Matematik Bölümü Tez Koleksiyonu
https://hdl.handle.net/11655/308
2024-02-29T04:39:10ZIntegrals of Motion in Curved Space-Time
https://hdl.handle.net/11655/34337
Integrals of Motion in Curved Space-Time
Demir, Toygun Kutkar
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 analysis for the motion of a relativistic particle in curved
space-time is given and the relation of the integrals of motion to the Killing vectors and the
Killing tensors of the space-time in which the particle moves is explained. As examples,
motion on the Schwarzschild, the Kerr and the generalized Lense-Thirring space-times are
studied.
2023-07-12T00:00:00ZRiesz Uzaylarında Netlerin Yakınsaklıkları Üzerine
https://hdl.handle.net/11655/34290
Riesz Uzaylarında Netlerin Yakınsaklıkları Üzerine
Eryüksel, Ezgi Han
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 are topological, some
of them are not. However they are convergences that only preserve the order struc ture. Unbounded order convergence was firstly defined by De Marr under the name of
"individual convergence" and then examined under the name of "uo-convergence" by
Nakano. Recently, many researchers have focused on the properties of different types
of unbounded convergence. Unbounded norm convergence was firstly introduced and
studied by Troitsky. Finally, Zabeti uaw-convergence defined and worked on. In this
thesis, all these types of convergence is studied and the relationships between them are
investigated.
2023-01-01T00:00:00Zf-Supplemented Lattices
https://hdl.handle.net/11655/34284
f-Supplemented Lattices
Can, Elif
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 f-small element under a lattice homomorphism
need not be f-small unlike the module case. For compactly generated compact lattices
f-supplement elements are compact. For compactly generated lattices, f-radical is the join
of all f-small elements. Moreover for compact lattices, f-radical itself is an f-small element.
Let L be a compactly generated compact lattice. If L is f-supplemented, then the quotient
sublattice 1/ rad_f (L) of L is semiatomic. A compact lattice L is f-supplemented if and
only if every maximal element m of L with f ≤ m has an f-supplement in L. A join of
f-supplemented lattices containing f is f-supplemented. Let L be a compact lattice and
f ≤ a be an element of L. If a/0 is f-supplemented and 1/a has no maximal element, then
L is f-supplemented. If a lattice L is amply f-supplemented, then the quotient sublattice
1/a is amply (f ∨ a)-supplemented for every element a of L and the sublattice a/0 is amply
f-supplemented for every f-supplement element a of L. L is amply f-supplemented if and
only if for every element a of L, there is an element x ≤ a such that the sublattice x/0 is
f-supplemented and the inequality x ≤ a is f-cosmall in L.
2023-01-01T00:00:00ZTheory of Orthogonally Additive Operators
https://hdl.handle.net/11655/34265
Theory of Orthogonally Additive Operators
Bolat, Sezer
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 significant role in constructing the theory of orthogonally additive
operators, and it is also studied in this thesis.
The first chapter is dedicated to the study of fragments. The concept is explored in the context
of vector lattices and lattice-normed vector spaces. The conclusions derived from Sections
2.2 and 2.3 of Chapter 2 can be found in [1].
The second chapter introduces the classes of orthogonally additive operators defined on
vector lattices and a novel class of vector lattice known as C-complete. This chapter also
addresses the extension problems associated with orthogonally additive maps. Various
examples and conclusions are provided to support the findings.
In the last chapter, orthogonally additive operators are examined in the context of lattice
normed spaces.
2023-01-01T00:00:00Z