14 results on '"Derivative function"'
Search Results
2. Wavelet estimations of the derivatives of variance function in heteroscedastic model.
- Author
-
Kou, Junke and Zhang, Hao
- Subjects
DERIVATIVES (Mathematics) ,NONPARAMETRIC estimation ,HETEROSCEDASTICITY - Abstract
This paper studies nonparametric estimations of the derivatives of the variance function in a heteroscedastic model. Using a wavelet method, a linear estimator and an adaptive nonlinear estimator are constructed. The convergence rates under risk of those two wavelet estimators are considered with some mild assumptions. A simulation study is presented to validate the performances of the wavelet estimators. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. A reverse Hardy–Hilbert-type integral inequality involving one derivative function
- Author
-
Qian Chen and Bicheng Yang
- Subjects
Weight function ,Hardy–Hilbert-type integral inequality ,Derivative function ,Parameter ,Beta function ,Reverse ,Mathematics ,QA1-939 - Abstract
Abstract In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.
- Published
- 2020
- Full Text
- View/download PDF
4. Hacia un planteamiento interdisciplinar en la iniciación a la modelización económica en el Bachillerato: una propuesta en torno a la derivada y el análisis marginal.
- Author
-
Gutiérrez-Portilla, María, Gutiérrez-Portilla, Paula, and Álvarez-Causelo, Pedro
- Published
- 2021
- Full Text
- View/download PDF
5. A reverse Hardy–Hilbert-type integral inequality involving one derivative function.
- Author
-
Chen, Qian and Yang, Bicheng
- Subjects
- *
INTEGRAL inequalities , *BETA functions - Abstract
In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
6. Analyse praxéologique des pratiques des enseignants et de leur utilisation des ressources pour l’enseignement de la dérivée : une étude de cas dans l’enseignement secondaire général au Cameroun
- Author
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Nseanpa, Casimir J. and González-Martín, Alejandro
- Subjects
Taux de variation ,Ressources ,Dérivée ,Praxeology’s ,Praxéologies ,Tangente ,Derivative ,Pratiques enseignantes ,Resources ,Rate of change ,Fonction dérivée ,Derivative function ,Teaching practices ,Tangent - Abstract
La dérivée est un concept important dans les cours de calcul. Dans certains pays comme au Canada et en France, il est enseigné au niveau collégial tandis qu’en Afrique et en particulier au Cameroun, on l’enseigne au niveau secondaire car la dérivée intervient dans l’étude des variations d’une fonction. Cette thèse dont le titre est : Analyse praxéologique des pratiques des enseignants et de leur utilisation de ressources pour l’enseignement de la dérivée. Une étude de cas dans l’enseignement secondaire général au Cameroun part du constat selon lequel de nombreux élèves et étudiants rencontrent des difficultés avec la notion de dérivée et que ces difficultés s’observent dans leurs résultats scolaires et académiques. Au vu de l’importance de la dérivée pour les différents parcours universitaires en sciences, nous nous intéressons aux pratiques des enseignants de mathématiques et notamment leurs praxéologies didactiques autour de la dérivée mais aussi, nous voulons comprendre les raisons qui justifient les choix faits par ces enseignants. La recherche essaie de répondre à la question de savoir quelles sont les pratiques des enseignants et les ressources utilisées par ces derniers pour l’enseignement de la dérivée? La recherche se propose ainsi d’identifier les praxéologies que les enseignants développent dans leur utilisation des ressources pour préparer leurs leçons et pour enseigner la dérivée. Nous ne nous limitons pas aux praxéologies observables mais nous aimerons comprendre les raisons qui justifient les choix opérés par ces enseignants et les contraintes institutionnelles auxquelles ils font face. Deux cadres théoriques encadrent cette recherche : la Théorie Anthropologique de la Didactique (TAD) qui nous permet d’analyser les types de tâches, les techniques, les technologies et les théories justifiant les technologies employées dans les ressources des enseignants et dans leurs pratiques enseignantes. De même, nous utilisons l’Approche Documentaire du Didactique (ADD) afin d’analyser les ressources institutionnelles