Master Thesis
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Item Open Access Sur une suite de polynomes orthogonaux(Mohamed Boudiaf University of M'sila, 2025-06-15) Sabrina, Ben aissi; Encadreur: Aissa, LakhalL'objectif de ce mémoire est d'étudier les suites de polynômes orthogonaux d'un point de vue théorique et analytique, en identifiant leurs propriétés fondamentales, leurs relations de récurrence et les conditions d'orthogonalité dans un espace fonctionnel. Il vise également à mettre en lumière les suites classiques telles que les polynômes de Legendre, Hermite et Laguerre, et à montrer leur rôle dans l'approximation des fonctions, la résolution des équations différentielles, ainsi que certaines applications numériques et physiques.Item Open Access Study and Design of an Interactive System for Learning Letters and Words(Mohamed Boudiaf University of M'sila, 2025-06-29) Meryem, Ben ziane; Supervisor1: Abdelkader, DJERAD; Supervisor2: Mostafa, TABBAKH; Supervisor3: Amina, KHIRANICe projet propose l’étude et la réalisation d’un système pédagogique intelligent basé sur la reconnaissance des caractères arabes, intégrant des technologies avancées telles que les réseaux de neurones convolutifs (CNN). Le système est conçu pour identifier avec précision les lettres arabes grâce à des algorithmes de reconnaissance optimisés, prenant en compte les spécificités de l’alphabet arabe.Item Open Access Approximation des équation et des inéquation de type monotone(Mohamed Boudiaf University of M'sila, 2024-06-10) Sabrina, Lachache; Encadreur: Khlifa, ChadiNotre 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 Analytical solutions for Navier-Stokes Equations with Caputo Fractional Derivative(Mohamed Boudiaf University of M'sila, 2025-06-10) Mariam, NOUIOUA; Supervisor: Hamza, MIHOUBIIn this work, we will use the residual power series (RPS) method to generate the solution of the nonlinear time fractional Navier-Stokes equation with Caputo fractional derivative in two dimensions in the form of a rapidly convergent series,where we adopted the definition of generalized Fractional calculus operators, including those of Riemann-Liouville.Hadamard,Katugampula of the Caputo type. We gave an illustrative application to demonstrate the effectiveness and leverage of the proposed method, where numerical results and graphical representations reveal that the proposed method performs extremely well in terms of efficiency and simplicity and it can be utilized to solve more problems in the field of non-linear fractional differential equations (FDEs).Item Open Access Numerical and Analytical Approaches to freesurface and potential flow(Mohamed Boudiaf University of M'sila, 2025-06-15) Chaima, Mammeri; Supervisor: Abdelkader, GasmiThis work deals with the study of a free surface flow of an ideal, two-dimensional, steady and, irrotational fluid inside a horizontal channel huid is assumed to be incompressible, and surface tension effects are neglected, while channel with an obstacle on the bottom. The gravity is taken into is based on the long-wave approximation, using a small parameter : 0 < epsilon = (H/l) ^ 2 << 1 The bottom profile function y = b(x) and the free surface by y = H + eta(x, t) where 7 is the main unknown of our problem.Item Open Access Application of potential flow theory to free surface flow problem(Mohamed Boudiaf University of M'sila, 2025-06-15) Asma, Khazari; Supervisor: Abdelkader, GasmiThis thesis addresses the application of potential flow theory) to free surface flow problems, using both analytical and numerical solutions. The research focuses on solving the fundamental equations (continuity, Bernoulli, Laplace) under specific boundary conditions, with particular emphasis on the Boundary Element Method (BEM) as an accurate and computationally efficient tool. This study provides practical insights for the fields of hydraulic engineering and aerodynamics.Item Open Access Existence and regularity of the solution of some elliptic problems(Mohamed Boudiaf University of M'sila, 2025-06-15) Souad, Berrabeh; Rapporteur: Rabah, Mecheterin this work, we prove the existence and regularity of a weak solutions of elliptic problem (P) defined by (P) { Au fin 2: u= 0 on 20, the operator Audiv( Vu - Vu), 1Item Open Access Résolution des formes intégro-différentielles de Volterra des problèmes d'Emden-Fowler(Mohamed Boudiaf University of M'sila, 2025-06-14) Riadh, Saadallah; Encadreur: Mustapha, DilmiDans ce mÈmoire, nous avons ÈtudiÈ les Èquations di§Èrentielles de type