用于积分方程解的函数值Padé逼近的Pfaffin公式

1　Introduction　Letf(x ,λ)beagivenpowerserieswithfunction valuedcoefficients,f(x ,λ) =c0 (x) c1(x)λ c2 (x)λ2 … 　　cn(x)λn … (1)wherecj(x)isarealorcomplexfunctionwithre specttox∈ (a ,b) .Suppoethatf(x ,λ)isanalyticasafunctionofλattheoriginλ =0 .　Chisholm[1] pointedoutPad啨ａｐｐｒｏｘｉｍａｎｔｍｅｔｈｏｄｃａｎｂｅｕｓｅｄｆｏｒｏｂｔａｉｎｉｎｇｔｈｅｓｏｌｕｔｉｏｎｏｆａｗｋｗａｒｄｉｎ tegralequations,andespeciallythosewhichpossessageneratingfunctionoftheform (1) ,sinceth…     

Continued Fraction Algorithm for Matrix Exponentials

A recursive rational algorithm for matrix exponentials was botained by making use of the generalized inverse of a matrix in this paper.On the basis of the n-th convergence of thiele-type continued fraction expansion,a new type of the generalized inverse matrix-valued pade approximant(GMPA)for matrix exponentials was defined and its remainder formula was proved.The resuts of this paper were illustrated by some examples.     

Degeneracy cases of generalized inverse function-valued Padé approximation

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application. Project supported by the National Natural Science Foundation of China (Grant No. 10271074)     

Orthogonal polynomials and Padé approximation

The diagonal Padé approximants for exp (x), tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on [−1,1] P _r1(x) is orthogonal to every polynomial of lower degree. Gauss’s quadrature formula is used to find the denominators of some functions.     

Some algebraic properties of generalized inverse matrix-valued Padé approximation

The matrix Padé approximant based on generalized inverse is characterized by keeping approximation order and without multiplication of matrices in the construction process. The aim of this paper is to give and prove some algebraic properties of generalized inverse matrix-valued Pade approximation by means of its definition. Computational examples are given to illustrate the applications of the properties, which greatly simplify the computation process. Supported by the National Natural Science Foundation of China (19871054)     

估计第二类Fredholm 积分方程特征值的函数值部分Pad´e-型逼近方法

Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation.     

A matrix padé-type-routh model reduction method for multivariable linear systems

In the present paper, the formulae for matrix Padé-type approximation were improved. The mixed model reduction method of matrix Padé-type-Routh for the multivariable linear systems was presented. A well-known example was given to illustrate that the mixed method is efficient. Project supported by National Natural Science Foundation of China (Grant No. 10271074)     

Least-squares function-valued Padé-type approximation and its application in solving integral equations

To solve the Fredholm integral equations of the second kind, a new notion of the least-squares orthogonal polyno- mials of function-valued Pade-type approximation is introduced. On the basis of the error formula, the least-squares function： valued Pad＆type approximation is constructed. Their existence and uniqueness are studied. A recursive computation formula of the least-squares function-valued Padetype approximation is given. In the end, an example is given to show that the method is effective and stable.     

估计第二类Fredholm积分方程特征值的函数值部分Padé-型逼近方法

A new function-valued partial Padé-type approximation was introduced in the polynomial space,and an explicit determinant formula was derived by means of some orthogonal polynomials.This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known,and at the same time,it can be applied to solving the approximating solution of the given equation.     

广义（3＋1）-维浅水波方程的3种Grammian解

孤子方程的多孤子解可表示成Grammian形式的行列式解,进而写成Pfaff的形式,从而在求解双线性方程以及证明中可以直接把解代入方程进行验证。借助于Pfaff式技巧,得到了广义（3＋1）-维浅水波方程的3种不同Grammian解。     

退化的广义逆函数值Padé逼近

A new generalized inverse function-valued Padé approximation (GIFPA) was defined. Existence condition of GIFPA was given and its uniqueness theorem was proved. All possible degeneracy cases of GIFPA were discussed and constructed. An example was given to illustrate its application.     

C~2连续的有理三次Bézier样条插值曲线

有理Bézier曲线具有很多良好的性质,是曲线曲面设计的重要方法.根据给定的型值点,通过构造有理Bézier样条插值曲线的公式,给出了计算方法,并且分析了重节点情形曲线的形状和特点,最后通过数值实例验证了方法的有效性.     

The ε-algorithm and η-algorithm for generalized inverse rectangular matrix pade approximants

An axiomatic definition for the generalized inverse matrix Pade approximation (GMPA) is introduced. The matrix rational approximants are of the form of the matrix-valued numerator and the scalar denominator. By means of generalized inverse for matrices, the ε-algorithm for the computation of GMPA is established. The well-known Wynn identity for GMPA is proved on the basis of ε-algorithm. The η-algorithm is defined in a similar way. The equivalence relation between ε-algorithm and η-algorithm is proposed. Some common examples and a numerical example are given to illustrate the methods in this paper. Project supported by the National Natural Science Foundation of China(19871054)     

Key concepts in postgraduate certificates in higher education teaching and learning in Australasia and the United Kingdom

Post‐colonial theories about liminality, hybridity, unhomeliness, and identity form a novel lens through which to re‐theorise educational development work. Applying these conceptual frameworks allows practitioners and the academics they work with the opportunity to problematise some of educational development’s colonial underpinnings and assumptions. They also enable an exploration of the states of betweenness that form educational developers’ identities and impact implicitly and explicitly upon the nature of their changing practices. This paper seeks to read educational development and research supervisor development in particular “against the grain”. It also seeks to illustrate these concepts through some vignettes of my academic development practice.