et les autres ressources que les enseignants utilisent pour enseigner la dérivée. Pour analyser l’utilisation des ressources des enseignants, nous mettons un accent sur les objectifs et les sous-objectifs visés, les règles d’action, les invariants opératoires et les inférences éventuelles. Sur le plan méthodologique, nous utilisons une étude de cas impliquant trois enseignants qui enseignent la dérivée aux élèves de première. Nous utilisons des entretiens semi-dirigés afin d’analyser les choix que font les enseignants lors de la préparation des cours mais et surtout les raisons qui justifient ces choix; les observations vidéo-filmées permettent de savoir comment les enseignants introduisent la dérivée en un point et sur un intervalle et l’analyse des documents tels que les programmes de mathématiques, les manuels scolaires et d’autres ressources des enseignants employés dans la préparation des cours. Le principal résultat de cette thèse est l’identification du poids des ressources institutionnelles et de l’examen de fin d’année sur les praxéologies mathématiques et sur la manière dont les enseignants utilisent ces ressources. Nous discutons de ce résultat en tenant compte du rapport personnel des enseignants et des praxéologies développées dans les manuels et lors de l’enseignement., Derivatives are one of the most important topics studied in high school (in many countries) and postsecondary mathematics. Many students must learn this topic to pursue their university studies and as a gateway to learn other mathematical topics in various other fields. In Cameroon, secondary teaching lasts from 12 to 18 years old. In this context, what in other countries is considered as pre-university courses, or college, in Cameroon is still called secondary. Derivatives are introduced in the last but one year of this cycle, called première (students are 17), after the topics of function, limit, and continuity. In this thesis, we examined teachers’ practices and their use of resources while teaching derivatives. This study in general secondary education in Cameroon starts from the observation that many pupils and students encounter difficulties with the notion of derivative and that these difficulties are observed in their academic results. The research attempts to identify the tasks, techniques and technologies developed in the resources used by these teachers. It also tries to describe the patterns of use of resources by closely observing the objectives pursued, the rules of action and the operational invariants put in place when using resources. We do not limit ourselves to describing the practices of teachers, but we would like to understand the reasons that justify their choices and the institutional constraints they face. Since we are interested in teachers’ practices and their use of resources to teach derivatives, we use elements of the anthropological theory of the didactic (ATD) to analyze the types of tasks, the techniques, technologies, and theories justifying the technologies used in teachers' resources and teaching practices. By using DA, we understand that teachers, to prepare their teaching, use variety of resources. These resources aiming to teach this content together with the schemes of use of these resources result in a document and these schemes of use of resources is influenced by the teacher’s own personal relationship. The participants in this study were three teachers who teach derivatives to first-class students. We use semi-structured interviews to analyse the choices teachers make when preparing courses, but above all the reasons that justify these choices and video to observe how teachers introduce the derivative. The video shows how teachers introduce the derivative at a point and on an interval. Others analyses helps us understanding how this content is introduced on math programs, textbooks and other teacher resources used in the preparation of courses. The main result of this thesis is the identification of the weight of institutional resources and the end-of-year examination on mathematical praxeology’s and on the way, teachers use these resources. We discuss this result considering the personal relationship of teachers and the praxeology’s developed in textbooks and during teaching.
