Analysis of a fractal boundary: the graph of the Knopp function

A usual classification tool to study a fractal interface is the computation of its fractal dimension. But a recent method developed by Y. Heurteaux and S. Jaffard proposes to compute either weak and strong accessibility exponents or local Lp regularity exponents (the so-called p-exponent). These exponents describe locally the behavior of the interface. We apply this method to the graph of the Knopp function. The Knopp function itself has everywhere the same p-exponent. Nevertheless, using the characterization of the maxima and minima done by B. Dubuc and S. Dubuc, we will compute the p-exponent of the characteristic function of domain under the graph of F at each point (x,F(x)) and show that p-exponents, weak and strong accessibility exponents change from point to point. Furthermore we will derive a characterization of the local extrema of the function according to the values of these exponents

Concomitant Humanistic Dimensions in Welsh New Media Deployments

The following article is going to center around the implications of Welsh language revitalization—a very fascinating phenomenon that has received a great deal of insight and speculation over the last decades. As regards the methodology, it is going to make use of a qualitative study by having recourse to some interviews and emails carried out with some Welsh media experts in 2007 in the United Kingdom. A specific emphasis, however, will be placed on Tsunoda’s theory and Hughes’s assumptions that will attempt to confirm the points to be investigated. Finally, it will reveal the different concomitant humanistic benefits that have emerged as result of Welsh new media deployments

Investigating Motivation in Language Learning among University Students

Motivation, or the desire to learn, has been extensively studied for decades by many linguists and teachers because of its vast array of insights as far as language learning is concerned, and because of its acknowledgment as one of the most prominent factors in educational settings. In fact, we are living in an age where the desire to learn languages, and specifically English, has been pushed to its most explicit limit. In this article, I will talk about a study which I carried out with my third year students and which deals with some important aspects of SDT (The Self-Determination theory)- a theory that views motivation both intrinsically and extrinsically. Intrinsic motivation is a construct that reflects the human propensity to learn. However, extrinsic motivation is thought to reflect external control or self-regulation

Supporting English Language learners through technology

TEYL has taken on a new dimension recently, as it has become an issue of paramount importance. Indeed, it has become integrated in many university curricula and discussed in several academic institutions and circles. It should be noted, in this regard, that new technology has played a significant role in facilitating TEYL, especially when English language learners benefit from the rein-forcement of linguistic structures to express themselves through pictures, graphics, and from the use of new technology platforms. This paper is going to contextualize the use of technology in the digital era we are living in and then it is going to look at some aspects of its various uses among young learners and how it helps them cope with the changes and challenges of the 21st century

Regularity results for solutions of micropolar fluid equations in terms of the pressure

This paper is devoted to investigating regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. More precisely, we prove that the weak solution is regular on $(0, T]$ provided that either the norm $\left\Vert \pi \right\Vert _{L^{\alpha, \infty }(0, T;L^{\beta, \infty }(\mathbb{R}^{3}))}$ with $\frac{2}{\alpha }+ \frac{3}{\beta } = 2$ and \frac{3}{2} < \beta < \infty or $\left\Vert \nabla \pi \right\Vert _{L^{\alpha, \infty }(0, T;L^{\beta, \infty }(\mathbb{R} ^{3}))}$ with $\frac{2}{\alpha }+\frac{3}{\beta } = 3$ and 1 < \beta < \infty is sufficiently small

Étude du formalisme multifractal pour les fonctions

The aim of this thesis is the multifractal analysis of selfsimilar functions and the study of the validity of the multifractal formalism. First, we determine the exact pointwise Hölder regularity for functions such that locally the graph is roughly a contraction of the global graph, modulo an error; then we compute the Hausdorff dimensions of the sets of points which have the same Hölder exponent; and finally we verify the conjectures of Frish and Parisi and the one of Arneodo, Bacry and Muzy, which relate these dimensions to some averaged quantities extracted from the function. We study different types of selfsimilarities, and prove (by reformuling some times) that the wavelet analysis is a good tool to study the validity of these relations.L'objet de cette thèse est l'analyse multifractale des fonctions autosimilaires et l'étude de la validité du formalisme multifractal. Il s'agit d'abord de déterminer la régularité Hölderienne ponctuelle exacte pour des fonctions dont le graphe localement est grossièrement une contraction du graphe complet, à une fonction erreur près ; ensuite de calculer les dimensions de Hausdorff des ensembles de points où la fonction présente la même singularité; et enfin de vérifier les conjectures de Frish et Parisi et celle d'Arneodo, Bacry et Muzy, qui relient ces dimensions à des quantités moyennes extraites de la fonction. Nous étudions plusieurs types d'autosimilarités, et montrons (en reformulant parfois) que l'analyse par ondelettes permet d'étudier la validité de ces relations

