Hasan Keleş

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• Academician
• Akademician at Karadeniz Technical University

In this study, group(monoid) and structure of polyloid are investigated. The conditions in the construction of the group and the poloid structure are compared. Even the structure of a non-commutative group is not poloid, the poloid is also a group. The condition (P4) added to a group structure further enriched a group structure. New research is obt...

This paper is about the expression of several properties of known formal logic in ternary logic. The ternary logic is offered a prioritybbeyond the logic of existence and non-existence. It is offered a new perspective to our studies. The main aim of the study is to provide a solution to the concepts of uncertainty in societies [2]. The change of De...

This paper is about the new developments of row and column co-divisors, which are the basis for solving the equations AX= B and XA= B. The algebraic expressions of the verbal expressions are given. The details of the new developments in the new notation are presented. New work is done on the special case for the Sylvester operator S(X) = AX +XB. Th...

This paper is about g-classes of regular matrices and their divisions 1. New investigations using divisibility are done in addition to the work on the collection of g-matrices. Relations with multipliers of regular matrices are analysed. New results obtained from this relation are discussed. The relation of the structure associated with the transpo...

In this study, the generalised Frank matrix is considered. Specialised matrices are lead to the search for new properties. The relation of this special matrix to division is attractive. Hessenberg matrix called the generalized max r-Frank matrix. The min and max matrices with minimum and maximum entries are first given by Pólya and Szegö in the fol...

This study is about th n order derivatives of any differentiable function. For n +  if there exist all derivatives of f of order up to n , then we calculate () () n f x , where x  and its antiderivative using integral calculus approach. The antiderivative (up to a constant) of a function of a single variable at a chosen input value is the main pr...

This study is about row and column co-divisors and products of matrices. Row and column co-divisors on regular matrices are analyzed. The existence of common properties between row and column co-divisors is determined. New developments on previously known column co-divisors are discussed. The relations of properties with row co-divisors and their c...

This article is about logical values. Known logical values are explored in the definition of logic given in B2. The statement “not both” is analyzed. The logical definition B3 is given according to the results obtained. The expansion of logical values in B2 is investigated in logic B3. New logical values are added to the literature. True correspond...

The study is about real functions and their derivatives. In the literature, there are reflections of real functions with respect to the y= f( x) line. This reflection is conditional on being one-to-one and implicit. In this reflection, the condition that the function is defined and continuous is important. The projected part of the function is defi...

This study is about triple fuzzy sets and logic. In the literature, fuzzy logic is expressed as 0,1. This expression is extended to B3. The understanding in 0,1 is not analyzed for cases not involving0 and1 . Statements based on2B definitions are explained inB3. Classification is performed on subsets of the universal set. The reason for this is to...

Hyper g-matrices are studied here. G-classes of regular matrices are first defined by Fiedler and Hall2. Products of regular matrices are analyzed. The situation in the equation AB CD= is considered. For regular matrices, A B C D, i. If B= C , then these matrices are escort elements. ii. If B=(C^-1)^T and regular and diagonal matrices, A, D then...

Citations

Citation and reference status of articles.

This study is about division and right multiplication in ma- trices. The discussion of the properties of multiplication and division is examined. Some results between multiplication based on the row-column relationship and division based on the same relationship are discussed. The commonalities of these results between the processes are emphasized....

This study is about similarity and poloid.

This chapter is first done on the enrichment of formal logic on a monoid. Here, new features, definitions, lemmas and propositions gained with the enrichment of logic are examined. Emphasis is placed on enriched structures. Additional developments in the usage areas of known structures are discussed. The connections of algebraic structures with pow...

This study is about the divisions of defined the Narayana matrix sequence (NMS). The study establishes some common areas of matrices and sequences, which constitute the basic structure of linear algebra. Studies on the subject are brought together here. The definition of division is used. in matrices this study. Transfer of known definitions with d...

https://m.youtube.com/watch?v=OW6SL4nLKCg About 1. Smilarity and Poloid. Presentation time 9.15-9.30 2. On The Base Structure of Logic B3 Presentation time 9.30-9.45

This report is about the matrices of the Narayana sequence.

This study is about multiplication of matrices. Multiplication of real numbers, which can be written along a line, is also two way. Here, the direction is not an influential factor even when the elements are switched. For example 3.2 = 6 and 2.3 = 6. In matrices this makes left and right multiplication is mandatory. Left multiplication is already d...