- Published
- 2022
7. Математичний аналіз: Диференціальне числення функцій однієї змінної
- Subjects
диференційовність функції ,похідна функції ,derivative function ,tangent to the curve ,517.2 ,differentiability of the function ,дотична до кривої - Abstract
Викладено теорію границь послідовностей і функцій однієї змінної, диференціальне числення та його застосування. Навчальний посібник «Математичний аналіз: Диференціальне числення функцій однієї змінної» призначено для вивчення тем «Границі послідовностей та функцій, диференціальне числення функцій однієї змінної» студентами 122 «Компьютерні науки». Він містить основні теоретичні положення з названої теми. Разом зі стандартними фактами теорії послідовностей розглядаються методи знаходження границь, що базуються на теоремах Тьоплиця та Штольца, а також теоремі Банаха про стискаючі відображення, що вміщено в Доповненні. Викладено теорію границь функцій, теорію неперервних функцій та диференціальне числення, що ілюструється численними прикладами, в тому числі, підвищеної складності. The textbook "Mathematical Analysis: Differential calculus of functions of one variable" is designed to study the topics "Boundaries of sequences and functions, differential calculus of functions of one variable" by students 122 "Computer Science". It contains the main theoretical provisions on this topic. Along with the standard facts of sequence theory, methods for finding boundaries based on Toplice and Stoltz theorems, as well as Banach's theorem on compressive mappings, which are contained in the Addendum, are considered. The theory of function boundaries, the theory of continuous functions and differential calculus are presented, which is illustrated by numerous examples, including those of increased complexity. Учебное пособие «Математический анализ: дифференциальное исчисление функций одной переменной» предназначено для изучения тем «Границы последовательностей и функций, дифференциальное исчисление функций одной переменной» студентами 122 «Компьютерные науки». Он содержит основные теоретические положения по названной теме. Вместе со стандартными фактами теории последовательностей рассматриваются методы нахождения границ, основанные на теоремах Тёплица и Штольца, а также теореме Банаха о сжимающие отображения, помещены в Приложении. Изложена теория пределов функций, теорию непрерывных функций и дифференциальное исчисление, что иллюстрируется многочисленными примерами, в том числе, повышенной сложности.
- Published
- 2021
8. Hacia un planteamiento interdisciplinar en la iniciación a la modelización económica en el Bachillerato: una propuesta en torno a la derivada y el análisis marginal
- Author
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María Gutiérrez-Portilla, Paula Gutiérrez-Portilla, Pedro Álvarez-Causelo, and Universidad de Cantabria
- Subjects
Función derivada ,Virtual learning object ,Análisis marginal ,Objeto virtual de aprendizaje ,Interdisciplinariedad ,Economic models ,Derivative function ,Interdisciplinary approach ,Marginal analysis ,Modelos económicos - Abstract
RESUMEN. En este trabajo se describe un objeto virtual de aprendizaje (OVA) elaborado bajo una perspectiva interdisciplinar que abarca las materias de Economía y Matemáticas aplicadas a las Ciencias Sociales, correspondientes ambas a la modalidad de Humanidades y Ciencias Sociales del Bachillerato. Dicho OVA está constituido por una secuencia de construcciones elaboradas con el software Geogebra y organizadas en torno al concepto matemático de función derivada y su papel como herramienta básica en la modelización económica (asociado fundamentalmente a lo que suele denominarse análisis marginal). La propuesta se realiza con la intención de ejemplificar el tipo de materiales y actividades que podrían diseñarse y utilizarse de una manera integradora por parte del profesorado de ambas materias. Desde el punto de vista de la docencia de la economía, se considera que este tipo de planteamientos facilitaría la transferencia de los conocimientos de matemáticas al ámbito de la modelización económica, lo que resulta especialmente relevante en relación con la finalidad propedéutica del Bachillerato. Desde el de la docencia de las matemáticas, tanto la investigación relacionada con su didáctica como el propio currículo de la materia para la Educación Secundaria Obligatoria (ESO) y el Bachillerato, reflejan la importancia de incluir la modelización, no sólo por su interés como contenido, sino también por su función vehicular en tanto que facilitadora del aprendizajede los conceptos matemáticos. ABSTRACT.The paper describes a virtual learning object (VLO) built under an interdisciplinary perspective integrating Economíaand Matemáticas aplicadas a las Ciencias Sociales, which are both subjects within the Humanidades y Ciencias Socialesarea in Bachillerato. Such VLO is created out of a sequence of applications designed in the software Geogebra and organized around the mathematical concept of the derivative function and its role as an essential tool in economic modelling (mainly linked to what is usually known asmarginal analysis). The proposal aims to exemplify a set of materials and activities that could be designed and used in an integrated way by teachers of both subjects. From the viewpoint of teaching Economía, this type of approaches may facilitate the transfer of mathematical knowledge to the field of economic modelling, which is especially relevant when taking into consideration the propaedeutic purpose of Bachillerato. Concerning the teaching in Matemáticas, research on its didactics as well as thecurriculum content for the Educación Secundaria Obligatoria (ESO)and Bachilleratohighlight the dual goal of developing students? modelling competency and enhancing their learning of the mathematical concepts involved.
