HASAN KELEŞ | Karadeniz Technical University (original) (raw)

Teaching Documents by HASAN KELEŞ

Conic sections are formed when you intersect a plane with a right circular cone. In this tutorial... more Conic sections are formed when you intersect a plane with a right circular cone. In this tutorial, we will learn more about what makes conic sections special. Here we will have a look at three different conic sections ellipses, parabolas, and hyperbolas.

In this study, the matrix division that I described in 2010, is brought on developments in measur... more In this study, the matrix division that I described in 2010, is brought on developments in measurement and evaluation. Mathematics education takes the goals the development of thought and finalization. Therefore; the role multiple division (division of matrix) is very important. Today, there are one 1st, one 2nd and 3the,… in the scoring system of the Group. This operation explains n times  1 st , n times  2 nd and n times  3 the ,… in the scoring system of the group. Thus avoided fragility of success. This process reveals the diversity of different individuals. If considering the growing population and its functions then solidarity and improving their success soul in society, by destroying the vicious bickering, continues integrity and continuity in education.

In this study, we deal with functions from the square matrices to square matrices, which the same... more In this study, we deal with functions from the square matrices to square matrices, which the same order. Such a function will be called a linear transformation, defined as follows: Let M n (R) be a set of square matrices of order n, n ϵ S, and A be regular matrix in M n (R), then the special function T A : M n (R) → M n (R)   A X X T X A  is called a linear transformation of M n (R) to M n (R) the following two properties are true for all X,Y ϵ M n (R), and scalars α ϵ R: i. T A (X+Y) = T A (X) + T A (Y). (We say that T A preserves additivity) ii. T A (αX)= αT A (X) (We say that T A preserves scalar multiplication) In this case the matrix A is called the standard matrix of the function T A. Here, we transfer some well known properties of linear transformations to the above defined elements in the set all { T A : A regular in M n (R)} [1].

Papers by HASAN KELEŞ

Al-Salam Journal for Engineering and Technology, 2022

In this study, the relationships between matrix division and some matrix properties such as trans... more In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided features is discussed under which conditions. These features have been determined. Examples are given for features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.

On Results Between Matrix Division and Some other Matrix Operations, 2022

In this study, the relationships between matrix division and some matrix properties such as trans... more In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided
features is discussed under which conditions. These features have been determined. Examples are given for
features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.

In this study, the different approaches of the matrix division and the generalization of Cramer&#... more In this study, the different approaches of the matrix division and the generalization of Cramer's rule and some examples are given.

As we known that the notion of linear space can be given in tern the lines of the set of points, ... more As we known that the notion of linear space can be given in tern the lines of the set of points, which satisfying certain axioms. In this case all the linear spaces in the usual sense, in particular the Euclidean plane (spaces), are a linear space in the sense line and points. In this work we want begin and investigate the generalization of the notion of linear space in tern the fuzzy lines. Let ℙ be a finite set with at least three points, L be a finite F-lattice (i.e. completely distributive lattice with an order-reversing involution ':LL ) and í µíµ ⊆ í µí°¿ ℙ be a set of the all Fuzzy subsets of ℙ. MSC2000: 06F20, 46A16, 47S50, 54F05.

arXiv: General Mathematics, 2018

In this study we follow a new framework for the theory that offers us, other than traditional, a ... more In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy Linear Spaces (FLS) S=(N,D). In this case, to operate on these spaces the necessary preliminaries, concepts and operations in lattices relative to FLS are introduced. Some definitions, such that k-fuzzy point, k-fuzzy line are given. Then we correspond these definitions to the definitions in usually linear spaces. We investigate some combinatorics properties of FLS. In some examples in the case where ILI=3*. We see some differences. In general, taking an ordered lattice Ln={0,a1,a2,...,an,1} we observe how some combinatorics formulas and properties are changed. In FLS the dimension concept is a set. We produce some general formulas by using some trivial examples. Furthermore, we generalize de Bruijn-Erd\"os Theorem in [2].

In this study we follow a new framework for the theory that offers us, other than traditional, a ... more In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy Linear Spaces (FLS)   D N S , . In this case, to operate on these spaces the necessary preliminaries, concepts and operations in lattices relative to FLS are introduced. Some definitions, such that k-fuzzy point, k-fuzzy line are given. Then we correspond these definitions to the definitions in usually linear spaces. We investigate some combinatorics properties of FLS. In some examples in the case where   L . We see some differences. In general, taking an ordered lattice       , ,..., , , n n a a a L  we observe how some combinatorics formulas and properties are changed. In FLS the dimension concept is a set. We produce some general formulas by using some trivial examples. Furthermore, we generalize de Bruijn-Erdös Theorem in [2]. Introduc...

