1,170 research outputs found
Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point, II -- Its relevance to the Mathieu equation and the Legendre equation
No full textWe develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation
Analysis of Mathieu Equation Stable Solutions in the First Zone of Stability
No full textAbstractThe paper presents the results of a homogeneous Mathieu equation studies. Mathieu equation solutions are oscillations, modulated in amplitude and frequency. In the computational experiments we found dependences of the given oscillations on the ratio of the coefficients. These dependences are shown in graphs that can be used for an approximate estimation of the Mathieu equation solutions without integration
Legendre approximation-based stability test for distributed delay systems
No full textInternational audienceThis contribution presents an exponential stability criterion for linear systems with multiple pointwise and distributed delays. This result is obtained in the Lyapunov-Krasovskii framework via the approximations of the argument of the functional by projection on the first Legendre polynomials. The reduction of the number of mathematical operations in the stability test is a benefit of the supergeometric convergence of Legendre polynomials approximation. For a single-delay linear system with a constant distributed kernel, a new computational procedure for the solution of the integrals involved in the stability test is developed considering the case of Jordan nilpotent blocks. This strategy is the basis for developing new procedures that allow the numerical construction of the stability test for different classes of kernels, such as polynomial, exponential, or γ distribution.</div
Pensar las escalas para pensar las luchas: Autor: Mathieu UHEL
No full textA través de un título sugerente, “pensar las escalas para pensar las luchas”, Mathieu Uhel entreteje la construcción teórico-crítica del concepto escala, generada por la geografía radical anglosajona de finales del siglo XX, con la necesidad/utilidad práctica de la escala para concienciar las luchas sociales. El artículo cumple un doble propósito: por un lado, delinear los elementos de lectura sobre el concepto escala; y, con ello, promover la atención de esta problemática en las luchas contemporáneas. En un primer apartado, Uhel ubica las discusiones académicas en torno a la escala, como herramienta metodológica útil para comprender la complejidad de las sociedades capitalistas; en el segundo apartado, el autor avanza la exposición en torno al contexto de la dimensión escalar del imperialismo capitalista; finalmente, el autor se centra en el rol de la actividad política a escala nacional en la tensa relación entre las imposiciones del capital y la lucha social.Por meio de um título sugestivo, “pensando escalas para pensar lutas”, Mathieu Uhel entrelaça a construção teórico-crítica do conceito de escala, gerado pela geografia radical anglo-saxônica do final do século XX, com a necessidade / utilidade prática escala para aumentar a consciência das lutas sociais. O artigo tem um duplo propósito: por um lado, delinear os elementos de leitura sobre o conceito de escala; e, com isso, promover atenção a esse problema nas lutas contemporâneas. Na primeira seção, Uhel localiza as discussões acadêmicas em torno da escala, como uma ferramenta metodológica útil para compreender a complexidade das sociedades capitalistas; na segunda seção, o autor avança a exposição em torno do contexto da dimensão escalar do imperialismo capitalista; por fim, o autor enfoca o papel da atividade política em escala nacional na tensa relação entre as imposições do capital e a luta social.Mathieu Uhel\u27s suggestive title, “Thinking about scales to think about struggles”, he interweaves the theoretical-critical construction of concept scale, generated by radical Anglo-Saxon geography in the late 20th century, with it´s practical utility to social struggles. The article serves two purposes: on the one hand, Uhel locates academic discussion around scale; and, with this, he promotes attention to this problem in contemporary struggles. In the first section, Uhel locates academic discussions around scale, as a useful methodological tool to understand the complexity of capitalist societies; in the second section, the author advances the argument around the context of the scalar dimension of capitalist imperialism; finally, the author focuses on the role of political activity on a national scale in the tense relationship between the impositions of capital and the social movement
Studies in the associated Mathieu equation and the spheroidal wave equation.
No full textThis thesis consists of two largely independent parts. Part I is a discussion of Campbell's work on the Associated Mathieu equation. This equation is a transformation of the spheroidal wave equation and it was to he expected that many of Campbell's results had their counterparts in the theory of spheroidal wave functions. This thesis examines Campbell's work, relates it to the latter theory, completes and corrects it at certain points. In particular, it is shown that Campbell's "finite solution" of the Associated Mathieu equation is erroneous. Part II is devoted to a study of the spheroidal wave equation in the case when the characteristic exponent is half an odd integen The standard method of construction of solutions as series of Legendre or Bessel functions, breaks down completely in this case. After a study of the form of the eigen value A , it is shown that the series of Legendre (or Bessel) functions is supplemented by a series involving derivatives of such functions with respect to the order. The corresponding second solution, and some special cases, are also considered
Studies in the associated Mathieu equation and the spheroidal wave equation.
