用多网格方法研究Poisson方程的解

本文给出了二种颜色的双网格方法．渐近缩减到一种颜色的双网格方法．用付立叶分析，通过红黑Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代，对Ｐｏｉｓｓｏｎ方程讲行研究，取得了较为满意的结果．     

关于自相似集的Hausdorff测度

得到了 Ｈａｕｓｄｏｒｆｆ容度与 Ｈａｕｓｄｏｒｆｆ测度相等的集的充分必要条件．对于满足开集条件的自相似集,验证了它的Ｈａｕｓｄｏｒｆｆ容度与Ｈａｕｓｄｏｒｆ测度相等并给出了它的Ｈａｕｓｄｏｒｆｆ测度的一个便于应用的公式．作为例子,给出了均匀康托集的Ｈａｕｓｄｏｒｆｆ测度的一种新的计算方法,对于Ｋｏｃｈ曲线的Ｈａｕｓｄｏｒｆｆ测度的上限也作了讨论．     

Bayes局部影响分析

本文从Ｂａｙｅｓ观点出发，利用Ｋｕｌｌｂａｃｋ－Ｌｅｉｂｌｅｒ距离和微分几何方法，系统地讨论了微小扰对于Ｂａｙｅｓ统计推断的局部影响，给出了Ｂａｙｅｓ局部影响分析的一般公式，作为应用，具体讨论了线性回归模型的Ｂａｙｅｓ估计和Ｂａｙｅｓ预测的局部影响问题，数值计算的结果表明，本文的方法是比较有效的。     

两种类型二元三角方程的图形的描绘

在中学数学里 ,我们讨论了ｙ =ｓｉｎｘ、ｙ =ｃｏｓｘ等特殊二元三角方程的作图方法 ,在 2 0 0 0年全国高考试卷中 ,出现了二元三角方程ｙ =-ｘｃｏｓｘ的图形 ,在这里我们通过例题讨论另两类二元三角方程的作图方法 ,通过讨论这两类二元三角方程的作图 ,可以加深对三角知识的理解 ,加强三角知识和平面解析几何知识之间的联系 ,也可以提高师生的作图技能 .1　形如Ｆ(ｃｏｓωｘ ,ｓｉｎｕｘ) =0的方程的图形例 1　画出在 0≤ｘ≤ 2π ,0 ≤ｙ≤ 2π范围内ｓｉｎ2 2ｘ ｃｏｓ2 ｙ =1的图形 .解　∵ｃｏｓ2 ｙ=1 -ｓｉｎ2 2ｘ,∴ｃｏｓ2 ｙ=…     

利用初等变换求解线性矩阵方程

本文给出了一般线性矩阵方程ＡｍｎＸｎｓ＝Ｂｍｓ，ＸｍｎＡｎｓ＝Ｂｍｓ，ＡｍｎＸｎｓＢｓｔ＝Ｃｍｔ的解的结构定理，并介绍了一种利用初等变换求解上述三类线性矩阵方程的方法．     

“现代外国统计学优秀著作译丛”书评(Ⅲ)

《寿命数据中的统计模型与方法》原著名：ＳｔａｔｉｓｔｉｃａｌＭｏｄｅｌｓａｎｄＭｅｔｈｏｄｓｆｏｒＬｉｆｅｔｉｍｅＤａｔａ原著作者：［加拿大］Ｊ．Ｆ．Ｌａｗｌｅｓｓ主译人员：茆诗松校译人员：葛广平中图分类号：Ｏ２１２　Ｃ８文献标识码：Ａ书评：《寿命数据中的统计模型与方法》一书是加拿大统计学家Ｊ．Ｅ．Ｌａｗｌｅｓｓ总结了六十年代以来在工程、医学和生物科学中迅猛发展起来的处理寿命数据的模型与方法而写成的,对这一领域进行了全面的介绍。成书之后畅销不衰,至今仍是这方面的主要参考书和研究生教科书。笔者八十…     

"0=1"错在哪里?

在微积分教材中 ,凡分部积分后可以循环的不定积分 ,通常认为是用解方程的方法解出不定积分的 ,这常常给学生以误导 .例如 ,用分部积分法计算如下不定积分∫ｃｏｓｘｓｉｎｘｄｘ =∫1ｓｉｎｘｄｓｉｎｘ =1ｓｉｎｘ·ｓｉｎｘ - ∫ｓｉｎｘｄ 1ｓｉｎｘｄｘ =1 - ∫ｓｉｎｘ ·- ｃｏｓｘｓｉｎ2 ｘ ｄｘ=1 +∫ｃｏｓｘｓｉｎｘｄｘ ,①所以有 0 =1 . ②如果①式继续计算下去 ,∫ｃｏｓｘｓｉｎｘｄｘ=1 +∫ｃｏｓｘｓｉｎｘｄｘ=2 +∫ｃｏｓｘｓｉｎｘｄｘ… =ｎ+∫ｃｏｓｘｓｉｎｘｄｘ ,③于是有 0 =1 =2 =… =ｎ . ④用同样的方法计算…     

