应用、重知识轻能力的局面，给课堂以生机与活力．     

水果摊的机会

以前，一个水果摊的老板因为年岁大了，无法久站招呼客人，于是就发启事招聘一名店员。
　　来了一个30多岁的男子，问老板一个月用多少钱请他来帮忙，老板笑着说：“我这小摊生意，哪里付得出月薪，当然是看你的努力了，一天能卖多少水果，收到的钱就给你十分之一，每天领现。”这个男子听了，上下打量打量小水果摊，说太没保障了，掉头走了。     

快速遴选优胜者

本文给出了一个行之有效的方案来确定某次竞赛的优胜者．首先，假定裁判是理想的（无误差的），我们提出了一个基本模型在几乎最短的时间内确定出前W名．在我们的方案中，用一个矩阵来记录从当前已知的裁判评分中所得到的“当前名次”，并且在一轮之后尽可能多地淘汰试卷．然后，我们考虑现实中的裁判（有误差的），估计了最后选出的W名中包含有非前2W名试卷的概率．进一步，考虑到打分方案中的系统偏差，我们用贝叶斯估计对模型做了改进，使不同裁判的评分有了一定的可比性．为检验模型的可行性，我们做了大量的计算机模拟，模型检验中我们发现，如果适当增加从第一轮中选拔出来的试卷数，将使我们的模型结果更好．我们还通过改变参数P，J，W对模型作了稳定性分析，并且得到了一个经验公式，可以用来预测在一定P，J，W值下评卷的总时间．接下来，我们采用了现实生活中的数据来检验模型，结果相当好当P=50，J=3时，若取W=2，用我们的方案得到了第一名和第三名若取W=3，得出的正是前三名．最后，我们总结出了一个灵活实用的方案，并提出了一些建议在模型推广中，我们还利用经验公式对开支做了预算．     

线性约束规划内点法及其修正算法

凸规划的内点算法是目前较热门的课题之一，参考资料「２」，「３」等均给出了较深入的研究，本文在参考前人的工作前提下，提出了带线性约束凸规划的内点算法结论及相应算法，另外，本文定义了偏移因子，偏移因子对的概念，对下降方向作出了修正，并给出了相关算法。     

第一章 勾股定理

亲爱的同学们，新课程与你为伴已经有一年的时间．在其中，你了解了很多的数学知识，学会了一些数学技能，体味了数学学习的过程，掌握了一定的学习方法，在学习数学的各方面都有了长足的进步．     

含T—fuzzy数据的聚类与识别模型

本文给出了Ｔ－ｆｕｚｚｙ数据的定义，性质及度量公式，并用正规标准化方法统一量纲。首先探讨了Ｍｉｎ－Ｍａｘ传递闭包和α（或β）阈值原理，提出了求传递背包的简捷算法，首次，建立了含Ｔ－ｆｕｚｚｙ数据的聚类分析模型，最后，提出了含Ｔ－ｆｕｚｚｙ数据的模式识别模型及其三种算法，实例说明，用本文算法，其结果与实际基本吻合。     

货运量预测方法的比较

本在对货运量预测理论和程序描述的基础上，介绍并比较了常用预测方法的优缺点，重点研究了三层BP神经网络的基本原理，构思了BP神经网络中长期货运量预测模型，并进行了预测，最后根据预测结果，分析了其用于预测的优缺点。     

On consistency of recursive least squares identification algorithms for controlled auto-regression models

The recursive least squares (RLS) algorithms is a popular parameter estimation one. Its consistency has received much attention in the identification literature. This paper analyzes convergence of the RLS algorithms for controlled auto-regression models (CAR models), and gives the convergence theorems of the parameter estimation by the RLS algorithms, and derives the conditions that the parameter estimates consistently converge to the true parameters under noise time-varying variance and unbounded condition number. This relaxes the assumptions that the noise variance is constant and that high-order moments are existent. Finally, the proposed algorithms are tested with two example systems, including an experimental water-level system.     

