Browsing by Author "American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics."

Now showing items 1-20 of 22

Arithmetic of quaternion algebras - by Abdalla Said Nimer.

Nimer, Abdalla Said. (2011)

If K is a field whose characteristic is not 2, a quaternion algebra over K is a an algebra over the basis [1,i,j,ij] where i and j satisfy the relations: i2=a j2 =b ij=-ji for a,b in K*. It turns out that for general ...
The bilinear approach to the distance set problem - by Razane Abdel Nasser Berjaoui.

Berjaoui, Razane Abdel Nasser. (2011)

We are interested in the following open problem (known as the distance set problem or Falconer's conjecture): Let K be a compact set in Rd with Hausdorff dimension strictly greater than half of the dimension d, then the ...
Bruhat, Cartan and Iwasawa decompositions in GLn(R), O(p, q) and GLn(Qp) / by Malak Adel Dbouk.

Dbouk, Malak Adel. (2012)

Throughout my thesis I will discuss three main decompositions: the Bruhat, Cartan and Iwasawa decompositions. In the first chapter I will prove these decompositions in the general linear group of invertible matrices G. The ...
Combinatorial properties of tropical intersections

Fares, Manal Haidar. (2012)
Congruences of the Fourier coefficients of the modular invariant j(Tau) - by Ola Bassam Shami Nasr.

Shami Nasr, Ola Bassam. (2011)

In 1949, Joseph Lehner published some arithmetic congruences of the Fourier coefficients of the modular invariant j. His method involved applying a certain linear operator to determine congruences modulo primes. Then, he ...
Converting trilinear restriction estimates to linear estimates in R³

Saad, Marie-Jose Ronald. (2013)

Our thesis starts by explaining the Bourgain-Guth method in dimension n = 2, then proceeds to dimension n = 3 and presents the argument form [1] for q 33=10.
Decay of one-dimensional averages of Fourier transforms of measures in the plane - by Fida Michel Nashef.

Nashef, Fida Michel. (2011)

Consider a positive compactly supported measure in Rn, and alpha between zero and n. We are interested in obtaining decay estimates on the integral over the sphere of the Fourier transform of the above measure. Such decay ...
The distance set problem and Wolff's exponent in the plane - by Zeina Ziad El Rawas.

El Rawas, Zeina Ziad. (2011)

Let K be a compact set in Rn with Hausdorff dimension h. The distance set D of K is the set of absolute values of the difference of x and y for every two points x and y in K. A major open problem in geometric measure ...
The Eichler cohomology theorem

Riman, Nour Fawzi. (2013)

Modular forms are associated with many problems that arise in mathematics and physics. They attain their importance due to the following properties, ﬁnite dimensionality of the space of entire modular forms Mk , rationality ...
Floor decomposition of tropical planar curves

El Maalouf, Loulwa Rachid. (2013)

Mikhalkin showed that when counted with appropriate (r-real) multiplicities, the number of tropical curves in (R*)2 of genus g and Newton polygon Δ passing through s generic points in (R*)2 agrees with the corresponding ...
Gauge theories and Seiberg-Witten monopoles - by Hagop Bedros Tossounian.

Tossounian, Hagop Bedros. (2011)

In 1983, Donaldson achieved a breakthrough in differential topology by using the moduli space of solutions of an SU(2)-gauge theory to construct new invariants of smooth 4-manifolds. The methods revealed by Donaldson, ...
Killing spinors and Cartan connections - by Aram Garabed Dedeyan.

Dedeyan, Aram Garabed. (2011)

Killing vector fields are the infinitesimal generators of isometries, on a Riemannian manifold. Killing spinors can be thought as “square roots” of Killing vectors they are the infinitesimal generators of supersymetry ...
Local restriction theorems in R² and R³

Fakhry, Rami Mohamad. (2013)
The local-global principle for diophantine equations

Yakoob Al Hakeem, Roy Hanna. (2013)

The p-adic numbers were first introduced by Kurt Hensel in 1897 in an attempt to carry the techniques of power series methods from complex analysis into number theory. In this thesis we discuss the relationship between ...
On probabilistic proofs of some real variable results - by Hassanah Labban

Labban, Hassanah (1986)
Recent estimates on exponential sums in higher dimensions

El-Wali, Sara Mohamad. (2013)

One of the two important developments concerning the restriction theory in Fourier analysis during the last ten years was the development of the multi-linear restriction theory by Bennett, Carbery, and Tao in [2]. The ...
Reduction in linear groups and orthogonal groups - by Zeina Wajih Nahle.

Nahle, Zeina Wajih. (2012)

The thesis deals with reduction in linear groups and orthogonal groups. Any matrix y in the set of all n by n symmetric positive definite matrices, can be written as the transpose of an invertible matrix g multiplied by ...
Rings with finiteness conditions on certain subsets

Gebai, Ryma Ismail. (2013)

Finiteness conditions on a ring or on certain subsets of a ring have several implications on the structure of the ring. This study of finiteness conditions was motivated by a well-known theorem of Wedderburn which states ...
Some classical and p-adic L-functions over number fields

Taha, Razan Khalil. (2013)

L-functions are generalizations of the Riemann zeta function. We define and study L-functions L(s,χ) attached to Hecke characters χ over number fields Q(α). Such functions converge only when Re(s)1 but have an analytic, ...
Some discrete series representations of noncompact unitary lie groups

Riman, Manar Najib. (2013)

Now showing items 1-20 of 22

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Browsing by Author "American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics."

Browsing by Author "American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics."

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Copyright Statement