Cramer法则在数值计算中的若干应用

用Cramer法则给出了Lagrange插值公式和Newton插值公式的简洁证明,同时得到了Vandermonde矩阵的逆矩阵的LU分解.     

关于差商和Newton插值公式教学的一些体会

针对讲授Newton插值多项式之前,如何自然地引入差商概念,介绍了一些心得体会;同时对Newton插值公式给出了一种简便、学生易于理解的证明方法.     

关于一类多元有理插值(英文)

[1]中给出了一类多元有理插值公式。本文揭示了它的递推性质,并导出了相应的Newton型 Hermite和 Hermite—Fejer 插值公式。借助于广义有理函数,本文还构造了两种圆弧上的复插值公式。文中所得结果都有显式表示。     

三元New ton-Thiele型插值方法

本文以 Newton插值及 Thiele型连分式插值为基础 ,将线性与非线性插值方法相结合 ,通过混合差商的定义 ,给出了三元 Newton-Thiele型插值公式及误差估计式 .     

三元Newton—Thiele型插值方法

本以Newton插值及Thiele型连分式插值为基础，其线性与非线性插值方法相结合，通过混合差商的定义，给出了三元Newton-Thiele型插值公式及误差估计式。     

二元向量值有理插值存在性的一种判别方法

文章给出了对于矩形网格上基于二元Newton插值公式的二元向量值有理插值存在性的充要条件.在存在的情况下,建立了具有显式表达式的不同于向量连分式的二元向量值有理插值函数,并且这种方法具有承袭性.最后给出的实例说明了这种算法的有效性.     

ACM元各向异性分析的Newton方法

本文将一维Lagrange插值多项式的Newton表达式推广到二维非标准的Hermite插值,给出著名板元-ACM元插值多项式的Newton表达式,由此给出ACM元对四阶和二阶椭圆问题的各向异性插值误差估计,为复杂单元的各向异性分析开辟了新的途径.     

一类二元有理插值函数的存在性及算法

文[3]构造了对于矩形网格上基于二元Newton插值公式的一类二元有理插值函数,并给出了其存在性的充分条件.本文进一步证明了这类二元有理插值函数存在性的必要条件,特别地,当m=n时,给出了具有三角形结构的系数矩阵的判别方法,该方法计算简便且具有承袭性,文章最后给出的实例说明了方法的有效性.     

二元向量值有理插值存在性的一种判别方法

1 引言 一元向量值有理插值问题在[1-5]中有了比较系统的研究．文[6—13]成功地将一无的结果推广到了二元的情形,但它们采用的大多是向量值连分式的方法,且没有给出二元向量值有理插值存在性的判别方法及其证明．本文利用二元Newton插值公式,     

利用反级数关系构造插值公式的一种方法

这篇文章指出,互反级数关系可以成为等距插值公式的一个来源。从原则上说来,只要一对互反级数关系中的“求和核”(级数变换核)容许扩充为连续变量的函数,则相应地便可获得一个插值公式。本文举出一系列例子说明了这个方法。特别,我们从广义M?biusRota反演公式出发,造出了一类借助于差分表出的插值公式。这类公式不同于Newton插值法,其特点是具有大范围插值性质;并且由于公式中只使用阶数固定的差分,故还能避免出现“Runge现象”。本文给出了四条定理,论述了这类公式的性质。最后,我们还对具有代数精度的分段(分片)     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Scientists and mathematicians collaborating to build quantitative skills in undergraduate science

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better QS than at any time in the past. Ways in which mathematics and science academics are working together to build the QS of their undergraduate science students, together with the mathematics and statistics needed or desired in a science degree, are reported on in this paper. The emphasis is on the life sciences. Forty-eight academics from eleven Australian and two USA universities were interviewed about QS in science. Information is presented on: what QS academics want in their undergraduate science students; who is teaching QS; how mathematics and science departments work together to build QS in science and implications for building the QS of science students. This information leads to suggestions for improvement in QS within a science curriculum.     