Analyzing the Performance of Generalized Hill Climbing Algorithms

Generalized hill climbing algorithms provide a framework to describe and analyze metaheuristics for addressing intractable discrete optimization problems. The performance of such algorithms can be assessed asymptotically, either through convergence results or by comparison to other algorithms. This paper presents necessary and sufficient convergence conditions for generalized hill climbing algorithms. These conditions are shown to be equivalent to necessary and sufficient convergence conditions for simulated annealing when the generalized hill climbing algorithm is restricted to simulated annealing. Performance measures are also introduced that permit generalized hill climbing algorithms to be compared using random restart local search. These results identify a solution landscape parameter based on the basins of attraction for local optima that determines whether simulated annealing or random restart local search is more effective in visiting a global optimum. The implications and limitations of these results are discussed.     

A convergence theory for a class of anti-jamming strategies

A convergence theory for a class of anti-jamming strategies for nonlinear programming algorithms is presented. This theory generalizes previous results in this area by Zoutendijk, Topkis and Veinott, Mangasarian, and others; it is applicable to algorithms in which the anti-jamming parameter is fixed at some positive value as well as to algorithms in which it tends to zero. In addition, under relatively weak hypotheses, convergence of the entire sequence of iterates is proved.This research was sponsored by the United States Army under Contract No. DA-31-124-ARO-D-462.     

Convergence of over-relaxed contraction-proximal point algorithm in Hilbert spaces

The proximal point algorithm (PPA) is a classical method for finding zeros of maximal monotone operators. It is known that the algorithm only has weak convergence in a general Hilbert space. Recently, Wang, Wang and Xu proposed two modifications of the PPA and established strong convergence theorems on these two algorithms. However, these two convergence theorems exclude an important case, namely, the over-relaxed case. In this paper, we extend the above convergence theorems from under-relaxed case to the over-relaxed case, which in turn improve the performance of these two algorithms. Preliminary numerical experiments show that the algorithm with over-relaxed parameter performs better than that with under-relaxed parameter.     

On the accelerated iterative method for estimating the optimum overrelaxation parameter

This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.     

Convergence results for continuous-time adaptive stochastic filtering algorithms

The adaptive stochastic filtering problem for Gaussian processes is considered. The self-tuning synthesis procedure is used to derive two algorithms for this problem. Almost sure convergence for the parameter estimate and the filtering error will be established. The convergence analysis is based on an almost-supermartingale convergence lemma that allows a stochastic Lyapunov-like approach.     

On the choice of parameters for power-series interior point algorithms in linear programming

In this paper we study higher-order interior point algorithms, especially power-series algorithms, for solving linear programming problems. Since higher-order differentials are not parameter-invariant, it is important to choose a suitable parameter for a power-series algorithm. We propose a parameter transformation to obtain a good choice of parameter, called ak-parameter, for general truncated powerseries approximations. We give a method to find ak-parameter. This method is applied to two powerseries interior point algorithms, which are built on a primal—dual algorithm and a dual algorithm, respectively. Computational results indicate that these higher-order power-series algorithms accelerate convergence compared to first-order algorithms by reducing the number of iterations. Also they demonstrate the efficiency of thek-parameter transformation to amend an unsuitable parameter in power-series algorithms.Work supported in part by the DFG Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung.     

SOR-like Methods for Augmented Systems

Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.     

Asymptotic analysis of a path-following barrier method for linearly constrained convex problems *

In the present paper the logarithmic barrier method applied to the linearly constrained convex optimization problems is studied from the view point of classical path-following algorithms. In particular, the radius of convergence of Newton's method which depends on the barrier parameter itself is estimated in standard norms, being independent of the parameter, without explicitly using self-concordance properties. The obtained results establish a parameter selection rule which guarantees the overall convergence of a barrier technique with only one Newton step at each parameter level and the complexity of the method can be estimated.     

结合修正Curry-Altman步长搜索一个新的共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameter in the search directions. In this note, conditions are given on the parameter in the conjugate gradient directions to ensure the descent property of the search directions. Global convergence of such a class of methods is discussed. It is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continuously differentiable function with a modification of the Curry-Altman‘s step-size rule and a bounded level set. Combining PR method with our new method, PR method is modified to have global convergence property.Numerical experiments show that the new methods are efficient by comparing with FR conjugate gradient method.