AUB ScholarWorks

Browsing AUB Students' Theses, Dissertations, and Projects by Author "Department of Mathematics"

Browsing AUB Students' Theses, Dissertations, and Projects by Author "Department of Mathematics"

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  • Admissible representations of GL(2,Qp), the Kirillov model and application to local new vectors. 
    Krayem, Janane Moussa (2019)
    Jacquet and Langlands (1970) showed that every infinite dimensional, irreducible, admissible representation of GL(2,Qp) has a unique Kirillov model, i.e. is isomorphic to a representation (π,K), where the space K consists ...
  • Analysis and Implementation for an Time Euler Implicit - Space Finite ElementApproximation To a Hasegawa-Mima Plasma Model 
    Saleh, Adel (2/8/2022)
    In Magnetohydrodynamics, the Hasegawa-Mima equation appears as a model for pseudo three-dimensional turbulence of a confined plasma inside a Tokamak reactor. This equation bears close resemblence to the 2d Navier-Stokes ...
  • Analytic Disks and Mapping Problems for Real Hypersurfaces in Complex Spaces 
    Hussein, Ahmad (2024-01-29)
    The thesis will review the theory of certain invariant objects associated to CR submanifolds of C^n, especially families of attached analytic disks, and their implications for the study of the properties of holomorphic ...
  • Asymptotic Behaviour of Probabilistic Cellular Automata 
    Halawi, Ali (9/8/2022)
    The automaton iteratively evolves from one configuration to another using local transition rules based on the neighborhood of each cell. The aim of this project is to study the notions of ergodicity and uniform ergodicity ...
  • Discrete Optimal Transport 
    Fakih, Israa (2023-05-02)
    We introduce the Assignment Problem, which involves minimizing the cost of transporting goods from a finite number of sources to a finite number of targets. Due to the discrete nature of the assignment problem, a solution ...
  • Entire Function with Two Separated Values 
    Saab, Batoul (2023-08-07)
    It’s known that an entire function with zeros and 1-points lying on a finite number of rays must have finite order. This thesis considers a transcendental entire function with two separated values in disjoint sectors. ...
  • A Fixed-Point Argument for Existence of Dichromatic Lens 
    Alharakeh, Zeinab (5/18/2022)
    In this paper, we are going to solve a system of functional differential equations and use Banach Fixed Point Theorem to prove existence and uniqueness of solution. This will help us in a problem in geometrical optics. Our ...
  • Fourier coefficients of modular forms of positive dimensions - by Mary Tanous Assaad. 
    Assaad, Mary Tanous (2011)
    The unrestricted partition function p(n) counts the number of ways a positive integer n can be expressed as a sum of positive integers less than or equal n. The number of summands is unrestricted, repetition is allowed ...
  • Frequency Analysis and Applications 
    Fneich, Fatima (2023-08-18)
    The goal of this thesis is to study signals that have a regularity property defined in the frequency space, such as a decay on average of the amplitude of their Fourier transform, by using techniques from frequency ...
  • Identification of Gas Diffusion Coefficients in Polar Firn. 
    Maad, Sara (9/12/2022)
    The use of data analysis cooperatively with partial differential equations is a successful technique to estimate the main parameters of diverse phenomena in many fields (medicine, biology, ecology,...). In the area of ...
  • Integrable Generators of Lie Algebras of Vector Fields on the Koras--Russell Cubic Threefold 
    Ashkarian, Estepan (5/18/2022)
    The Koras--Russell cubic threefold is a complex-affine manifold that is diffeomorphic to the three-dimensional complex-Euclidean space, but not algebraically isomorphic to the three-dimensional complex-affine space as an ...
  • L-series of Harmonic Maass Forms 
    Bou Aoun, Elena (2024-05-08)
    We introduce Harmonic Maass forms and present some of their analytic properties. We continue to define their related L-series by using Laplace transform, and prove their functional equations. Our primary objective is to ...
  • Least Gradient Problem 
    Chaaya, Marie-Jose (9/21/2020)
    If f is a given function defined on the boundary of a domain Omega in d-dimensional Euclidean space, the least gradient problem (LGP) asks for the following: among all functions u in the space bounded variation functions ...
  • Least Gradient Problem 
    Lahoud, Jolie (2024-05-08)
    For a given continuous function g defined on the boundary of Ω where Ω is a bounded lipschitz domain in ℝ𝑛satisfying some conditions, we consider proving the existence of a function u in the space of BV(Ω) that is equal ...
  • Monge-Ampère Equation 
    Berjawi, Fatima (2024-05-09)
    In this work, we focus on studying the Aleksandrov solution of the Monge-Ampère equation. Initially, we develop the notion of a normal mapping and discuss its properties through proving concepts from convex analysis. ...
  • Monomial ideals, multigraded resolutions and the subadditivity problem. 
    Chalhoub, Nour (2019)
    Let R=k[x1, . . . , xn] be the polynomial ring in n variables, and I a monomial ideal in S. Let F be a minimal graded free resolution of S=R-I. We study properties of multigraded resolutions to establish results on the ...
  • NON-VANISHING OF HECKE L-FUNCTIONS OF CUSP FORMS OF INTEGER AND HALF-INTEGER WEIGHT 
    Zebiane, Lara (9/21/2020)
    We show a non-vanishing result for L-functions of cuspidal Hecke eigenforms of integer weight in the full modular group and of half integer weight in the plus space. In chapter 1, we review definitions of modular forms of ...
  • On Enlarged Krylov Subspace Conjugate Gradient Method: MSDO-CG 
    El Owayed, Hiba (8/18/2022)
    Solving systems of linear equations of the form Ax=b has always been a challenge for scientists because the input matrix A is very large and sparse. These systems are derived mainly from the discretization of Partial ...
  • On the Enlarged Krylov Subspace Method: SRE-CG2 
    Al Hajj, Youmna Abbas (9/12/2021)
    We are interested in solving sparse systems of linear equations Ax=b with Krylov subspace methods. A new approach for reducing communication in Krylov subspace methods was introduced that consists of enlarging the Krylov ...
  • On the generalization of the Riemann mapping theorem in the theory of several complex variables. 
    El Zini, Najwa Wajdi (2019)
    One of the most powerful results in complex analysis is The Riemann Mapping Theorem which states that every non-empty simply connected domain in the complex plane which is not the entire ₵ is biholomorphically equivalent ...

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