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Item Open Access On n-Bounded and n-Continuous Operators in n-Normed space(University of Mohamed Boudiaf, M’sila, 2024-06) KECHIDA, Marwa; Supervisor: TALLAB, Abdelhamid; Co-supervisor: MAZOUZ, AhmedThis memory deals with the concepts of bounded(n-bounded) and continuous(n-continuous) n-linear operators in n-normed spaces introduced by. Also, we study the properties of the corresponding spaces of operators to obtain results analogous to the case of normed space, also we have studied other notions of continuity of these operators.Item Open Access Image Processing Based on Fractional Partial Differential Equations(Mohamed Boudiaf University of M'sila, 2024-06) MOUAFAK, AZEDINE; Supervisor: Chouder, RafaaThis work presents a fractional diffusion model, which modifies the Perona-Malik model by incorporating the Caputo-Fabrizio fractional gradient into the diffusivity function. A theoretical investigation was conducted to examine the existence and uniqueness of the solution. Additionally, we carried out a numerical study, enabling us to perform experiments that confirmed the model’s effectiveness in noise reduction and edge preservation. This also allowed us to compare our results with those of the classical Perona-Malik model.Item Open Access Application multivaluée compacte dans un espace de Banach(Mohamed Boudiaf University of M'sila, 2024-06-10) HERIZI, Ibtihal; Rapporteur: MAZOUZ, Ahmed; Co-superviseur: TALLAB, AbdelhamidDans cette note, nous avons étudié les applications multivaluées dans l’espace de Banach, ainsi que les relations linéaires démi-compactes, en donnant des examples.Item Open Access Application multivaluée compacte dans un espace de Banach(Mohamed Boudiaf University of M'sila, 2024) HERIZI, Ibtihal; MAZOUZ, Ahmed: Rapporteur; TALLAB, Abdelhamid: Co-superviseurDans cette note, nous avons étudié les applications multivaluées dans l’espace de Banach, ainsi que les relations linéaires démi-compactes, en donnant des exemples.Item Open Access Some weights of linear codes over finite fields(Mohamed Boudiaf University of M'sila, 2024-06-09) Benia, Nihal; LEBED, Khawla: SupervisorLinear codes can have different weights, which are measures of the distance between codewords. The most common weights are Hamming, Lee, and Distribution weights, in which Hamming and Lee weight counts the number of nonzero positions in a codeword, as they determine the error-correcting capability of the code. The weight distribution of a code, which specifies how many codewords have each possible weight, it can be used to compute the error probability of the code under various decoding algorithms. They are utilized in various applications within coding theory, and one of its most important uses is detecting and correcting errors. In this work, we study some weights of linear codes over finite fields and their results.Item Open Access Résolution d’un problème d'optimisation quadratique sans contraintes(Mohamed Boudiaf University of M'sila, 2024-06) Abdelli, Samira; Saadi, Khalil: EncadreurL’objectif de ce mémoire est d’explorer en profondeur les techniques de résolution des problèmes d’optimisation quadratique sans contraintes, en analysant les principes théoriques ainsi que les aspects pratiques de leur mise en œuvre. Ce mémoire s’articule autour de trois chapitres : Chapitre 1 : Généralités et notions de bases. Chapitre 2 : Traitement analytique d’un problème d’optimisation quadratique sans contraintes. Chapitre 3 : Résolution numérique d’un problème d’optimisation quadratique sans contraintes.Item Open Access Radial Basis Function approximations for partial differential equations(Mohamed Boudiaf University of M'sila, 2024-06-11) BRIK, OSEMA; GAGUI, Bachir: SupervisorIn this work, we introduce the radial basis functions and their types, and we applied this technique to solve the Laplace, Poisson and telegraph equations, these solutions are approximates solutions.Item Open Access ON THE WEYL AND BROWDER THEOREMS OF BOUNDED LINEAR OPERATOR(Mohamed Boudiaf University of M'sila, 2024-06-10) Bouguerra, Malika; Toufik, HERAIZ: SupervisorThe Weyl and Browder theorems stand as pivotal landmarks in the realm of functional analysis, offering profound insights into the spectral behavior and structural properties of bounded linear operators. Pietro Aiena's seminal contributions have significantly enriched our understanding of these theorems, unraveling their intricate connections and extending their applicability to various classes of operators. In this research endeavor, we embark on a comprehensive