College of Natural and Computational Sciences

Permanent URI for this college

http://etd.aau.edu.et/handle/123456789/24

Browse

Browsing College of Natural and Computational Sciences by Author "Ababaw Tilahun (PhD)"

Now showing 1 - 2 of 2
  • No Thumbnail Available
    Item
    On the length of D-modules over Hyperplane Arrangements in Space
    (Addis Ababa University, 2016-07) Demelash Smegnsh; Ababaw Tilahun (PhD)
    A D-module is a module over a ring of Di_erential Operators. The major interest of such D-modules is as an approach to the theory of linear partial di_erential equations. Algebraic D-modules are modules over the Weyl algebra An over the _eld C of complex numbers. The main purpose of this thesis to work on the A3=module C[x;y;z]_; where _ is the product of linear forms. In this thesis we computed the decomposition factors and hence the length of A3 -module C[x; y; z]_ using the method of partial fractions of rational functions
  • No Thumbnail Available
    Item
    Proving Some Geometric the O rems Usingrorb ner base
    (Addis Ababa University, 2011-01) Weldegiorgis Aregawi; Ababaw Tilahun (PhD)
    Algebraic Geometry can be used to prove geometric theorems in Euclidean Plane Geometry. This can be done when the geometric theorem has the property that the hypothesis and the conclusion of the theorem can be translated into polynomial equations. Such theorems are called admissible theorems. The geometric theorems considered involve points, lines, or circles in the Euclidean Plane which have common intersection points. In this project, first we translate the hypothesis and conclusion of the theorem in to polynomial equations. Then, the method Groebner basis is used to answer the ideal membership problem of the ideal generated by the polynomials in the hypothesis and the polynomials in the conclusion. The geometric theorems considered are the Theorem of Apollonius and Pappus Theorem which demonstrate the applicability of our method