Hybrid resonance and long-time asymptotic of the solution to Maxwell's equations

We study the long-time asymptotic of the solutions to Maxwell's equation in the case of a upper-hybrid resonance in the cold plasma model. We base our analysis in the transfer to the time domain of the recent results of B. Despr\'es, L.M. Imbert-G\'erard and R. Weder, J. Math. Pures Appl. {\bf 101} ( 2014) 623-659, where the singular solutions to Maxwell's equations in the frequency domain were constructed by means of a limiting absorption principle and a formula for the heating of the plasma in the limit of vanishing collision frequency was obtained. Currently there is considerable interest in these problems, in particular, because upper-hybrid resonances are a possible scenario for the heating of plasmas, and since they can be a model for the diagnostics involving wave scattering in plasmas.Comment: This published version has been edited to improve the presentation of the result

Computation of sum of squares polynomials from data points

We propose an iterative algorithm for the numerical computation of sums of squares of polynomials approximating given data at prescribed interpolation points. The method is based on the definition of a convex functional $G$ arising from the dualization of a quadratic regression over the Cholesky factors of the sum of squares decomposition. In order to justify the construction, the domain of $G$, the boundary of the domain and the behavior at infinity are analyzed in details. When the data interpolate a positive univariate polynomial, we show that in the context of the Lukacs sum of squares representation, $G$ is coercive and strictly convex which yields a unique critical point and a corresponding decomposition in sum of squares. For multivariate polynomials which admit a decomposition in sum of squares and up to a small perturbation of size $\varepsilon$, $G^\varepsilon$ is always coercive and so it minimum yields an approximate decomposition in sum of squares. Various unconstrained descent algorithms are proposed to minimize $G$. Numerical examples are provided, for univariate and bivariate polynomials

Convergence for PDEs with an arbitrary odd order spatial derivative term

We compute the rate of convergence of forward, backward and central finite difference $\theta$-schemes for linear PDEs with an arbitrary odd order spatial derivative term. We prove convergence of the first or second order for smooth and less smooth initial data

Hybrid resonance of Maxwell's equations in slab geometry

Hybrid resonance is a physical mechanism for the heating of a magnetic plasma. In our context hybrid resonance is a solution of the time harmonic Maxwell's equations with smooth coefficients, where the dielectric tensor is a non diagonal hermitian matrix. The main part of this work is dedicated to the construction and analysis of a mathematical solution of the hybrid resonance with the limit absorption principle. We prove that the limit solution is singular: it is constituted of a Dirac mass at the origin plus a principle value and a smooth square integrable function. The formula obtained for the plasma heating is directly related to the singularity.Comment: This published version has been edited to improve the presentation of the result

Quelques aspects du débat sur la traduction littéraire à Moscou au début du XIXème siècle

At the beginning of the XIXth century, the translations of the English or German poets by Joukovski, or Greek and Latin by professor Merzliakov, the Fables of Krylov translated from La Fontaine (etc.) are considered as literary works, the name of the translator has so much importance, otherwise more, as that of the author of the original. The debate which bursts into 1816 about two translations of Bürger's Leonora, that of Zhukovski and that of Katenin, revealed clearly that they are considered as representative works of the poetic system of each of the writers - translators. Ludmila, of Zhukovski, is a ballad in the style of the karamzinien pre-romanticism. The style of Zhukovski is smooth and without harshness, the tone is meditative. On the contrary, the translation of Katenine, Olga, highlights the possibilities of the Russian language and mix registers by using the words of folk popular, as on the slavonismes of the highest "style". A deep change occurs in the Russian educated society in the middle of the twenties of the XIXth century. The translator - Poet becomes a scientist who must respect the author of the original, according to the spirit of the romanticism and the myth of the genius- prophet. Then he becomes a popularizer, who has to be accountable to the reader, or rather to the critic, who monopolizes, in the name of the mass of the readers, the monopoly of the esthetic sense what lets anticipate the advent of critical realism

Finite Volume Transport Schemes

We analyze arbitrary order linear nite volume transport schemes and show asymptotic stability in L1 and L1 for odd order schemes in dimen- sion one. It gives sharp fractional order estimates of convergence for BV solutions. It shows odd order nite volume advection schemes are better than even order nite volume schemes. Therefore the Gibbs phenomena is controled for odd order nite volume schemes. Numerical experiments sustain the theoretical analysis. In particular the oscillations of the Lax- Wendro scheme for small Courant numbers are correlated with its non stability in L1. A scheme of order three is proved to be stable in L1 and L1

La Russie comme expérience de vie et d'écriture.: Le Journal d'un loup de Mariusz Wilk(trad. Laurence Dyèvre, Noir sur Blanc, 1999)

