Orthogonal Polynomials and Padé Approximation

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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.     

Rationalité des Pratiques et Conditions de leur Transformation

The present article deals with the transformation of teaching practices in the light of recent research carried out in the field of the context‐process approach and of the sociology of education. We distinguish two main lines of reflection: (1) The teaching practices form systems the elements of which are functionally interdependent; (2) The teaching practices result—historically and at a given moment—from a complex interplay between more individual factors (in particular, the hierarchy of the teacher's criteria of value) and contextual liberties and constraints (in particular, institutional ones). The former hypothesis leads to the proposed intervention models centred on the modification of key variables of the teaching practice (e.g. the way in which the activities are organised) the transformation of which is likely to transform other elements of the system (the nature of feedbacks, for instance). The latter hypothesis leads to a formulation in terms of both compatibility and feasibility of the combined conditions of the transformation of these key variables in a given teaching practice: the compatibility condition defines the modifications that do not irremediably clash with the teacher's criteria of value; the feasibility condition defines the changes that can be introduced in the institution, having taken into account the kind of relationship the teacher has with it.

     

Degeneracy Cases of Generalized Inverse Function-Valued Padé Approximation

1　Introduction　Thispaperisprimarilyconcenredwiththeanalysisofthedegeneracycaseswhichmayoccurinthepro cessofconstructinggeneralizedinversefunction val uedPad啨ａｐｐｒｏｘｉｍａｎｔｓ .　Letf(s,λ)beagivenpowerserieswithfunctionalcoefficients,i.e .,f(s,λ) =c0 (s) +c1(s)λ +c2 (s)λ2 +… +　　cn(s)λn+… , (1)wherecj(s)isanalytic ,andf(s ,λ)isalsoanalyticatλ =0 .Thenon degeneratefunction valuedPad啨ａｐｐｒｏｘｉｍａｎｔｗａｓｉｎｔｒｏｄｕｃｅｄｂｙＧｒａｖｅｓ Morris[1] .Anintactdetermi…     

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)     

Interacción profesor/alumnos y comprensión de textos. Qué se hace y qué se puede hacer

Resumen

El objetivo fundamental de este trabajo es mostrar la distancia que existe entre lo que los profesores hacen en sus aulas y los estados ideales propuestos por la investigación educativa. Para ello, hemos diseñado un sistema de análisis que nos permite describir cómo son las interacciones entre los profesores y sus alumnos cuando tratan de comprender un texto. Fundamentalmente, el sistema de análisis nos permite obtener información sobre dos cuestiones básicas. En primer lugar, permite estudiar qué contenidos incluidos en el texto escrito se hacen públicos en el aula. En segundo lugar, da una idea completa sobre el grado de participació n que tienen profesor y alumnos en la elaboración de este texto público. Utilizando este procedimiento se ha analizado un fragmento de una clase de lectura. Una vez realizado el análisis, se han propuesto algunas alternativas que permitan acortar la distancia existente entre la realidad del aula y las propuestas formuladas desde la teoría educativa.     

guā guɑ hé wá wɑ

guāguɑhéwáwɑjīnguāguɑyínguāguɑguāguɑluòxiɑlɑidǎzhexiǎowáwɑwáwɑjiàomāmɑmāmɑbàowáwɑwáwɑguàiguāguɑguāguɑxiàowáwɑguā guɑ hé wá wɑ     

Critical Depictions of Agency in Pura Belpré Awarded Texts

Given the need for multiple representations of historically underrepresented voices in children’s literature, this research study explored critical depictions of agency of Latinx youth within the Pura Belpré awarded texts from 1996 to 2021. The findings report a critical multicultural analysis of depictions of age, sex, socio-economic status, ethnicities, and geographic regions of these awarded texts. Using a secondary analysis of opportunities for agency, we examine how focal subjects (Vaughn et al., 2021; Crisp, 2015) exert their agency in their respective contexts. Our aim in doing so is to highlight the notion of agency in these texts of Latinx children and youth, specifically understanding who exerts agency, how, and for what purposes. Implications for practice and future research are discussed.

     

Yánɡ hé qiánɡ

HáishiSānɡjiāyàoZhānɡjiāxiānbǔqiánɡ.Zhānɡjiāyǒuzhīyánɡ,Sānɡjiāyǒudǔqiánɡ,ZhānɡjiādeyánɡzhuànɡdǎoleSānɡjiādeqiánɡ,SānɡjiādeqiánɡyāshānɡleZhānɡjiādeyánɡ,BùzhīshìZhānɡjiāyàoSānɡjiāxiānpéiyánɡ,HáishiSānɡjiāyàoZhānɡjiāxiānbǔqiánɡ.Zhānɡjiāyǒuzhīyánɡ,Sānɡjiāyǒudǔqiánɡ,ZhānɡjiādeyánɡzhuànɡdǎoleSānɡjiādeqiánɡ,SānɡjiādeqiánɡyāshānɡleZhānɡjiādeyánɡ,BùzhīshìZhānɡjiāyàoSānɡ…     

jùtǐ hé chōuxiàng

xiāohuá zài zuò zuòwén, tā yǒu ge wèntí gǎo bù dǒng, biàn wèn dāng jiàoshi de māma:"māma! shnén·me jiào 'jùtǐ' māma shuō: "'jùtǐ' jiùshì kànde jiàn、mōdedào de, 'chōuxiàng' jiùshì kàn bú jiàn、mō bú dào de……"     

Analyzing The Ballad of the Sad Café with Actantial Model

The actantial model is an appropriate and universal way to analyze the deep structure of any novel.By analyzing Carson McCullers’famous novel The Ballad of the Sad Café with actantial model,the theme and the beauty of the novel are easier to acquire.     

Where Do They Go? Students’ Sources of Résumé Advice,and Implications for Critically Reimagining the Résumé Assignment

This article explores what sources students use for advice while writing their résumés, their reasons for choosing those sources, and their perceptions about the sources’ quality. Results from surveys, interviews, and focus groups with 86 undergraduates and 20 career counselors and instructors suggest issues with educators’ credibility and students’ access. To address these issues, the author suggests that educators approach the résumé as a research project, which empowers students and legitimizes educators’ expertise.