exploration of Aiena's work, delving deep into the nuanced implications and far-reaching consequences of the Weyl and Browder theorems. Through a meticulous examination of Aiena's results, we elucidate the underlying principles governing the spectral decomposition, essential spectra, and related spectral properties of bounded linear operators. Moreover, we investigate the interplay between these theorems and other fundamental concepts in functional analysis, such as compact operators, spectral mapping theorems, and perturbation theory. By synthesizing Aiena's insights with contemporary developments in the field, we aim to provide a unified framework for understanding the spectral theory of bounded linear operators, with implications for diverse areas including operator theory, mathematical physics, and dynamical systems. Our research not only consolidates and extends Aiena's seminal contributions but also sheds light on new avenues for theoretical exploration and practical applications in functional analysis and its myriad interdisciplinary ramificationsItem Open Access On Spectral Theory of Ordinary Differential Operator Of Fractional Order(Mohamed Boudiaf University of M'sila, 2024-06-10) Lachache, Qamar; Toufik, HERAIZ: SupervisorFractional analysis is a branch of mathematical analysis which studies the possibility of defining noninteger powers of derivative and integrating operators. we define some useful functions such as Gamma function, Beta function and MittagLeffler function. These functions play a very important role in the theory of fractional order differential calculus. we will present the definition of a fractional derivative and then we study the three most popular approaches to fractional derivatives: the Grünwald-Letnikov, Riemann-Liouville and Caputo approaches as well as their properties. Finally, we study some examples of fractional derivatives. Keywords: Fractional derivation, Grünwald-Letnikov, Riemann-Liouville, Caputo. and operator theory to study the spectral properties (such as eigenvalues and eigenfunctions) of fractional differential operators.Item Open Access Approximation des équation et des inéquation de type monotone(Mohamed Boudiaf University of M'sila, 2024-06-10) Lachache, Sabrina; Chadi, Khlifa: EncadreurNotre objectif dans ce mémoire est d'approximer les équations et les inéquations monotones afin de trouver des solutions numériques pour des problèmes analytiquement complexes. Pour ce faire, il est souvent nécessaire de diviser l'espace ou le temps en parties finies, en plus d'utiliser des techniques d'approximation pour obtenir des solutions approchées. Cette approche explore diverses méthodes numériques, telles que les schémas aux différences finies et les méthodes des éléments finis, pour résoudre ces problèmes.Item Open Access Polynômes de Lagrange pour les équations intégrales(Mohamed Boudiaf University of M'sila, 2024-06-10) SEDDIKI, Feriel; NADIR, Mostefa: EncadreurLe but de ce mémoire est la résolution numérique de l’équation intégrale de Fredholm du second type, en utilisant les polynômes de Lagrange. De nombreux exemples sont présentés pour illustrer la précision et l’efficacité de la méthode proposéeItem Open Access Calcul numérique des équations intégrales de première espèce(Mohamed Boudiaf University of M'sila, 2024-06-10) HAFID, Houda; NADIR, Mostefa: EncadreurLe but de ce mémoire est la résolution numérique des équations intégrales de Volterra-Fredholm du première espèce, après la régularisation de cette équation, on utilise la méthode de trapèze de nombreux exemples sont présentés pour illustrer la précision et l’efficacité de la méthode proposéeItem Open Access Matrices Opérationnelles des polynômes de Lucas pour la Résolution des Equations Intégrales Linéaires de Volterra(Mohamed Boudiaf University of M'sila, 2024-06-10) BENGHADA, Dalal; KHIRANI, Amina: EncadreurLe but de ce mémoire, est la résolution numérique de l’équation intégrale de Volterra du second type, en utilisant le polynôme de Lucas . De plus de nombreux exemples sont présentés pour illustrer la précision et l’efficacité de la méthode proposéeItem Open Access Operational Matrices of Lucas Polynomials for Solving Linear Fredholm Integral Equations(Mohamed Boudiaf University of M'sila, 2024-06-10) LAIZI, KHADIDJA; KHIRANI, Amina: SupervisorIn this work, we studied the matrix collocation method using Lucas polynomials to solve the Fredholm integral equations. The purpose of this work is to show the effectiveness of the method presented and their advantages. Then, we made a comparison between the results of this method and