Théorie locale et comportement en long temps des solutions des équations de Schrödinger non linéaires

Notre recherche principale est d'étudier les équations de Schrödinger non linéaires, en particulier les équations de Schrödinger non linéaires dérivées. Notre premier objectif est de répondre aux questions sur l'existence et l'unicité des solutions, de considérer si le temps d'existence est fini ou infini et de vérifier si les solutions dépendent continuellement des données initiales ou non. Lorsque des solutions existent, nous étudions le comportement des solutions à des temps grands, en répondant à des questions sur la stabilité et l'instabilité des solitons/ondes stationnaires algébriques/ondes périodiques, l'existence de solutions d'explosion, l'existence de trains multi-solitons, et l'existence de trains multi kink-solitons. Le problème de Cauchy des équations de Schrödinger non linéaires dérivées a été traité plusieurs fois dans l'espace de Sobolev H^1(R). Le premier objectif principal est d'établir une théorie locale avec des conditions aux limites non nulles. Nous utilisons une méthode de transformation de jauge pour transférer l'équation d'origine dans un système sans termes dérivés. En étudiant le problème de Cauchy de ce système, on obtient les résultats pour l'équation originale. Ensuite, nous considérons l'équation de Schrodinger non linéaire avec des non-linéarités dérivées dans le cas d'une demi-droite avec une condition aux limites de Robin. Nous prouvons l'existence de solutions d'explosion. De plus, nous prouvons que l'équation admet des solutions particulières appelées ondes stationnaires. Cette solution est un minimiseur d'un problème variationnel. Nous prouvons la stabilité et l'instabilité de ce type de solution en fonction du signe du paramètre de condition de Robin donné. Ensuite, nous étudions la théorie multi solitons des équations de Schrödinger non linéaires dérivées. L'existence de ce type de solution montre qu'il existe une solution globale avec un nombre arbitraire de données initiales. La méthode utilisée pour les équations de Schrödinger non linéaires classiques ne peut pas s'appliquer dans ce cas aux non linéarités dérivées. Nous profitons de la transformation de jauge pour surmonter cette difficulté. Enfin, nous considérons l'équation de Schrödinger non linéaire à puissance triple. Notre objectif est de prouver l'instabilité des ondes stationnaires algébriques, c'est-à-dire les ondes stationnaires de fréquence nulle. Notre motivation vient des travaux de Liu-Tsai-Zwiers où les auteurs ont donné une image de la stabilité et de l'instabilité des ondes stationnaires de triple puissance NLS en une dimension et des travaux de Fukaya-Hayashi où les auteurs ont démontré l'instabilité des ondes algébriques ondes dans le cas d'un NLS à double puissance.Our main research is to study nonlinear Schrodinger equations, especially derivative nonlinear Schrödinger equations. Our first goal is to answer questions about the existence and uniqueness of solutions, considering whether the time of existence is finite or infinite and checking whether solutions depend continuously on initial data or not. When solutions exist, we study the behaviour of solutions at large times, answering questions about stability and instability of solitons/algebraic standing waves/periodic waves, the existence of blow-up solutions, the existence of multi-soliton trains, and the existence of multi kink-soliton trains. The Cauchy problem of the derivative nonlinear Schrodinger equations was treated many in the Sobolev space H^1(R). The first main goal is to establish local theory with nonvanishing boundary conditions. We use a Gauge transform method to transfer the original equation into a system without derivative terms. By studying the Cauchy problem of this system, we obtain the results for the original equation. Next, we consider the nonlinear Schrodinger equation with derivative nonlinearities in half-line case with Robin boundary condition. We prove the existence of blow-up solutions. Moreover, we prove that the equation admits the special solutions which are called standing waves. This solution is a minimizer of a variational problem. We prove the stability and instability of this kind of solution depending on the sign of the given Robin condition parameter. Next, we investigate the multi solitons theory of derivative nonlinear Schrodinger equations. The existence of this kind of solution shows that there exists a global solution with an arbitrary large of initial data. The method used for classical nonlinear Schrodinger equations can not apply in this case with derivative nonlinearities. We take advantage of Gauge transform to overcome this difficulty. Finally, we consider the nonlinear Schrodinger equation with triple power. Our goal is to prove the instability of algebraic standing waves i.e the standing waves with zero frequency. Our motivation is from the work of Liu-Tsai-Zwiers where the authors gave a picture of the stability and instability of standing waves of triple power NLS in one dimension and the work of Fukaya-Hayashi where the authors proved the instability of algebraic waves in the case of double power NLS

