This dissertation examines the study of rigidity of collections of objects in various geometric spaces, and the correspondences shared between geometries. In particular, we take a look at vectors and lines in Lorentz (n+1)-space, points, ideal points and hyperplanes in hyperboli…
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We study some historical developments of the crossing ball structure in the link complements introduced by Menasco (1981). In particular, we give an alternative proof to show that the complement of a fully alternating link in thickened surface is hyperbolic. In the last chapter,…
This dissertation is composed of two parts. The first part concerns the general result on the following variance associated with the distribution of a real sequence {an} in arithmetic progressions:
The author's purpose in this dissertation is to introduce, develop and apply the tools of discrete fractional calculus to the arena of fractional difference equations. To this end, we develop the Fractional Composition Rules and the Fractional Laplace Transform Method to solve a…
In this work, I offer an alternative presentation theory for C*-algebras with applicability to various other normed structures. Specifically, the set of generators is equipped with a nonnegative-valued function which ensures existence of a C*-algebra for the presentation. This m…
In the first chapter we study the meromorphic continuation of the Dirichlet series [Special characters omitted.] <display-math> <fd> <fl>F<inf>r</inf><fen lp="par">s<rp post="par"></fen>=<sum align="c"> <ll><stk><lyr>m,&ldots;,m<inf>r</inf>≥1</lyr><lyr>m<inf>1</inf> &cdots;m<…
Bu tez dört bölümden oluşmaktadır. Birinci bölümde, konuya giriş yapılmış ve konunun tarihsel gelişiminden bahsedilmiştir. İkinci bölümde, diğer bölümlerde kullanılacak olan bazı temel kavramlar tanıtılmıştır. Riemann manifoldlar,hemen hemen değme manifoldlar, Kenmotsu manifoldl…