Les théories postcoloniales portant sur les notions de “liminality”, “hybridity”, “unhomeliness”, ainsi que sur la notion d’identité constituent un nouvel angle sous lequel nous pouvons réenvisager les travaux dans le domaine du développement pédagogique. L’application de tels cadres conceptuels offre aux praticiens, ainsi qu’aux universitaires auprès de qui ils/elles oeuvrent, l’occasion d’envisager les problèmes associés aux bases et pré‐supposés colonialistes du développement pédagogique. Ces cadres facilitent aussi l’exploration des états reliés à la notion de “between‐ness”, lesquels contribuent à la formation de l’identité des conseillers pédagogiques et ont un impact à la fois implicite et explicite sur la nature des pratiques en mutation. Cet article cherche à effectuer une lecture du développement pédagogique et du développement de la supervision de recherche en adoptant plus particulièrement une approche “against the grain”. L’article cherche aussi à illustrer ces cadres par des vignettes de ma pratique.     

英汉语中通音／1，r，w，j／的语音对比分析

英语通音／1,r,w,j／和汉语中的／1,r,w,y／在发音方式和发音部位等方面既存在相似之处也有很多不同之处。本文以对比分析假设为指导,详尽叙述英汉两种语言中通音的语音特征和声学特征的相似性和差异性,试图解释学习者在习得过程中可能忽略的问题,希望引起语言学习者和语言教学者的关注。     

Interactivity Between Protégés and Scientists in an Electronic Mentoring Program

Interactivity is defined by Henri (1992) as a three-step process involving communication of information, a response to this information, and a reply to that first response. It is a key dimension of computer-mediated communication, particularly in the one-on-one communication involved in an electronic mentoring program. This report analyzes the interactivity between pairs of corporate research scientists (mentors) and university biology students (protégés) during two consecutive implementations of an electronic mentoring program. The frequency and structure of the interactions within each pair were examined to provide context: 542 messages were posted among the 20 mentors and 20 protégés. These messages were formed into 5–10 threads per pair, with 3–4 messages per thread, indicating a high level of interactivity (there were more responses posted than independent messages). Mentor–protégé pairs rated as effective by both mentors and protégés posted more messages overall, had well-structured threads, had protégé and mentor postings that were similar in topic coverage and message length, and had little overt “management” behavior by mentors. However, there appears to be no clear recipe for successful interaction. Not only are there a variety of factors at play in developing an online relationship in this context, but mentor–protégé pairs can falter at various stages in the process and in various ways.     

Troubling our Desires for Research and Writing within the Academic Development Project

In this paper, I speculate on the work ‘usefulness’ does to regulate the research and writing of the scholarship of academic development project. My argument is not that academic developers ought to repudiate a fidelity to usefulness; rather, I want to expand our ideas for the possibilities of research and writing beyond purposes of institutional performativity that so often dominate the agenda. In essence, it is an argument for redeploying how we see usefulness. My search has led me to traditions of arts‐based inquiry. It is that form of inquiry that invites the academic development community to consider the narratives that constitute, organize, and render its scholarship meaningful. It is also that form of inquiry that supports academic developers’ inhabiting, perhaps even desiring, a creative space in which to examine and re‐imagine what can be legitimately written about the project of academic development.

Dans cet article, je spécule sur comment la notion « d’utilité » régule la recherche et la rédaction relatives au projet de développement pédagogique érudit. Mon argument n’est pas que les conseillers pédagogiques doivent renoncer à être fidèles à cette notion d’utilité ; plutôt, je désire élargir nos idées de façon à rendre possible la recherche et la rédaction au‐delà des buts reliés à la performativité institutionnelle qui dominent si souvent l’agenda. Essentiellement, il s’agit là d’un argument en faveur du redéploiement de notre façon d’envisager l’utilité. Mes recherches m’ont menée vers les traditions artistiques d’investigation. Cette forme d’investigation invite la communauté du développement pédagogique à considérer les récits qui constituent, organisent et rendent significatifs son érudition. C’est aussi cette forme d’investigation qui amène les conseillers pédagogiques à habiter, voire même désirer, un espace créatif à l’intérieur duquel ils peuvent examiner ou ré‐imaginer ce qui peut légitimement être écrit au sujet du projet de développement pédagogique.     

Indigenous Métissage: a decolonizing research sensibility

This paper is a report on the theoretical origins of a decolonizing research sensibility called Indigenous Métissage. This research praxis emerged parallel to personal and ongoing inquiries into historic and current relations connecting Aboriginal peoples and Canadians in the place now called Canada. I frame the colonial frontier origins of these relations – and the logics that tend to inform them – as conceptual problems that require rethinking on more ethically relational terms. Although a postcolonial cultural theory called métissage offers helpful insights towards this challenge, I argue that the postcolonial emphasis on hybridity fails to acknowledge Indigenous subjectivity in ethical ways. Instead, I present an indigenized form of métissage focused on rereading and reframing Aboriginal and Canadian relations and informed by Indigenous notions of place. Doing Indigenous Métissage requires hermeneutic imagination directed towards the telling of a story that belies colonial frontier logics and fosters decolonizing.     

漫谈数列通项公式的求法

数列是定义在正整数集上的一类特殊函数,其表现形式是通项公式.通项公式是研究数列性质的重要形式,它能够帮助我们更好地把握数列的特征,因此学好通项公式是学好数列的首要任务.本文主要通过几道例题归纳总结了常见的几种通项公式的求法.