Matematik Bölümü Tez Koleksiyonu
https://hdl.handle.net/11655/308
2023-06-10T03:51:59ZTOPOLOJİK OYUNLARDA ÖRTÜSEL ÖZELLİKLER
https://hdl.handle.net/11655/33407
TOPOLOJİK OYUNLARDA ÖRTÜSEL ÖZELLİKLER
SARAF, Haidar dh jafar
This thesis consists of five chapters. The first chapter is devoted to game theory and the
historical development of topological games, which is the subject of the thesis. In the second
part, some definitions and theorems that will be used in the thesis are given.
In the third chapter, Menger and Rothberger covering properties are defined and some
examples providing these properties are given. In the fourth chapter, topological games are
examined in detail. Some examples of games such as point-open game, Rothberger game,
Menger game are given and these games are examined with winning strategies. In addition,
the concepts of equivalent and dual games are also defined.
In the fifth chapter, which is the last chapter, Banach-Mazur games, which form the basis
of game theory and are associated with Baire Category theorem, are included. In addition,
D-spaces and their relations with covering properties are also examined.
2023-01-01T00:00:00ZLES-C Modeli İle Akışkan-Akışkan Etkileşimi Problemlerinde Modelleme Hatasının Azaltılması
https://hdl.handle.net/11655/33390
LES-C Modeli İle Akışkan-Akışkan Etkileşimi Problemlerinde Modelleme Hatasının Azaltılması
Önal, Eda
In this study, a numerical method is proposed for a fluid-fluid interaction problem where two flows are coupled through a nonlinear joint interface and one or both of these flows are at high Reynolds numbers. It is known that the nonlinear coupling equation, known as the rigid-lid condition, creates some difficulties for atmosphere-ocean problems. For this interaction problem, a novel turbulence model NS-ω-C is proposed from the family of LES- models. Combining this NS-ω-C model with the Geometric Averaging partitioning method (GA), the NS-ω-C-GA model is obtained, which is shown to have essential numerical properties. First of all, the previous solvers can be used for the subdomains in applications of atmosphere-ocean problems. Furthermore, it is numerically shown that the NS-ω-C model gives better results than the NS-ω model, as LES-C turbulence models use the defect correction approach to efficiently reduce the modeling error of the LES models. It will be proved both theoretically and numerically that the proposed method gives stable results with high accuracy.
2023-01-01T00:00:00ZHelson Beurling Teoremi ve Uygulamaları
https://hdl.handle.net/11655/27155
Helson Beurling Teoremi ve Uygulamaları
Taş, Gizem
In thesis we treat the celebrated Helson-Beurling Theorem which charac- terizes the closed subspaces of L2 which are invariant under the shift operator. We also treat the characterization of invariant subspaces of the Volterra op- erator as an application of Helson-Beurling Theorem due to D. Sarason, char- acterization of multiplication and translation invariant subspaces of L2(R) as an application of Helson-Beurling theorem due to A. Katavolos and S. Power and characterization of multiplication and dilation invariant subspaces of L2(R) as an application of Helson-Beurling theorem due to A. Katavolos and S. Power.
2018-01-01T00:00:00ZPure Direct Injectıve Objects in Grothendıeck Categorıes
https://hdl.handle.net/11655/27121
Pure Direct Injectıve Objects in Grothendıeck Categorıes
Yiğit, Aliye
We study generalizations of the concept of direct-injectivity (respectively pure-direct-injectivity) from module categories to abelian categories (respectively Grothendieck categories). We examine for which categories or under what conditions direct-injective objects are injective or quasi-injective. Also we examine for which categories or under what conditions pure-direct-injective objects are injective, quasi-injective, pure-injective or direct-injective. We investigate classes all of whose objects are direct-injective (respectively pure-direct-injective). We also give applications of some results to module categories and comodule categories.
2022-01-01T00:00:00Z