Das walisische Beispiel

The topic of my dissertation is about the appropriation of new technology for the revitalization of the Welsh language—a Celtic and minority language that has undergone many historical developments in the course of time. When a language declines, humanity loses linguistic and cultural knowledge about minorities or people. In the first part of my work, I have introduced the topic along with the major points to be explored. There are three major hypotheses to be checked. First, technology plays a big role in Welsh language revitalization. Second, technology facilitates the use of the language in daily life. Third, pedagogical implications can be drawn if technological devices are put into practice. The second part is concerned with language endangerment and language revitalization. Here, the causes of language loss and the techniques of language modernization are explored. In the third part of my dissertation, I have concentrated on Celtic languages and revealed many standpoints pertaining to Celtic Englishes. The fourth part gives an introduction into minority languages spoken in the United Kingdom. Moreover, it explains the position of Welsh and tries to describe it in a larger frame. In the fifth section, I have explained specific aspects that relate to Welsh language planning and described some measures of family language transmission along with education. In the sixth part, I have spoken about the development of new technology and explored recent issues about minority language media. In the seventh part, I have analyzed methods of language revitalization programs from different parts of the world. The eight part of my work is concerned with the diverse technological media that the Welsh minority has appropriated to modernize its language. In the ninth part, I have analyzed the data collected about the participants to understand the use of technological tools by the Welsh community. In the tenth section, I have assessed the Welsh language revitalization programs with the help of three models proposed by Giles, Fishman, and Tsunoda and attempted to visualize the new media outcomes in economic, linguistic, and symbolic terms. Besides, I have confirmed my three hypotheses. As a conclusion, I have shown that my dissertation is in itself comprehensive because of the various insights it reveals. The hypotheses tested, the abundance of technological tools, and the personal interviews conducted during my visit to Wales give my work a special dimension, which shows its concrete value and unique contribution. My study also opens up avenues on many interdisciplinary fields that involve translation studies, distance teaching, computational linguistics, as well as postmodern culture. Research still needs to be developed in these fields in connection with technology and minority languages to fully optimize the insights into the scope of language modernization.Das Thema meiner Dissertation ist die Bereitstellung der Technologie für die Revitalisierung der Walisischen Sprache—eine Keltische und Minderheitssprache, die verschiedene historische Entwicklungen im Laufe der Zeit erlebt hat. Wenn eine Sprache stirbt, weil sie nicht mehr gesprochen und benutzt wird, die Menschheit damit nicht nur linguistisches Wissen verliert, sondern auch kulturelle Kenntnisse über bestimmte Minoritäten oder Menschen. Im ersten Teil meiner Arbeit habe ich mein Thema eingeführt, indem ich die wichtigsten Aspekte erwähnt habe. Es gibt drei kapitale Hypothesen. Erstens, die Technologie spielt eine grosse Rolle bei der Revitalisierung der Walisischen Sprache. Zweitens, die Technologie erleichtert den Gebrauch der Sprache im täglichen Leben. Drittens, man kann pädagogische Schlussfolgerungen ziehen, wenn die technologischen Geräte für Walisisch bereitgestellt werden. Der zweite Teil beschäftigte sich mit dem Thema Language Endangerment and Language Revitalization. Hier werden die Gründe für Sprachbedrohung und Methoden für Belebung von Minderheitssprachen erklärt. Im dritten Teil habe ich mich auf die Keltischen Sprachen konzentriert und über Celtic Englishes gesprochen. Das vierte Kapitel meiner Dissertation gibt eine Einführung in die Minderheitssprachen, die in dem Vereinigten Königsreich gesprochen werden. Ausserdem habe ich die Position vom Walisisch erklärt und versucht diese Sprache in einem grossen Rahmen zu beschreiben. Im fünften Teil habe ich über Sprachplanung in Wales gesprochen und Massnahmen von Sprachtransmission in der Familie und Bildung beschrieben. Im sechsten Teil habe ich über die Entwicklung der neuen Technologie und Themen über Medien für Minderheitssprachen gesprochen. Im siebten Teil habe ich Revitalisierungsmethoden aus verschiedenen Orten der Welt analysiert. Der achte Teil beschäftigte sich mit den technologischen Medien, die die Walisische Gesellschaft bereitgestellt hat, um ihre Minderheitssprache zu revitalisieren und modernisieren. Im neunten Teil habe ich die Antworten der Teilnehmer im Online-Fragenbogen analysiert, um den Gebrauch der Walisischen technologischen Geräte zu verstehen. Im zehnten Teil meiner Dissertation habe ich die Programme bewertet anhand von Modellen von Giles, Fishman, und Tsunoda. Ich habe auch versucht, die ökonomischen, linguistischen, symbolischen Beiträge der neuen Medien zu zeigen. Die bestätigten Hypothesen, die Reihe von technologischen Begriffen, und die in Wales gemachten Gespräche geben meine These eine besondere Dimension—eine Dimension, die den konkreten Wert meines innovativen Beitrages reflektiert. Forschung wird noch benötigt in den Bereichen von Distance Teaching, Computational Linguistics, und Translation Studies in Verbindung mit Minderheitssprachen und Technologie, damit man eine umfangreiche Idee haben kann über das grosse Spektrum der Sprachrevitalisierung und deren verschiedene Aspekte

Pointwise Rectangular Lipschitz Regularities for Fractional Brownian Sheets and Some Sierpinski Selfsimilar Functions

We consider pointwise rectangular Lipschitz regularity and pointwise level coordinate axes Lipschitz regularities for continuous functions f on the unit cube I 2 in R 2 . Firstly, we provide characterizations by simple estimates on the decay rate of the coefficients (resp. leaders) of the expansion of f in the rectangular Schauder system, near the point considered. We deduce that pointwise rectangular Lipschitz regularity yields pointwise level coordinate axes Lipschitz regularities. As an application, we refine earlier results in Ayache et al. (Drap brownien fractionnaire. Potential Anal. 2002, 17, 31&ndash;43) and Kamont (On the fractional anisotropic Wiener field. Probab. Math. Statist. 1996, 16, 85&ndash;98), where uniform rectangular Lipschitz regularity of the trajectories of the fractional Brownian sheet over the total I 2 (or any cube) was considered. Actually, we prove that fractional Brownian sheets are pointwise rectangular and level coordinate axes monofractal. On the opposite, we construct a class of Sierpinski selfsimilar functions that are pointwise rectangular and level coordinate axes multifractal