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Department of Mathematics, Thesis
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Existentially closed groups
Gürel, Yağmur; Kuzucuoğlu, Mahmut; Koçak Benli, Dilber; Department of Mathematics (2021-12-10)
A group G is called an Existentially Closed Group (Algebraically Closed Group) if for every finite system of equations and inequations with coefficients from G which has a solution in an over group H ≥ G, has a solution in...
BEM SOLUTIONS OF MAGNETOHYDRODYNAMIC FLOW EQUATIONS UNDER THE TIME AND AXIAL-DEPENDENT MAGNETIC FIELD
Ebren Kaya, Elif; Tezer, Münevver; Department of Mathematics (2021-9-6)
In the thesis, four different MHD duct flow problems are solved by using the Dual Reciprocity Boundary Element Method (DRBEM) with the suitable boundary conditions according to the physics of the problem. The two-dimension...
The Wronski map for flag varieties
Güngör, Emre; Kişisel, Ali Ulaş Özgür; Department of Mathematics (2021-9)
In this thesis, we studied flag varieties, the Grassmann variety G(d; n) and their behavior under the Wronski map. We begin by introducing algebraic, topological and geometric tools that are required to define flag varieti...
Computation of the Primary Decomposition of Polynomial Ideals Using Gröbner Bases
Tolgay, Betül; Karayayla, Tolga; Department of Mathematics (2021-8-06)
In this thesis, we investigate algorithms for computing primary decompositions of ideals in polynomial rings. Every ideal in a polynomial ring over a Noetherian commutative ring with identity has a primary decomposition, t...
A survey on multidimensional persistence theory
Karagüler, Dilan; Pamuk, Semra; Department of Mathematics (2021-8)
Persistence homology is one of the commonly used theoretical methods in topological data analysis to extract information from given data using algebraic topology. Converting data to a filtered object and analyzing the topo...
Invariant Metrics and Squeezing Functions on Bounded Domains
Ökten, Ahmed Yekta; Yazıcı, Özcan; Department of Mathematics (2021-8)
In this thesis we will study the biholomorphically invariant objects called squeezing functions. They are closely releated to invariant metrics on bounded domains and describe how much a domain looks like the unit ball loo...
Coefficients of folding polynomials attached to Lie algebras of rank two
Aydoğdu, Muhammed; Küçüksakallı, Ömer; Department of Mathematics (2021-7-9)
Let g be a Lie algebra over a field F, and let h be a Cartan subalgebra of g. The dual space h∗ of h forms a root system. Reflections in the hyperplanes orthogonal to the simple roots of h∗ generate the Weyl group of g. If...
Stacky formulations of Einstein gravity
Berktav, Kadri İlker; Kişisel, Ali Ulaş Özgür; Tekin, Bayram; Department of Mathematics (2021-5-28)
This is a thesis on higher structures in geometry and physics. Indeed, the current work involves an extensive and relatively self-contained investigation of higher categorical and stacky structures in (vacuum) Einstein gra...
Algebraic properties of the Richard Thompson’s groupfand its applications in cryptography
Yeter, Hakan; Benli, Mustafa Gökhan; Department of Mathematics (2021-3-05)
Thompson’s groupsF,TandV, especiallyF, are widely studied groups in grouptheory. With their unique properties, they appear and become counterexamples formany general problems in different areas of mathematics. Developm...
Limit monomial groups
Bostan, Sezen; Kuzucuoğlu, Mahmut; Department of Mathematics (2021-3-03)
In this thesis, monomial groups, which are obtained by using strictly diagonal embeddings of complete monomial groups over a group of finite degree, are studied. The direct limit of complete monomial groups of finite degre...
Generating the surface mapping class group by torsion elements
Yıldız, Oğuz; Korkmaz, Mustafa; Department of Mathematics (2020-12-24)
n this thesis, we study generators of the mapping class groupMod(Σg)of a closedconnected orientable surfaceΣgof genusg. The mapping class groupMod(Σg)isknown to be generated by three involutions ifg≥8and by two torsion el...
Some New Bounds on Closed Ordinal Ramsey Numbers
Sağlam, Irmak; Kaya, Burak; Department of Mathematics (2020-12-22)
Partition calculus on ordinals was introduced by Erd ̋os and Rado and is a well-studiedsubject. Later on, Baumgartner extended this investigation to topological spaces andstudied topological partition relations on ordinal ...
About the decomposability of almost completely decomposable groups
Budak, Canan; Solak, Ebru; Department of Mathematics (2020-8)
Almost completely decomposable groups are extensions of completely decomposable groups of finite index. They can be written as a sum of indecomposables. Every almost completely decomposable group is the direct sum of indec...
DRBEM solutions of cauchy problem for the magnetohydrodynamic duct flow
Aydın, Cemre; Tezer-Sezgin, Münevver,; Department of Mathematics (2020)
In this thesis, the direct and inverse problems of the MHD flow in rectangular ducts are solved in terms of the velocity of the fluid and the induced magnetic field by using the Dual Reciprocity Boundary Element Method (DR...
Maximal page crossing number of embedded closed legendrian surfaces in closed contact 5-manifolds
Erşen, Özlem; Arıkan, M. Fırat,; Department of Mathematics (2020)
The main purpose of this thesis is to introduce a new Legendrian isotopy invariantfor any closed orientable Legendrian surfaceLembedded in a closed contact5- man-ifold(M,ξ)which admits an "admissable" open book(B,f)(suppor...
BEM solution of unsteady convection-diffusion type fluid flow problems
Fendoğlu, Hande; Bozkaya, Canan; Department of Mathematics (2020)
The time-dependent convection-diffusion-reaction (CDR) type equations with constant and variable convective coefficients are solved by using two different boundary element methods (BEM), namely dual reciprocity BEM (DRBEM)...
Studies on non-weakly regular bent functions and related structures
Pelen, Rumi Melih; Özbudak, Ferruh; Department of Mathematics (2020)
Interest in bent functions over finite fields arises both from mathematical theory and practical applications. There has been lots of literature addressing various properties of bent functions. They have a number of applic...
Van Kampen theorem for persistent fundamental group
Batan, Mehmet Ali; Pamuk, Mehmetcik; Department of Mathematics (2019)
Persistent homotopy is one of the newest algebraic topology methods in order to understand and capture topological features of discrete objects or point data clouds (the set of points with metric defined on it). On the oth...
An Application of the rayleigh-ritz method to the integral-equation representation of the one-dimensional schrödinger equation
Kaya, Ruşen; Taşeli, Hasan; Department of Mathematics (2019)
In this thesis, the theory of the relations between differential and integral equations is analyzed and is illustrated by the reformulation of the one-dimensional Schrödinger equation in terms of an integral equation emplo...
The Compressible euler system and its numerical analysis
Yılmaz, Eda; Okutmuştur, Baver; Department of Mathematics (2019)
In this thesis we analyze the compressible Euler equations in one and two dimensions. For this purpose, we firstly consider a particular form of this system, namely the inviscid Burgers equation, which can be derived by im...
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