In this thesis, we consider pants decomposition of orientable Riemann surfaces. First, using the notion symplectic chain complex, we prove a new formula Reidemeister torsion of a pair of pants. By using this, we establish ...

This study is devoted to the blow up solutions of the Cauchy problem for the weakly dissipative Camassa-Holm equation. In introductory chapter, the problem we studied has been introduced and other authors' studies done on ...

This thesis is concerned with universal differential operator modules of order n. Let R be a commutative k-algebra where k is an algebraically closed field of characteristic zero. Let m and n be positive integers such that ...

Dedekind domain are the rings in which every nonzero proper ideal has a prime factorization. In this thesis, we first study valuation rings and Prüfer domains. Then we characterize Dedekind domains which are also Noetherian ...

This work consists of five chapters. In the first chapter, the basic properties of useful certain kind of submodules in module and ring theory which are named as essential and complement submodules are given. In the second ...

Differential equations are mostly used to model real life problems. However, it is known that in general, these equations do not have complete solutions. For that reason, researchers have tried to solve these problems by ...

The commutative theory of Dedekind domains is well developed in literature and much isknown about the arithmetic of ideals and also the structure of modules over a Dedekinddomain. There have been many studies on the ...