- Published
- 2021
9. A reverse Hardy–Hilbert-type integral inequality involving one derivative function
- Author
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Bicheng Yang and Qian Chen
- Subjects
Reverse ,Pure mathematics ,Inequality ,Parameter ,media_common.quotation_subject ,02 engineering and technology ,Type (model theory) ,01 natural sciences ,Beta function ,symbols.namesake ,0202 electrical engineering, electronic engineering, information engineering ,Hardy–Hilbert-type integral inequality ,Discrete Mathematics and Combinatorics ,Derivative function ,0101 mathematics ,Mathematics ,media_common ,Real analysis ,lcsh:Mathematics ,Applied Mathematics ,010102 general mathematics ,020206 networking & telecommunications ,lcsh:QA1-939 ,Constant factor ,Weight function ,Kernel (statistics) ,symbols ,Analysis - Abstract
In this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.
- Published
- 2020
10. UNDESIRABLE CONSEQUENCES OF NEGLECTING NONLINEARITY: RESPONSE TO COMMENTS BY LIEFTING ET AL. (2013) ON ROCHA & KLACZKO (2012).
- Author
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Rocha, Felipe Bastos and Klaczko, Louis Bernard
- Subjects
- *
DROSOPHILA development , *LATITUDE variation , *PHENOTYPIC plasticity , *QUADRATIC forms , *STATISTICAL correlation - Abstract
In response to our previous study, Liefting et al. argue, in defense of their work on latitudinal variation of developmental-rate reaction norms (RNs), that (1) developmental rate (the reciprocal of development time: rate = time−1) is a more biologically relevant variable than development time; (2) the linear RN model is a valid approximation; and (3) three experimental points suffice to estimate RN parameters. Here, we reply to their comments. First, we give evidence that the complexity of actual development challenges the appealing simplicity of developmental rate. Using the same analysis as Liefting et al. to test their hypothesis with development time, instead of rate, reveals a pattern that is the opposite of their conclusion. Second, we show that a quadratic model is consistent with the whole development-time RNs and explains this contradiction. Third, with the quadratic model, we introduce two parameters to study plasticity: the RN shape (the quadratic coefficient) and RN local plasticity (the derivative of the RN function). The first showed a statistically significant correlation with latitude; and the second showed a continuous variation pattern where all localized patterns can be found (positive, negative, or nonsignificant correlations with latitude) but certainly cannot be generalized. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
11. Solapamientos entre flexión y derivación: sobre la llamada derivación genérica en español
- Author
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Stehlík, Petr and Stehlík, Petr
- Abstract
This article discusses the possible derivative functioning of the vocalic morphemes -o and -a, traditionally considered as gender endings, but interpreted, in certain uses (from the gender inflection of animate nouns to the formation of deverbative nouns, such as gasto, paga), as derivative suffixes. Our objective is to demonstrate, through a detailed analysis of the different functions that can be performed by these morphemes in question, that the diversity of opinions about their inflectional or derivative nature reflects, in this case, the existence of a zone of transition between inflection and derivation, whose degrees we also attempt to determine., Este artigo ocupa-se do possível funcionamento derivativo dos morfemas vocálicos -o e -a, tradicionalmente considerados como desinências de gênero, mas interpretados, em determinados usos (desde a flexão de gênero nos nomes animados até a formação de substantivos deverbais do tipo gasto, paga) como sufixos derivativos. O nosso objetivo é demonstrar, através de uma análise detalhada das diferentes funções que os morfemas em questão podem desempenhar, que a diversidade de opiniões acerca do seu caráter flexivo ou derivativo reflete, neste caso, a existência de uma zona de transição entre a flexão e a derivação, cujos graus também tentamos determinar., El presente artículo se ocupa del posible funcionamiento derivativo de los morfemas vocálicos -o y -a, considerados tradicionalmente como desinencias de género, pero interpretados, en determinados usos (desde la moción de género en los nombres animados hasta la formación de sustantivos deverbales del tipo gasto, paga), como sufijos derivativos. Nuestro objetivo es demostrar, a través de un análisis detallado de las diferentes funciones que pueden desempeñar los morfemas en cuestión, que la diversidad de opiniones acerca de su carácter flexivo o derivativo refleja, en este caso, la existencia de una zona de transición entre la flexión y la derivación, cuyos grados igualmente tratamos de determinar.