Emden-Fowler en les transformant en Èquations intÈgro-di§Èrentielles, dans le but de trouver des solutions approchÈes. Nous avons utilisÈ la mÈthode de transformation di§Èrentielle et comparÈ les rÈsultats obtenus avec les solutions exactes aÖn díÈvaluer líe¢ cacitÈ et la prÈcision de cette mÈthode.Item Open Access Résolution des formes intégro-différentielles de Volterra des problèmes de Lane-Emden(Mohamed Boudiaf University of M'sila, 2025-06-14) Hamza, AMMARI; Encadreur: Mustapha, DilmiDans ce travail, nous Ètudions les Èquations di§Èrentielles de Lane-Emden en les trans formant en Èquations intÈgro-di§Èrentielles aÖn díobtenir des solutions approchÈes. Nous utilisons la mÈthode de Collocation-Touchard et comparons les rÈsultats avec des solutions exactes pour Èvaluer la prÈcision et líe¢ cacitÈ de líapproche proposÈe.Item Open Access Some properties of LCD cyclic codes over finite fields(Mohamed Boudiaf University of M'sila, 2024-06-15) seddik, Attallah; abdelhafid, Gherabi; Supervisor: Lakhdar: HeboubThis work focuses on the theory of error-correcting codes, specifically the investigation of cyclic codes A cyclic code of length N over the finite field F can be defined as a principal ideal of the quotient ring R= F[x]/(x-1) The main objective of this memory is the study of LCD cyclic codes.Item Open Access On the Vibrations of Traveling Strings and Membranes(Mohamed Boudiaf University of M'sila, 2024-06-10) Nour, Bourenane; Supervisor: Abdelmouhcene, SengougaIn this study, we examine the one-dimensional and two-dimensional wave equations in time-dependent domains. We derive the wave equation using Hamilton’s principle. Then, we employ the method of separation of variables to solve the equation. We also consider the case with interior linear damping.Item Open Access Équation de Riccati et commande optimale(Mohamed Boudiaf University of M'sila, 2025-06-15) Sarra, Yahiaoui; Encadreur: Touahria, MessaoudUne fois le problème de contrôlabilité résolu, on peut également chercher à passer d’un état initial à un état final tout en minimisant un certain critère. On parle alors d’un problème de commande optimale. quadratique, qui a fait l’objet de nombreuses investigations depuis l’article publié par L’objectif de ce travail est d’étudier le problème de la commande optimale linéaire Kalman en 1960. Dans ce type de problème, le système est linéaire et le coût est quadra tique. Le but est de déterminer une commande par retour d’état qui stabilise le système, en utilisant l’équation de Riccati.Item Open Access Variational and Numerical Analysis of Some Problems at the Contact Limits(Mohamed Boudiaf University of M'sila, 2025-06-15) Wiam, Saadi; Supervisor: Khelifa, ChadiThe variational and numerical study of some contact problems with or without friction, between a deformable body and a foundation. Here we consider nonlinear laws of behavior for viscoplastic materials. For these problems we obtain variational formulations followed by existence and uniqueness results of weak solutions. The techniques employed are based on the theory of monotone operators followed by a version of the Cauchy-Lipschitz theorem and Banachís fixed point arguments. Finally, we propose a numerical approximation of the purely mechanical problem using discrete schemes. For these schemes, we obtain error estimation resultsItem Open Access The Number of Fuzzy Clopen Sets in Fuzzy Topological Spaces(Mohamed Boudiaf University of M'sila, 2025-06-14) Fatima Zahra, Salamani; Supervisor: Kheir, SaadaouiThis thesis presents a comprehensive exploration of topological structures, beginning with the foundational concepts of classical topology and advancing toward the nuanced and flexible framework of fuzzy topology. In Chapter 1, we established the groundwork by discussing key topological concepts such as open and closed sets, interior and closure, continuity, homeomorphisms, and different types of topologies. These classical ideas form the basis for understanding more complex and abstract structures. Building upon this foundation, Chapter 2 introduced fuzzy topological spaces, extend ing classical topology to accommodate uncertainty and gradation. By allowing degrees of membership, fuzzy topology offers a powerful framework for modeling situations where classical binary logic proves insufficient. This chapter underscored the theoretical impor tance and practical relevance of fuzzy systems in addressing imprecision and ambiguity in various real-world contexts. In Chapter 3, we focused on the concept of fuzzy