Mariusz Wilk is a Polish prose-writer, who travels to the remote north of Russia. His firstbook, The journals of a White Sea wolf reveals his originality. He tries to delve into the mysteriesof the ‘Russian soul’ and history, for that he chooses to blend in with local life. That is why hesettled in a faraway, but representative place, the Solovetsky Islands. He writes of the ordinaryfolk he meets on a daily basis. He discovers a world marked by the ruins of the Soviet prisonsystem, but also by the secular presence of the monastery. In his notes, Wilk stops on somedetails with strong metaphorical potential. Finally, he writes of himself as a writer and a traveler.For in his writing and his travels, Wilk’s main aim is to find himself, to understand who he is, tothink about writing that allows self-transcendence, about the language and about the specificityof each word, with its emotional and symbolic charge. The journals of a White Sea wolf is atestimony on past and today’s Russia, a reflection on practice and literary genre of travel prose.Mariusz Wilk est un auteur polonais qui voyage dans la Russie du grand Nord. Son premierouvrage, le Journal d’un loup, révèle l’originalité de son regard. Wilk cherche à découvrir laRussie en profondeur, en choisissant de se fondre dans la vie locale. Pour cela il s’installe dansles îles Solovki, un lieu excentré, mais représentatif à ses yeux, de l’histoire et de la mentalitérusses. Il y découvre un monde en sursis, marqué par les ruines du système pénitentiairesoviétique, mais aussi par la présence séculaire du monastère. Dans ses notes, Wilk s’arrête surcertains détails à forte potentialité métaphorique. Enfin, il se livre à une auto-réflexion sur sondouble statut d’écrivain et d’étranger, sur l’écriture qui permet le dépassement de soi, sur lalangue et le mot, avec sa charge émotive et symbolique. Le Journal d'un loup est autant untémoignage sur la Russie d'hier et d'aujourd'hui, qu'une réflexion sur la pratique et sur l'écriturelittéraire du voyage

Paroles étranges : De l'École des idiots à La prise d'Izmail.

In this paper we compare two Russian postmodernists novels, A School for Fools, Sacha Sokolov, andThe Taking of Izmail, Mikhail Shishkin. We try to show that the first one can be considered as acontinuum with the experiments of Futurists on the word and on the time. We study alliteration, writinggames, anagrams , alterations of words. The disappearance of paragraphs and punctuation suggests thattext lets place to a stammering . We see that the sounds and rhythms take over the logical relationshipsbetween words. The text imitates music. Shishkin 's novel is very dense and contains heterogeneouswords , direct or veiled quotations from authors of all countries and of all times ( Russian classics , Greek,Latin , Slavonic texts ...) . But it also contains an infinite number of details about the life and men .Everything is intertwined, giving an almost autonomous existence to words, and conjuring the reality towhich they relate .L’article compare deux romans postmodernistes russes, L'École des idiots, de Sacha Sokolov, et La Prised’Izmail de Mikhail Chichkine. Le premier est considéré dans sa continuité avec les expériences desfuturistes sur le mot et sur le temps. On étudie les allitérations, les jeux d’écriture, les anagrammes, lesaltérations de mots. La disparition des paragraphes et de la ponctuation suggère que la parole setransforme par endroits en un balbutiement. On constate que les sons et les rythmes prennent le dessus surles rapports logiques entre les mots. L’écriture imite la musique. Le roman de Chichkine est dense deparoles hétérogènes, de citations directes ou voilées d’auteurs de tous les pays et de toutes les époques(classiques russes, grecs, latins, textes slavons...). Mais il contient aussi une infinité de détails sur la vie etsur les hommes. Le tout est savamment entremêlé, donnant une existence quasi autonome aux mots, etconjurant la réalité auxquels ils se rapportent.В статье сравниваются два российских постмодернистских романа, Школа для дураков СашиСоколова, и Взятие Измаила Михаила Шишкина. Первый рассматривается как продолжениеэкспериментов футуристов над словом и временем. Изучаются аллитерации, словесные игры ,анаграммы , изменения слов. Исчезновение абзацев и пунктуации создаёт иллюзию, что текстместами превращается в лепет и щебетание. Звуки и ритмы берут верх над логическимиотношениями между словами. Текст имитирует музыку. Роман Шишкина отличается большойплотностью и наличием разнородных стилей, прямых или завуалированных цитат авторов всехстран и всех времен ( Русская классика , греческие, латинские авторы , славянский текст ...) . Но онтакже содержит огромное количество деталей о жизни и людей. Всё переплетается так, что словастановятся почти автономными, и реальность, к которой они относятся, обезвреживается

L'enseignement public de la philosophie au Québec depuis trente-cinq ans /

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