- Published
- 2018
12. Graphical Understanding in Mathematics Education: Derivative Functions and Students’ Difficulties
- Author
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Nevin Orhun, Isman, A, Anadolu Üniversitesi, Fen Fakültesi, Matematik Bölümü, and Orhun, Nevin
- Subjects
Effective Teaching ,Derivative Function ,Computer science ,ComputingMilieux_COMPUTERSANDEDUCATION ,Mathematics education ,Graph of a function ,Language of mathematics ,General Materials Science ,Derivative ,Function ,Graph ,Graph of Derived Function - Abstract
3rd International Conference on New Horizons in Education (INTE) -- JUN 05-07, 2012 -- Prague, CZECH REPUBLIC, WOS: 000313019500082, Effective teaching is one of the most important factors to improve students' achievement. Therefore, many researchers in mathematics education are looking for several ways to improve the quality of learning. The purpose of this paper is to investigate an overview of specific difficulties based on the graph of derived function, another words, how students find the connections between the graph of derived function and the some properties of the original function. The subjects were 102 high school students in grade 11. The study was conducted during the fall semester in two calculus classes. The data of the research has been collected from 5 diagnostic the graph of derived function involved the chance in slope, decreasing, increasing, a local maximum, a local minimum, the point of inflection. The questionnaires were designed to assess how well the students had learned procedures the connections between the graph of derived function and the some properties of original function. Each student was asked explain how you arrived at your answers. While working on the answers of the students, not only the accuracy of the students' answers was examined but also the methods were being analysed even if they were incorrect. The results indicated that the students find it difficult to make connections between the graph of derived function and the original function. Usually, they were to interpret the graph of derived function as the graph of function. The students did not use the mathematical language to describe the graph of derived function Effective teaching in calculus course should be informal, intuitive and conceptually based on graphs and functions in order to improve the quality of learning and develop the understanding of calculus concepts. Selection and/or peer-review under responsibility of The Association of Science, Education and Technology, Sakarya Univ, Istanbul Univ, Suleyman Sah Univ, Natl Pingtung Univ Sci & Technol, Natl Univ Tainan, Inst Politecnico Guarda, Turkish Online Journal Educ Technol, Egitim Teknolojileri Arastirmalari Dergisi, Ohio Univ, Cleveland State Univ, Governors State Univ, Near E Univ, Cyprus Int Univ, Natl Cent Univ, Assoc Sci, Educ & Technol, Online Journal New Horizons Educ
- Published
- 2012
13. Empirical likelihood based inference for the derivative of the nonparametric regression function
- Author
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Gengsheng Qin and Min Tsao
- Subjects
Statistics and Probability ,Asymptotic distribution ,empirical likelihood ,nonparametric regression function ,Nonparametric regression ,local linear fitting ,Empirical likelihood ,normal approximation ,Statistics ,derivative function ,Statistical inference ,Confidence distribution ,High Energy Physics::Experiment ,Bayesian linear regression ,Likelihood function ,CDF-based nonparametric confidence interval ,Mathematics - Abstract
We study statistical inference for the derivative of the nonparametric regression function using local linear model based empirical likelihood. We first derive a normal equation for the derivative through the local linear model and use this equation to construct an empirical likelihood for the derivative. We show that the limiting distribution of the empirical likelihood ratio is a scaled $\chi_1^2$ distribution rather than the usual (unscaled) $\chi_1^2$ distribution. We use this limiting distribution to construct pointwise confidence intervals for the derivative. Such empirical likelihood ratio confidence intervals are easier to obtain than the normal approximation based confidence intervals. A small simulation study also suggests that they are more accurate.
- Published
- 2005
14. Empirical Likelihood Based Inference for the Derivative of the Nonparametric Regression Function
- Author
-
Qin, Gengsheng and Tsao, Min
- Published
- 2005
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