clopen sets—sets that are simulta neously fuzzy open and fuzzy closed. We examined the number and structural properties of such sets. Overall, this thesis demonstrates the progression from classical to fuzzy topology, highlighting both the theoretical advancements and the broader applicability of topolog ical thinking. By bridging these domains, the study not only deepens our understanding of topological structures but also opens new avenues for research and application in areas involving uncertainty, such as decision theory, artificial intelligence, and systems analysis.Item Open Access Fractional Sobolev Spaces With Applications To Boundary Values Problems(Mohamed Boudiaf University of M'sila, 2025-06-15) Selma, Nasri; Supervisor: Brahim, BoughraraThis thesis aims to study fractional differential equations of both linear and nonlinear types, based on Riemann–Liouville derivatives of non-integer order. We begins by presenting the necessary mathematical background, including Lebesgue and fractional Sobolev spaces, and introduces the fundamental concepts of fractional inte gration and differentiation. These tools are then applied to analyze three main cases of the studied equation: the sublinear case 1 ≤ q < 2, the superlinear case 2 < q < 2 ∗ , and the linear case q = 2. In each case, we prove the existence of weak solutions within suitable functional spaces, taking into account the variation of conditions related to the spectral parameter λ.Item Open Access Linearization of Nonlinear Operators in the Theory of Summability(Mohamed Boudiaf University of M'sila, 2025-06-15) Zahra, Seghiri; Surpervisor: Khalil, SaadiThis thesis addresses linearization in functional analysis, where it transforms nonlinear map pings, such as Lipschitz and multilinear mappings, into linear mappings. The goal is to understand the properties of these mappings and the possibility of studying them using p-summing properties.Item Open Access On Pell and Pell-Lucas numbers(Mohamed Boudiaf University of M'sila, 2025-06-15) Samia, Zikem; Fatima Zohra, Sayhi; Supervisor: Abdelmajid, BoudaoudIn this work, we consider the linear recurrent sequences with constant coefficients of order 2, focusing on those defining Pell and Pell-Lucas numbers. In this context, we have examined the corresponding Binet formulas and the possibilities for a Pell or Pell-Lucas number to become a member of another family such as the families of triangular, pentagonal, heptagonal numbers, ... . We also reviewed some identities linking these numbers, and finished our work with some formulas involving the sum and multiplication of these numbers.Item Open Access Fractional differential equations in Orlicz spaces(Mohamed Boudiaf University of M'sila, 2025-06-14) Fatima, Salmi; Encadreur: Bachir, GaguiThis dissertation deals with the existence of solutions to fractional order differential equations of Riemann-Liouville type in Orlicz spaces, based on fixed point theory and Kuratowsli’s measure of noncomactness.Item Open Access Hyper nuclear multilinear operators(Mohamed Boudiaf University of M'sila, 2025-06-15) Noureddine, Nekbil; Supervisor: Dahmane, AchourThis memory examines hyper-ideals of multilinear operators, a framework introduced by Botelho and Torres that extends classical Pietsch multi ideals by incorporating composition properties. We study their general theory and, as a principal example, focus on hyper right p-nuclear multilinear operators. For these operators, we establish the linearization theorem and prove a decomposition characterized by mappings through ℓ p -spaces via a linear operator followed by a multilinear operatorItem Open Access Weak Solutions for elliptic equations with lower-order terms and L 1 data(Mohamed Boudiaf University of M'sila, 2025-06-15) Naasira, Bentoum; Rapporteur: Rabah, MecheterIn this work, we study the existence of weak solutions for a class of linear elliptic equations with lower-order terms and integrable data. More precisely, we consider problems of the form: − u = 0 div( , M(x)∇u) + a(x)u = f(x), in on Ω ∂ , Ω, where Ω ⊂ R N is a bounded domain, M(x) is an elliptic matrix, a(x) ∈ L 1 (Ω), and f ∈ L 1 (Ω). Since the right-hand side lies in L 1 (Ω), standard variational methods are not applicable. To address this, we construct a sequence of approximate problems whose solutions are well-defined, and establish uniform a priori estimates. Then, using compactness arguments and the theory of pseudo-monotone operators, we prove the existence of a weak solution to the original problem.