This study is about digits of numbers in system logic B3. Any real number is written as digits in the binary system, in the ternary system. The numbers in base two and base three are also written in the B3 system ternary logic. These two writing methods are transferred into the third method. The real numbers 0,1 and 0, 1, 2 are written as digits. T...

This article is about the base complement in 𝐵3. The complement method consists of the course of operations around the centroid. The centroid is played an important role in the encoding of numbers. Some of the numbers are smaller than the centroid and some are larger than the centroid. Thus subtraction of any number is implemented by adding its...

This study is about right multiplication of matrices. The size of each real number is not measured. The substitution of two real numbers is not affect the operation. Therefore, the property of commutativity for operations is not noticeable. Multiplication of real numbers, which can be written along a line, is also two way. Here, the direction is no...

This study is about logic 3 B and Boolean. The history of science is first introduced to Boolean Logic by George Boole. George Boole is introduced this subject to science with his book "The Mathematical Analysis of Logic". Today, this beginning is taken to great conclusions. Vital activities in the history of mankind are differentiated. The subject...

This article is about the centroid of any real number. In mathematics, real numbers are the basic of the concept of measure. Real numbers are contributed a lot to the history of Humanity and pioneered the structure of technological developments. Real numbers are enabled the concept of numbers to be unified in the process and this expansion of numbe...

This group is founded with the aim to follow and manage international social and technological logic updates.All researchers who want to contribute to logic updates are welcome to join.

This study is about spin half add operations in B2 and B3. The burden of technological structures has increased due to the increase in the use of today’s technological applications or the processes in the digital systems used. This has increased the importance of fast transactions and storage areas. For this, less transactions, more gain and storag...

Introduction In this section, the solutions of equations and or , and are investigated, where and are functions matrices. More solutions of these are explored in articles in different ways. The focus is on solutions resulting from line and column co-divisors. In addition, the relationship between simplification and extension in rational mat...

Introduction This section is about the poloid created by introducing the new property to the monoid. The concept of monoid, which has a great place in algebraic theory, is the important categorical expression. The expression of monoids in a cryptic manner is made meaningful to new properties. This cryptic categorical structure is made even more...

This study is on a Boolean B or Boolean lattice L in abstract algebra with closed binary operation ∗, complement and distributive properties. Both Binary operations and logic properties dominate this set. A lattice sheds light on binary operations and other algebraic structures. In particular, the construction of the elements of this L set from ide...

In this study, linear transformations with division operation in matrices are investigated. Most of the linear transformations in the literature are done with vector. Examples are given over the field of real numbers. In the study, regular matrices are used instead of vectors. Known property, lemma, theorems of linear transformations are discussed....

This study is about the solution of the equation XA=B, similar to the matrix division revealed by obtaining the solution of the matrix equation AX=B in 2010. This study is about the solution of the equation XA=B, similar to the matrix division revealed by obtaining the solution of the matrix equation AX=B in 2010. The solution of the AX=B equation...

This article is about the symmetrical reflections of profit and loss functions and the functions obtained from them, which are widely used in economic, economic and financial applications of mathematics. It is seen that the applications in the literature are calculated according to the profit and loss accounts alone. Since the occurrence of loss in...

In this study, some features between a grup and a poloid are examined. The study is concerned with the simple group structure and the poloid structure. The group is defined as the mathematical structure that provides the properties of closure, the associativity, the invertibility, and the identy by an operation defined on a set. This mathematical s...

In this study, the definition of poloid and some poloid lemmas and theorems are considered. Parallel to the group structure, subpoloid definitions of the poloid structure are given. Similarities or differences with known subgroup characteristics are examined. Some examples are given. New definition, lemma theorem and properties are investigated. Al...

Introduction This section is about the justification of (iii), which is one of the conditions for the algebraic structure that forms the basis of abstract algebra. The structure monoid of and how it is displayed on the structure is investigated. The definition of the idempotent element on a monoid structure is discussed. The algebraic structures ac...

Introduction This section is on the similarity and equivalence of two matrices. Similar matrices associated with the bases of spaces do the same job. Comparisons of new lemma, theorem and properties are made over the definitions of equivalence and similarity, which are related to the multipliers of the martrices. In addition, the connection between...