Combinatorics of generalized q-Euler numbers

New enumerating functions for the Euler numbers are considered. Several of the relevant generating functions appear in connection to entries in Ramanujan's Lost Notebook. The results presented here are, in part, a response to a conjecture made by M.E.H. Ismail and C. Zhang about the symmetry of polynomials in Ramanujan's expansion for a generalization of the Rogers-Ramanujan series. Related generating functions appear in the work of H. Prodinger and L.L. Cristea in their study of geometrically distributed random variables. An elementary combinatorial interpretation for each of these enumerating functions is given in terms of a related set of statistics.     

火灾发生的周期性规律及其在火灾非线性组合预测模型中应用

研究火灾发生规律及发展趋势,具有实用价值.分析历年中国火灾统计数据,发现中国火灾的发生规律同时具有增长趋势性和周期波动性特征:①中国火灾从90年代开始大幅度增加,在2002年达到最大,然后逐年缓慢下降;②每年12个月呈正弦函数波动,周期为12,1、2月发生起数最大,8、9月最小.借助于M ATLAB软件,根据2000-2006年中国火灾统计数据,建立火灾的月发生起数的非线性周期性组合预测模型,预测值与实际值的平均相对误差小于0.07.研究结论为消防研究、消防部门决策提供科学依据.     

A graph theory approach to subcontracting, machine duplication and intercell moves in cellular manufacturing

We address in this paper the problem of finding an optimal strategy for dealing with bottleneck machines and bottleneck parts in the cell formation process in group technology. Three types of economic decisions are considered: subcontracting, machine duplication and intercell moves. The problem is formulated as a minimum weighted node covering problem in a hypergraph, and we show that it can be solved in polynomial time by finding a maximum weighted stable set in a bipartite graph. We extend this result to cellular manufacturing systems in which the sequence of operations of each part is known in advance.     

Reasoning about variation in the intensity of change in covarying quantities involved in rate of change

This paper extends work in the area of quantitative reasoning related to rate of change by investigating numerical and nonnumerical reasoning about covarying quantities involved in rate of change via tasks involving multiple representations of covarying quantities. The findings suggest that by systematically varying one quantity, an individual could simultaneously attend to variation in the intensity of change in a quantity indicating a relationship between covarying quantities. The results document how a secondary student, prior to formal instruction in calculus, reasoned numerically and nonnumerically about covarying quantities involved in rate of change in a way that was mathematically powerful and yet not ratio-based. I discuss how coordinating covariational and transformational reasoning supports attending to variation in the intensity of change in quantities involved in rate of change.     

On Potential Theoretic Skeletons of Polyhedra

We prove that any polyhedron in two dimensions admits a type of potential theoretic skeleton called mother body. We also show that the mother bodies of any polyhedron in any number of dimensions are in one-to-one correspondence with certain kinds of decompositions of the polyhedron into convex subpolyhedra. A consequence of this is that there can exist at most finitely many mother bodies of any given polyhedron. The main ingredient in the proof of the first mentioned result consists of showing that any polyhedron in two dimensions contains a convex subpolyhedron which sticks to it in the sense that every face of the subpolyhedron has some part in common with a face of the original polyhedron.     

Lightcone dualities for hypersurfaces in the sphere

In this paper, we consider hypersurfaces in the unit lightlike sphere. The unit sphere can be canonically embedded in the lightcone and de Sitter space in Minkowski space. We investigate these hypersurfaces in the framework of the theory of Legendrian dualities between pseudo‐spheres in Minkowski space.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

Nevanlinna theory of meromorphic functions on annuli

In this survey paper, we discuss the recent development of Nevanlinna theory of meromorphic functions on annuli, which extends results in Nevanlinna theory in the complex plane or in a disk. In particular, we show that the approach taken on annuli is a unified treatment of functions meromorphic in the complex plane, a disk and an annulus. It allows one to obtain many results in the complex plane and in a disk as corollaries of our results in annuli.