the exact solution of the equation.The results of lucas matrix collocation method are closer to the exact solution.Item Open Access Inverse source problems for lineair parabolic equation(MOHAMED BOUDIAF UNIVERSITY -M’SILA, 2024-06) LAKHDARI, Abd elbasset; MIHOUBI, Farid: SupervisorIn the present work , we study two classes of inverse problems for diffusion equation with source term, where the partial derivative is fractional in the time. The from of EDP problems are called sub-diffusion problems. The first investigation is devoted to the determination of the source term coefficient dependent on time of an inverse source problem with non-local boundary conditions and integral condition. We establish results of existence, uniquenss and continuous dependence data.Tools used for demonstration are based on one hand , the Fourier method for bi-orthogonal systems , the operator being not self-adjoint , in author hand the fixed point theory. The scend investigation is devoted to determination of source term coefficient dependent on the space for sub-diffusion problem with homogeneous boundary conditions and an initial weighted condition. For direct problem , the key point in our analysis is the use of Duhamel principle in addition Fourier method , to show existence, uniquenss of weak solution, then the question of regularity is treated. to determine a unique coefficient, we add an integral condition to introduce input output mapping. The inverse problem is reduces to the problem of ineversibility of the input output mapping,which shoud be monotone and it’s invers is bijectifItem Open Access Exact and approximate solutions for deformable fractional differential equations(University Mohamed Boudiaf of M'sila, 2024-06) MAKHLOUF, Nour elhouda; ABDELKEBIR, Saad: SypervisorIn this work, we find exact solutions and approximate solutions for fractional differential equations with a fractional derivative called the distormable fractional derivative of order α, where : 0<α≤1. To find the exact solutions, we used the Laplace transform depending on the fractional derivative used. As for the approximate solutions, we used two numerical methods: the Euler method and the Runge-Kutta-4 method.Item Open Access Some Properties of Mixed Morrey Spaces and Applications(Mohamed Boudiaf university of M’sila, 2024-06) ALI SAOICHA, MERZAKA; DJERIOU, Aissa: SupervisorIn this memory, we present some properties and examples of mixed norm Lebesgue spaces and Morrey spaces, which generalize classical Lebesgue and Morrey spaces. We utilized this family of function spaces to study the boundedness of certain operators.Item Open Access Simulation numérique d’un écoulement d’un Fluide autour d’un obstacle(Université Mohamed Boudiaf de M’sila, 2024-06) DILMI, Hasna; SERGUINE, Houria: RapporteurDans ce travail, nous avons étudié une problème d’un écoulement potentiel, bidimensionnel à surface libre d’un fluide incompressible et non visqueux devant un obstacle de forme rectangulaire où la gravité et la tension de surface sont négligées. Pour trouver la solution exacte de ce problème, nous avons utilisé les transformations de Schwartz Christoffel et la méthode d’hodographe.Item Open Access Analyse des conditions aux limites pour un écoulement d’un fluide parfait(Université Mohamed Boudiaf de M’sila, 2024-06) Chetta, madiha; Serguine, Houria: RapporteurCe travail consiste à étudier un écoulement potentiel bidimensionnel d’un fluide incompressible et non visqueux à surface libre où les effets de gravité et de tension de surface sont négligées. Alors, on va étudier un problème d’un écoulement autour d’un obstacle de forme triangulaire. Et pour résoudre ce problème, on a utilisé la technique des transformations conformes pour simplifier notre travail. On trouve la solution exacte du problème posé, qui donne la forme de la surface libre de cet écoulement.Item Open Access Numerical solution of free surface flow problem(Mohamed Boudiaf University in Msila, 2024) SOUALMIA, Asma; Gasmi, Abdelkader: SupervisorAn approximate method is presented to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite ramp in the bottom. Schwartz-Christoffel transformation is used to map the region of flow, in the complex potential-plane, onto the upper halfplane. The Hilbert transformation as well as the perturbation technique are used as a basis for the approximate solution of the problem for large Froude number and small inclination angle of the ramp. General equations, in integral form, for any order of approximation are obtained. Solution up to first-order approximation is discussed and illustrated.