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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  • A graph theoretical description of the universal Grobner bases of toric ideals of graphs - 
    Mantash, Batoul Hassan, (2015)
    We are going to study the paper: On the Universal Grobner Bases of Toric Ideals of Graphs by Christos Tatakis and Apostolos Thoma which gives a graph theoretical characterization of the elements of the universal Grobner ...
  • A new simulation model for the Hasegawa-Mima plasma equation - 
    Almaalouf, Dana Rashed, (2017)
    A nonlinear evolution of the drift-wave instability are investigated by means of numerical simulations based on a model equation derived from a two-fluid approximation that reduces to the Hasegawa-Mima equation. We intent ...
  • Central scheme for systems of shallow water equations with wet and dry states - 
    Kanbar, Farah Mohamad, (2017)
    In this thesis we present a new well-balanced, non-oscillatory, second-order accurate central scheme for the numerical solution of the two-dimensional shallow water equations (SWE) with wet and dry states. The numerical ...
  • Gromov's non-squeezing theorem and pseudoholomorphic discs - 
    El Chaar, Nagham Imad, (2015)
    In order to understand the geometry of a given symplectic manifold (M, w), one can study how elementary geometric subsets of M, such as balls, are transformed by symplectomorphisms, i.e. diffeomorphisms preserving the ...
  • Invariant metrics and complex geodesics in several complex variables - 
    Mrad, Preskella Mounir, (2015)
    Biholomorhically invariant metrics are important tools in Several Complex Variables which generalize Hermitian metrics and are particularly adapted for the study of holomorphic maps and function spaces. The Carath́eodory ...
  • Local holomorphic extension of CR-functions - 
    Al Akhdar, Mariam Abbas, (2017)
    This thesis involves the extension behavior of holomorphic functions in several variables, and the corresponding extension problem for CR functions defined on a real hypersurface of a complex manifold. However, the extension ...
  • On the magnitude of metric spaces - 
    El Khatib, Ola Ghassan, (2015)
    In this thesis, we consider the magnitude of finite metric spaces and that of compact subsets of Euclidean spaces. We will consider an extension of the definition of finite spaces to compact metric spaces using three ...
  • On the method of analytic discs - 
    Salameh, Mona Khalil, (2016)
    Initiated by Riemann and Hilbert, the method of analytic discs is a powerful technique in Several Complex Variables. Such invariants are indeed particularly adapted to the study of CR extension, boundary extension of ...
  • On the uniqueness of the Radon transform over lines, planes and spheres - 
    Al Hassanieh, Nour Ghassan, (2016)
    This thesis will discuss the uniqueness problem of the Radon transform over lines in the space, hyper planes in the Euclidean N space for N 2 and in more detail, the Radon transform over spheres whose centers are restricted ...
  • Structure of rings with conditions on certain subsets - 
    Samman Kaakaji, Tala Jamil, (2015)
    Rings are of different structures, altering some conditions on some subsets of a ring might cause a change in its structure. In this thesis, we study some of these alterations and their effects on the ring and its subsets. ...
  • Subadditivity of syzygies in a minimal graded free resolution - 
    Gabriel, Gaelle Rizkallah, (2017)
    Let R = k[x₁,...,xn] be the polynomial ring in n variables, and I a homogeneous ideal in (x₁, . . . xn). Let F be a minimal graded free resolution of S = R-I. We study the subaddivity of Gorenstein algebras and of monomial ...
  • The l² decoupling conjecture - 
    Mkhsian, Njteh Haroutioun, (2017)
    One of the guiding principles of harmonic analysis (more precisely, restriction theory) states that a finite family of functions in a Lebesgue space Lp are almost orthogonal under certain conditions. One particular ...
  • The zeroes of period polynomials - 
    Shami Nasr, Omar Bassam, (2016)
    A modular form is a function meromorphic in the upper half plane and at the cusps. It satisfies certain transformation conditions under the full modular group The space of entire modular forms of integer weight on the full ...
  • Topological classification of compact two dimensional hyperreal manifolds - 
    Al-Ahmadieh, Abeer Kamal, (2016)
    In this thesis we aim to extend the classical result on the classification of compact, two dimensional manifolds to the Hyperreal cases. The tools used are nonstandard analysis, as well as the analogue of the triangulation ...

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