Matematik Bölümü
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SOME RESULTS ON A GROUP UNDER WHICH SYMMETRIC REED-MULLER CODES ARE INVARIANT
(Fen Bilimleri Enstitüsü, 2024)The Reed-Muller codes are a family of error-correcting codes that have been widelystudied in coding theory. In 2020, Wei Yan and Sian-Jheng Lin introduced a variant ofReed-Muller codes so called symmetric Reed-Muller codes. ... -
Butson-Hadamard Codes and Related Quantum Codes
(Fen Bilimleri Enstitüsü, 2024)A Butson-Hadamard (BH) matrix H is a square matrix of dimension n whose entries are complex roots of unity such that HH∗ = nI. In the first part of this thesis, we deal with codes obtained from BH matrices, called BH codes, ... -
Ağırlıklı Projektif Uzaylar Üzerindeki Kodlar ve Onların Cebirsel Değişmezleri
(Fen Bilimleri Enstitüsü, 2024)Weighted projective spaces, when considered in light of the geometric definition for projective spaces and allowing non-trivial weights, exhibit unique structures both geometrically and algebraically. By non-trivial weights, ... -
Simitli Kodlar ve Kod Temelli Kriptografi
(Fen Bilimleri Enstitüsü, 2024)In recent years, improving both technology and information availability in any area is getting easier day by day. Classical encryption methods have to face the threat of quantum computers. Therefore, a new cryptographic ... -
Topolojik Vektör Latisleri Üzerinde Tanımlı Operatörlerin Oluşturduğu Ailelerin Özelliklerinin İncelenmesi
(Fen Bilimleri Enstitüsü, 2024)Recently, research on various classes of operators based on norm convergence and order convergence in Banach lattices has made significant progress. Similarly, the topological properties and vector lattice structures of ... -
Güçlü İkili Lineer Olmayan Schrödinger Sistemi için Yapı Koruyan Sayısal Bir Yöntem
(Fen Bilimleri Enstitüsü, 2024)In this thesis, a new structure-preserving numerical method for strongly coupled nonlinear Schrödinger equation (SCNLS) is presented. It is shown that the proposed new method conserves the discrete mass and energy. Numerical ... -
Riesz Uzayları Üzerinde Tanımlı Bazı Özel Operatörler ve Operatör Yarı gruplarının İncelenmesi
(Fen Bilimleri Enstitüsü, 2024)The study of operator classes in lattice theory holds great importance. The analysis of operators based on order convergence and norm convergence has made significant contributions to operator theory. Additionally, some ... -
Çatılar Üzerindeki Bazı Topolojik Özellikler
(Fen Bilimleri Enstitüsü, 2024)The aim of this thesis is to explore the concept of frame, which is a special kind of a lattice, and to examine their topological properties, such as separation axioms and compactness. The study consists of six chapters. ... -
Modüllerin Baer-Kaplansky Sınıfları Üzerine Bir Çalışma
(Fen Bilimleri Enstitüsü, 2024)If A and B are torsion groups whose EndZ(A) and EndZ(B) are isomorphic with Ψ, then A and B are isomorphic. Moreover, if A and B are isomorphic with ϕ, then Ψ(η) = ϕηϕ−1. This expression is known as “Baer-Kaplansky ... -
Integrals of Motion in Curved Space-Time
(Fen Bilimleri Enstitüsü, 2023-07-12)Integrals of motion are the quantities that remain constant during the motion of a point particle that allow to determine various important properties without solving the equations of motion. In this thesis, a systematic ... -
Riesz Uzaylarında Netlerin Yakınsaklıkları Üzerine
(Fen Bilimleri Enstitüsü, 2023)Banach lattices can be equipped with many convergence structures such as order, relative regular, unbounded order, unbounded norm convergence, and absolutely un bounded weak convergence. While some of these convergences ... -
f-Supplemented Lattices
(Fen Bilimleri Enstitüsü, 2023)The main purpose of this thesis is to generalize some known results about F-supplemented modules to lattices. Let L be a complete modular lattice with smallest element 0 and greatest element 1. A homomorphic image of an ... -
Theory of Orthogonally Additive Operators
(Fen Bilimleri Enstitüsü, 2023)An orthogonally additive operator is a map that satisfies the additivity property under the disjointness condition. This thesis focuses on the theory of orthogonally additive operators. The concept of fragments plays a ... -
Conditional Direct Summand Properties Via Relative Injectivity
(Fen Bilimleri Enstitüsü, 2023)In this study, CS-modules and some of their generalizations, conditional direct summands feature modules will be handled with the help of relative injectivity and the results in this direction will be compiled and the ... -
CONDITIONAL DIRECT SUMMAND PROPERTIES VIA RELATIVE INJECTIVITY
(Fen Bilimleri Enstitüsü, 2023)In this study, CS-modules and some of their generalizations, conditional direct summands feature modules will be handled with the help of relative injectivity and the results in this direction will be compiled and the ... -
Topolojik Oyunlarda Örtüsel Özellikler
(Fen Bilimleri Enstitüsü, 2023)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 ... -
LES-C Modeli İle Akışkan-Akışkan Etkileşimi Problemlerinde Modelleme Hatasının Azaltılması
(Fen Bilimleri Enstitüsü, 2023)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 ... -
Helson Beurling Teoremi ve Uygulamaları
(Fen Bilimleri Enstitüsü, 2018)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 ... -
Pure Direct Injectıve Objects in Grothendıeck Categorıes
(Fen Bilimleri Enstitüsü, 2022)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 ... -
Pure Direct Projective Objects in Grothendieck Categories
(Fen Bilimleri Enstitüsü, 2022)We study generalizations of the concept of direct-projectivity (respectively pure-direct-projectivity) from module categories to abelian categories (respectively Grothendieck categories). We examine for which categories ...
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