一元向量有理插值的误差公式

Ｇｒａｖｅｓ－Ｍｏｒｒｉｓ于１９８３年利用向量的Ｓａｍｅｌｓｏｎ逆变换建立了一种实用的向量有理插值方法。本文得到了该向量有理插值的一个精确的误差公式。     

L_2-Cross-Validation最近邻中位数估计的相合性:m-相依情形

给出了ｍ－相依情形的Ｌ２－Ｃｒｏｓｓ－Ｖａｌｉｄａｔｉｏｎ最近邻中位数估计的弱相合性和用Ｌ_２－Ｃｒｏｓｓ－Ｖａｌｉｄａｔｉｏｎ方法选择的光滑参数的下界．     

协方差矩阵的齐性检验

基于ＰＰ技术、Ｂｏｏｔｓｔｒａｐ方法和数论方法,对于ｋ个总体协方差矩阵相等的检验,给出了ＰＰ型检验统计量,并讨论了它的渐近分布和Ｂｏｏｔｓｔｒａｐ逼近,最后给出了一些实际模拟结果。     

A local search using solution fragments for the 2-machine bicriteria scheduling problem

In this work, we introduce a local search strategy for combinatorial optimization problems which explores neighborhoods obtained using fragments of current solutions. We apply the approach to the well-known -hard 2-machine bicriteria flowshop scheduling problem. Computational experiments using benchmark data show the approach to be effective when compared to other algorithms available for the problem.     

A parametric bootstrap approach for the equality of coefficients of variation

In this article, a parametric bootstrap approach for testing the equality of coefficient of variation of $k$ normal populations is proposed. Simulations show that the actual size of our proposed test is close to the nominal level, irrespective of the number of populations and sample sizes, and that this new approach is better than the other existing ones. Also, the power of our approach is satisfactory. An example is proposed for illustrating our new approach.     

On the chaotic properties of the von Foerster-Lasota equation

In this article we present a different approach to some of the results published in our recent paper (Brze?niak and Dawidowicz in Semigroup Forum, 78(1):118–137, 2009). This new approach is based on a deep result from a paper (Ergod. Theory Dyn. Syst. 17(4):793–819, 1997) by Desch Schappacher and Webb.     

High order methods for the numerical solution of two-point boundary value problems

In a recent paper, Cash and Moore have given a fourth order formula for the approximate numerical integration of two-point boundary value problems in O.D.E.s. The formula presented was in effect a one-off formula in that it was obtained using a trial and error approach. The purpose of the present paper is to describe a unified approach to the derivation of high order formulae for the numerical integration of two-point boundary value problems. It is shown that the formula derived by Cash and Moore fits naturally into this framework and some new formulae of orders 4, 6 and 8 are derived using this approach. A numerical comparison with certain existing finite difference methods is made and this comparison indicates the efficiency of the high order methods for problems having a suitably smooth solution.     

On the Accuracy of the MAP Inference in HMMs

In a hidden Markov model, the underlying Markov chain is usually unobserved. Often, the state path with maximum posterior probability (Viterbi path) is used as its estimate. Although having the biggest posterior probability, the Viterbi path can behave very atypically by passing states of low marginal posterior probability. To avoid such situations, the Viterbi path can be modified to bypass such states. In this article, an iterative procedure for improving the Viterbi path in such a way is proposed and studied. The iterative approach is compared with a simple batch approach where a number of states with low probability are all replaced at the same time. It can be seen that the iterative way of adjusting the Viterbi state path is more efficient and it has several advantages over the batch approach. The same iterative algorithm for improving the Viterbi path can be used when it is possible to reveal some hidden states and estimating the unobserved state sequence can be considered as an active learning task. The batch approach as well as the iterative approach are based on classification probabilities of the Viterbi path. Classification probabilities play an important role in determining a suitable value for the threshold parameter used in both algorithms. Therefore, properties of classification probabilities under different conditions on the model parameters are studied.     

A variant of the level set method and applications to image segmentation

In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of level set functions are utilized to identify up to phases. The novelty in our approach is to introduce a piecewise constant level set function and use each constant value to represent a unique phase. If phases should be identified, the level set function must approach predetermined constants. We just need one level set function to represent unique phases, and this gains in storage capacity. Further, the reinitializing procedure requested in classical level set methods is superfluous using our approach. The minimization functional for our approach is locally convex and differentiable and thus avoids some of the problems with the nondifferentiability of the Delta and Heaviside functions. Numerical examples are given, and we also compare our method with related approaches.

     

A new solution method for the finite-horizon discrete-time EOQ problem

We consider the finite-horizon discrete-time economic order quantity problem. Kovalev and Ng (2008) have developed a solution approach for solving this problem. Their approach requires a search for the optimal number of orders, which takes O(logn)$\text{O}(\log n)$ time. In this note, we present a modified solution method, which can determine the optimal solution without the need of such a search.     

On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

Iterative continuation and the solution of nonlinear two-point boundary value problems

In this paper we present a unified function theoretic approach for the numerical solution of a wide class of two-point boundary value problems. The approach generates a class of continuous analog iterative methods which are designed to overcome some of the essential difficulties encountered in the numerical treatment of two-point problems. It is shown that the methods produce convergent sequences of iterates in cases where the initial iterate (guess),x ₀, is far from the desired solution. The results of some numerical experiments using the methods on various boundary value problems are presented in a forthcoming paper.     

A new cluster-expansion approach to the calculation of the energy structure of crystals

We propose a new approach to the calculation of energy spectra for strongly compressed or imperfect crystals in the case where the localized orbitals (LO) of atoms with different space positions overlap considerably. This approach is based on the exact orthogonalization of the LO for all atoms according to Lövdin's method and on the cluster expansion (CE). In all nth orders of the CE, we take into account the overlapping integrals (OI) of the LO for atoms belonging to the same n-particle cluster. For every n, such clusters comprise the whole crystal. For n ; , the CE converges exponentially to the OI. The two-particle cluster expansion is discussed in detail.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 106, No. 3, pp. 498–512, March, 1996.Translated by M. V. Chekhova.