### Recent Submissions

• #### Riesz Uzayları Üzerinde Tanımlı Sıra Kompakt ve Sınırsız Sıra Kompakt Operatörler ﻿

(Fen Bilimleri Enstitüsü, 2020-08-28)
Order convergence and unbounded order convergence are not topological terms on Riesz space. On the other hand, compact operatör takes an important place in functional analysis. In this thesis, we investigate order compact ...
• #### Some Results on Operator Theory Based on Unbounded Convergence ﻿

(Fen Bilimleri Enstitüsü, 2020-08-31)
Main topic of the this work is to use the notion of unbounded convergences on vector lattices to derive properties of various classes of operators and nets of operators defined between vector lattices, Banach lattices, and ...
• #### The Injective Profile of a Ring and its Effect on the Structure of Rings ﻿

(Fen Bilimleri Enstitüsü, 2020)
This thesis is partly based on recent developments on the subject of what is known as “injectivity domains” in the theory of modules over rings with identity. The subject was suggested as a measurement of how far a module ...
• #### Genelleştirilmiş Splinelar Teorisi ﻿

(Fen Bilimleri Enstitüsü, 2020)
Let $R$ be a commutative ring with identity and $G=(V,E)$ be a finite graph, where $V$ is a set of elements of vertices and $E$ is a set of elements of edges. A map $\alpha : E \to \{\text{ideals in R}\}$ is called ...
• #### Geometric Structures on Riemann Surfaces and Reidemeister Torsion ﻿

(Fen Bilimleri Enstitüsü, 2020)
Let Σ be a closed orientable surface of genus at least 2 and Rep(Σ,G) be the smooth part of the representation variety of homomorphisms' conjugation classes from fundamental group of Σ to Lie group G. In this thesis, ...
• #### Algebraic Structure of Generalized Splines ﻿

(Fen Bilimleri Enstitüsü, 2019)
Given a fnite graph G=(V,E), a commutative ring R with unity and an edge labeling function α that assigns the ideals of R to the edges of G, the pair (G,α) is called an edge labeled graph. A vertex labeling F ⊂ R |V | is ...
• #### Ağırlıklı Projektif Uzaylardaki Parametrik Kodlar ﻿

(Fen Bilimleri Enstitüsü, 2019)
In this thesis we study parametric codes defined by any subset of a weighted projective space which is parameterized by monomials. The methods and notions used to study these codes are presented in detail. This work ...
• #### Alternative Digital Signature Schemes In Blockchain ﻿

(Fen Bilimleri Enstitüsü, 2019)
This thesis is a study on authentication methods of Bitcoin ecosystem which is an application of blockchain. Firstly, the facilities given by Bitcoin along with its security requirements are examined from a perspective ...
• #### Almost P-Ary Perfect Sequences And Their Applications To Cryptography ﻿

(Fen Bilimleri Enstitüsü, 2019)
In this thesis we study almost p-ary sequences and their autocorrelation coefficients. We first study the number L of distinct out-of-phase autocorrelation coefficients for an almost p-ary sequence of period n + s with s ...
• #### Bazı Seçme Özelliklerinin Zayıf ve Göreceli Formları ﻿

(Fen Bilimleri Enstitüsü, 2019-06-24)
The aim of this thesis is to introduce the weak forms of some classical selection properties in bitopological spaces, investigate the relationships between them and characterize these properties with topological games. ...
• #### Serbest veya Yüzey Grubunun Temsil Uzayları ve Reidemeister Torsiyon ﻿

(Fen Bilimleri Enstitüsü, 2019)
In this thesis, by using the algebraic topological instrument symplectic chain complex and the toplogical invariant Reidemeister torsion, which has also many applications in several branches of mathematics and theoretical ...
• #### A Study On Direct Summand Submodules Over Noncommutative Rings ﻿

(Fen Bilimleri Enstitüsü, 2018)
A natural problem to consider in ring and module theory is to investigate the cancellation property of a given object. This problem was first considered by Jónsson and Tarski for any algebraic system and then gave rise ...
• #### Torus Knots and Contact Surgeries ﻿

(Fen Bilimleri Enstitüsü, 2018)
A closed curve homeomorphic to the unit circle in a 3-manifold is called a knot. In particularly, a knot that can be drawn on a torus without intersecting itself is called a torus knot. In this thesis, we study torus knots ...
• #### Open Book Decompositions and Contact Surgeries ﻿

(Fen Bilimleri Enstitüsü, 2018)
By Alexander it was shown that an open book decomposition can be found for each closed, oriented 3-manifold. In this thesis, the importance of open book decompositions in terms of contact 3-manifolds will be studied by ...
• #### Some Families of Combinatorial Matrices and Their Algebraic Properties ﻿

(Fen Bilimleri Enstitüsü, 2018-09)
In this thesis, we will study some properties of certain families of combinatorial matrices. While some of the families will be examined throughout this thesis are new and firstly investigated, the others are the generalizations ...
• #### Diçatılara Genelleştirilmiş Bazı Topolojik Kavramlar ﻿

(Fen Bilimleri Enstitüsü, 2018)
The aim of this thesis is to define the notion of diframe as a generalization of ditopological texture spaces and to study the topological concepts such as separation axioms and compactness in diframe setting. This work ...
• #### Lineer Olmayan Kısmi Diferansiyel Denklemlerin Backlund Dönüşümleri ﻿

(Fen Bilimleri Enstitüsü, 2018)
In this thesis, it is studied how the B¨acklund transformations of nonlinear partial differential equations are obtained and deriving new solutions from the known solutions by using these transformations with the ...
• #### Legendre Düğümlerinin Sınıflandırılması ﻿

(Fen Bilimleri Enstitüsü, 2017)
A contact structure on a 3-manifold is a maximally non-integrable 2-plane field distributed all over the 3-manifold. There are two types of contact structures on 3-manifolds: tight and overtwisted. Knots that are everywhere ...
• #### Kuasilineer Dalga Denkleminin Uzun Zaman Davranışı ﻿

(Fen Bilimleri Enstitüsü, 2018)
In this thesis, we concern the long time behaviours of the one dimensional strongly damped nonlinear wave equation u_tt-u_txx-∂/∂x (|u_x |^(p-2) u_x )+f(u)=g(x) (1) in bounded domain and the one dimensional strongly ...
• #### Derivations and Automorphisms of Certain Subrings of Matrix Rings ﻿

(Fen Bilimleri Enstitüsü, 2018)
Let K be an arbitrary associative ring with identity. We denote by Mn(K) the ring of all nxn matrices over K. Say K=F for some field F. Then it is a consequence of Skolem-Noether theorem that every automorphism of Mn(F) ...