No full textThis thesis consists of two largely independent parts. Part I is a discussion of Campbell's work on the Associated Mathieu equation. This equation is a transformation of the spheroidal wave equation and it was to he expected that many of Campbell's results had their counterparts in the theory of spheroidal wave functions. This thesis examines Campbell's work, relates it to the latter theory, completes and corrects it at certain points. In particular, it is shown that Campbell's "finite solution" of the Associated Mathieu equation is erroneous. Part II is devoted to a study of the spheroidal wave equation in the case when the characteristic exponent is half an odd integen The standard method of construction of solutions as series of Legendre or Bessel functions, breaks down completely in this case. After a study of the form of the eigen value A , it is shown that the series of Legendre (or Bessel) functions is supplemented by a series involving derivatives of such functions with respect to the order. The corresponding second solution, and some special cases, are also considered
Poétiques du récit de retour aux origines : du documentaire au roman ; et, Je t'envoie des photos des primevères dans le sable
No full textThèse en recherche-création
Cotutelle avec l'Université de Lorraine, Nancy, FranceCette thèse porte sur le récit de retour aux origines dans la littérature contemporaine française et se concentre sur des auteurs transclasses, c’est-à-dire qui ont quitté leur milieu d’origine et changé de statut social. Elle s’intéresse spécifiquement à un corpus d’auteurs originaires de régions non attractives de l’Hexagone. Elle concentre son analyse sur des textes de Nicolas Mathieu, Annie Ernaux, Didier Eribon, Édouard Louis et Raymond Depardon. Ce travail détermine d’abord ce qui est entendu par « récit de retour » en littérature, notamment lorsqu’il s’agit de représenter les campagnes qui intéressent ces auteurs. Il dégage des poétiques du retour chez chacun de ces auteurs, en observant l’hybridité générique qui les traverse : la photobiographie et le documentaire avec Depardon, le roman avec Ernaux et Mathieu, l’autobiographie avec Louis, l’essai avec Eribon. Dans un second temps, la thèse examine la temporalité et la géographie du retour, en particulier les motifs de la nostalgie et du déplacement. La thèse explore ensuite le point de vue de l’auteur, narrateur ou personnage transclasse sur son milieu d’origine, point de vue tantôt décalé, renouvelé ou surplombant. À cette recherche succède un texte de création, Je t’envoie des photos des primevères dans le sable, qui allie, en deux temps, fiction et enquête photolittéraire et qui questionne lui aussi le geste de retour aux origines en milieu rural.This thesis focuses on the return to origins in contemporary French narratives. It examines the works of authors who left their hometown or their village and experienced social mobility. It specifically investigates the works of authors who come from post-industrial and non-touristy areas in France: Nicolas Mathieu, Annie Ernaux, Didier Eribon, Édouard Louis and Raymond Depardon. First, this work analyzes what the notion of return in literature implies, especially when French rural life is represented. The study aims to define a poetics of return for each of these texts, focusing on how these books are multi-genre or genre-bending: photobiography and documentary with Depardon, fiction with Ernaux and Mathieu, autobiography with Louis, essay with Eribon. In a second part, we examine the temporality and the geography of return, in particular nostalgia and displacement. This thesis also explores the author, narrator or character’s point of view on their background, as someone who left and changed their social status: the final chapter analyzes how this point of view has shifted, how it is renewed, but also how it can present itself as distant and apart. A creative text follows this research: titled I am sending you pictures of the primroses in the sand, it brings fiction and documentary (which includes photographs) together and reflects on the return gesture within rural areas
Frequency delay-dependent stability criterion for time-delay systems thanks to Fourier-Legendre remainders
No full textInternational audienceThis paper investigates the stability of a linear finite-dimensional system interconnected to a single delay operator. From robust approaches, to derive delay-dependent frequency tests, a characterization of the delay behavior is required. Based on approximation methods, one describes the transported signal by lumped parameters. More precisely, by the use of the first Fourier-Legendre polynomials coefficients, we split the delay block into a finitedimensional part interconnected to a specific infinite-dimensional residual part. Two models are investigated with residuals related to two Fourier-Legendre remainders of the delayed transfer function. The main contribution is to highlight that the finite-dimensional models based on the first Legendre coefficients are proven to be related to Padé approximations and are recognized to be more and more accurate as the dimension increases. Interestingly, this modeling allows computing in an accurate manner the root locus of time-delay systems. Furthermore, as a by-product of this result, taking into account the infinite-dimensional remainders to keep track of the initial time-delay system, stability criteria are proposed by H∞ analysis. Considering both infinite-dimensional remainders as bounded delay-free uncertainties, the small-gain theorem provides a new sufficient condition of stability for retarded time-delay systems, which can be implemented as a delay-dependent frequency-sweeping test. Our results are illustrated on several academic examples
Necessary and sufficient stability condition for time-delay systems arising from Legendre approximation
No full textRecently, sufficient conditions of stability or instability for time-delay
systems have been proven to be necessary. In this way, a remarkable necessary
and sufficient condition has then been developed by Gomez et al. It is
presented as a simple test of positive definiteness of a matrix issued from the
Lyapunov matrix. In this paper, an extension of this result is presented.
Without going into details, the uniform discretization of the state has been
replaced by projections on the first Legendre polynomials. Like Gomez et al.,
based on convergence arguments, the necessity is obtained in finite order,
which can be calculated analytically. Compared to them, by relying on the fast
convergence rate of Legendre approximation, the required order to ensure
stability has been reduced. Thanks to this major modification, as shown in the
example section, it is possible the find stable regions for low orders and
unstable ones for even smaller orders
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