This study is based on points, and some given properties and definitions about vertex, neighbours... more This study is based on points, and some given properties and definitions about vertex, neighbours and independent or dependent definitions in the Graphs are extended to FLS. It is seen that   , SD  FLS is a complete graph. Arguments of graphs are transferred to FLS. Therefore, as the necessary preliminaries, concept and operations in graph relative to FLS are introduced. Their combinatoric properties are investigated. We know from [2] that FLS is a generalization of graph in the idea fuzzy. Some studies are performed on Health and Engineering sciences particularly in Dentistry and Mining at the FLU [5]. MSC2000 : 05C15, 11B65, 06F20, 04A72,15A03.

In this study we follow a new framework for the theory that offers us, other than traditional, a ... more In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy Linear Spaces (FLS). In this case, to operate on these spaces the necessary preliminaries, concepts and operations in lattices relative to FLS are introduced. Some definitions, such that k-fuzzy point, k-fuzzy line are given. Then we correspond these definitions to the definitions in usually linear spaces. We investigate some combinatorics properties of FLS. In some examples in the case where ·. We see some differences. In general, taking an ordered lattice we observe how some combinatorics formulas and properties are changed. In FLS the dimension concept is a set. We produce some general formulas by using some trivial examples. Furthermore, we generalize de Bruijn-Erdös Theorem in [2]. Keywords k-fuzzy point; k-fuzzy line; FLS; Generalized de Bruijn-Erdös Theorem Introduction k-point, k-line forLinear Spaces, d-dimensional Linear Spaces were studied by some authors like Batten [5] and Barwick [6]. Here, we give a very short proof to well-known the theorem of de Bruijn and Erdös [4,5] . And also, we have been collected all them from the above papers and from [1,2]. In this paper, we extended the Theorem de Bruijn and Erdös. For this we have to give.

Al-Salam Journal for Engineering and Technology, 2022

On Results Between Matrix Division and Some other Matrix Operations, 2022

In this study, the relationships between matrix division and some matrix properties such as trans... more In this study, the relationships between matrix division and some matrix properties such as transpose, simplification, and expansion are discussed. Unless otherwise stated, our matrices are real number matrices. The relationship between our definitions of column co-divisor and row co-divisor of a matrix on another matrix is examined. Equality and differences of these connections are observed. The validity of the provided
features is discussed under which conditions. These features have been determined. Examples are given for
features that do not. Some of the obtained properties bring different solutions to the solution of linear equation systems, which are encountered in the literature and are more used. This led us to examine the relationship between the defined division operation and transpose. Investigations on this subject enabled the presentation of new definitions, lemmas and theorems. Examination of these offered a broader perspective on the given mathematical expressions.

arXiv: General Mathematics, 2018

In this study we follow a new framework for the theory that offers us, other than traditional, a ... more In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy Linear Spaces (FLS)   D N S , . In this case, to operate on these spaces the necessary preliminaries, concepts and operations in lattices relative to FLS are introduced. Some definitions, such that k-fuzzy point, k-fuzzy line are given. Then we correspond these definitions to the definitions in usually linear spaces. We investigate some combinatorics properties of FLS. In some examples in the case where   L . We see some differences. In general, taking an ordered lattice       , ,..., , , n n a a a L  we observe how some combinatorics formulas and properties are changed. In FLS the dimension concept is a set. We produce some general formulas by using some trivial examples. Furthermore, we generalize de Bruijn-Erdös Theorem in [2]. Introduc...

In this study we follow a new framework for the theory that offers us, other than traditional, a ... more In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy Linear Spaces (FLS). In this case, to operate on these spaces the necessary preliminaries, concepts and operations in lattices relative to FLS are introduced. Some definitions, such that k-fuzzy point, k-fuzzy line are given. Then we correspond these definitions to the definitions in usually linear spaces. We investigate some combinatorics properties of FLS. In some examples in the case where ·. We see some differences. In general, taking an ordered lattice we observe how some combinatorics formulas and properties are changed. In FLS the dimension concept is a set. We produce some general formulas by using some trivial examples. Furthermore, we generalize de Bruijn-Erdös Theorem in [2]. Keywords k-fuzzy point; k-fuzzy line; FLS; Generalized de Bruijn-Erdös Theorem Introduction k-point, k-line forLinear Spaces, d-dimensional Linear Spaces were studied by some authors like Batten [5] and Barwick [6]. Here, we give a very short proof to well-known the theorem of de Bruijn and Erdös [4,5] . And also, we have been collected all them from the above papers and from [1,2]. In this paper, we extended the Theorem de Bruijn and Erdös. For this we have to give.