Visual and Textual Analysis for Image Trustworthiness Assessment within Online News

The majority of news published online presents one or more images or videos, which make the news more easily consumed and therefore more attractive to huge audiences. As a consequence, news with catchy multimedia content can be spread and get viral extremely quickly. Unfortunately, the availability and sophistication of photo editing software are erasing the line between pristine and manipulated content. Given that images have the power of bias and influence the opinion and behavior of readers, the need of automatic techniques to assess the authenticity of images is straightforward. This paper aims at detecting images published within online news that have either been maliciously modified or that do not represent accurately the event the news is mentioning. The proposed approach composes image forensic algorithms for detecting image tampering, and textual analysis as a verifier of images that are misaligned to textual content. Furthermore, textual analysis can be considered as a complementary source of information supporting image forensics techniques when they falsely detect or falsely ignore image tampering due to heavy image postprocessing. The devised method is tested on three datasets. The performance on the first two shows interesting results, with F1-score generally higher than 75%. The third dataset has an exploratory intent; in fact, although showing that the methodology is not ready for completely unsupervised scenarios, it is possible to investigate possible problems and controversial cases that might arise in real-world scenarios

L’INITIATION EN SCIENCES EXPÉRIMENTALES À L’ÉDUCATION PRÉSCOLAIRE: PERSPECTIVES ÉPISTÉMOLOGIQUES

Dans cet article sont examinées les origines épistémologiques d’une initiation précoce des enfants d’âge préscolaire en sciences physiques et naturelles. En discutant le caractère des apprentissages scientifiques et le rôle du savoir scientifique dans l’éducation préscolaire a été approchée une série des conséquences éducatives, pédagogiques et didactiques. La dimension cruciale de cette approche reconnait qu’en âge préscolaire l’évolution des capacités de processus, liées au « faire », qui s’identifie à cet âge à des activités manuelles et corporelles, auront le dessus sur les activités conceptuelles. Elles constituent ainsi en un certain sens la base pour le développement de l’activité cognitive liée au développement de concepts empiriques concrets. The epistemological origins of early initiation of pre-schoolers in physical and natural sciences are discussed in this article. By examining the nature of scientific learning and the role of scientific knowledge in preschool education was approached a series of educational, pedagogical and didactic consequences. The crucial dimension of this approach recognizes that at pre-school age the evolution of process capabilities, related to 'do', identifying himself at that age to manual and corporeal activities, will have precedence over conceptual activities. They are thus in a certain sense the basis for the development of the cognitive activity related to the development of concrete empirical concepts.  Article visualizations

Lower and upper bound form for outage probability analysis in two-way of half-duplex relaying network under impact of direct link

In this paper, the system performance of the two-way of half-duplex (HD) relaying network under the impact of the direct link is studied. The model system has two sources (S) and one destination (D) communicate by direct link and via relay (R). For system performance analysis, we derived the lower and upper bound for outage probability (OP). Furthermore, the analytical expressions of the system performance are verified by using the Monte Carlo simulation in the effect of main parameters. As shown in the results, we can the simulation and analytical results have a good agreement

Performance analysis for three cases of outage probability in one-way DF full-duplex relaying network with presence of direct link

In this paper, the one-way decode-and-forward (DF) full-duplex relaying network system with presence of direct link is investigated. In the analysis section, we derived the exact, lower, and upper bound for outage probability (OP) with maximal ratio combining (MRC) at the receiver. Furthermore, the system performance's analytical expressions are verified by using the Monte Carlo simulation. In addition, we investigated the effect of the main parameters on the OP of the proposed system. Finally, we can sate that the simulation curves overlap the analytical curves to convince the analysis section. This research can provide a novel recommendation for the communication network

Lower and upper bound form of outage probability in one-way AF full-duplex relaying network under impact of direct link

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