In this study, the gradation of involutive matrices, whose definitions were given before, is conducted.The solutions of the equation x^2=1 in real numbers are -1, +1. Meanwhile, in the solution of the equation x^'k=1in real numbers, there is always the number-1,+1 that is independent of the power of k in Z^+. This feature, which isrevealed by this...

This study is about the poloids that are obtained by the formation of a new algebraic structure obtained by adding the condition (G4) obtained from the solution of the equation XA = B and B|A to the definition of monoid. The (G4) property is based on the factorial property of a noncommutative matrix. The (G4) property is based on the factorial prop...

This section consists of two main parts. First part is about the demand and supply function, which is one of the functions of a single variable, which is frequently used in economic, economic, business, financial, applications of mathematic.

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 d...

This work is on rational matrices. It is investigated whether there is a property similar to the known properties of rational numbers in real numbers. In previous studies, it is obtained to write rational matrices with equal denominators by adding them to the common denominator. If the denominators are different, it is given as a research problem (...

In this study, the definition of co-division by row is used in March-2022, which is required to solve some of the problems arising in the columnar co-division operation, which is the source of the "Division in Matrices" I defined in 2010 (Keleş, 2022). Let A and B be two regular square matrices of order n . The determinant of the new matrix obtaine...

demand, average demand, supply, average supply, profit, loss, income

demand, supply, breakeven point, profit, loss, income function, expense function, profit function, loss function

horizontal division, vertical division, row co-divisor, column co-divisor

Bu makale, Matematiğin ekonomik, iktisadi, mali uygulamalarında oldukça fazlaca kullanılan, kâr ve zarar fonksiyonlarının ve bunlardan elde edilen fonksiyonların simetrik yansımaları üzerinedir. Literatürde var olan uygulamalarda kâr ve zarar hesapları tek başlarına göre hesaplandıkları görülmektedir. Bir ekonomik faaliyette, zararın oluşması, kârı...

This article is about the symmetrical reflections of profit and loss functions and the functions obtained from them, which are widely used in economic, economic and financial applications of mathematics. It is seen that the applications in the literature are calculated according to the profit and loss accounts alone. Since the occurrence of loss in...

In this book we give, for the first time, the definitions of “co-divide” and division of two matrices with the same dimension. We will see that the definitions here are analogous to the case in real numbers. Here we research their properties and give some examples. Rational matrices was define by “Matrix Division”. We will see that the properties h...

Introduction to linear algebra.

In this paper, the main purpose of the analysis of variance, for example more than two i x 's changing average end x from deviation of the sum of squares of the partitioning as factors that cause this deviation and analyzing the discussion is made. At the end of this analysis, the difference between the fixed and the changing average is examined, i...

In this paper, Average variants according to the changing mean. According to the constant average, some known average varieties; Arithmetic mean, Geometric mean, and Harmonic mean.

In this paper, the main axes of conic sections given according to a simple function as the axis of reflection y =g( x) is studied. it is observed that there is no conical section after the reflected conical section. There, we consider reflection axes are the linear function. In this case, the conic section is reflected as a distinct reflection. Whe...

In this work, we have given examples of how systems make it impossible to use applications with constant averages over time. Examples of time, space, opportunities, and changing the average increase the load and speed of the systems are given. The problem is formalized using our knowledge of probability theory.

In this paper, the main axes of conic sections given according to a simple function as the axis of reflection y =g( x) is studied. it is observed that there is no conical section after the reflected conical section. There, we consider reflection axes are the linear function. In this case, the conic section is reflected as a distinct reflection. Whe...

In this study, the symmetrical state is of simple function given according a simple function y= g (x) the axis of reflection. Some kind of reflections are explored. The general conditions under which the reflecting function is one-to-one are studied. If the reflecting function is one-to-one, it is determined how the results will emerge.

In-nested n-function is a study of the state of infinity.

ÇÖZÜMLÜ MATEMATİK-I-, ANALİZ-I-, MÜHENDİSLER, EKONOMİSTLER, MATEMATİKÇİLER İÇİN

In this work, we have given examples of how systems make it impossible to use applications with constant averages over time. Examples of time, space, opportunities, and changing the average increase the load and speed of the systems are given. The problem is formalized using our knowledge of probability theory.

Please prove the identity given in the picture is correct.

In this paper, the symmetrical situation is of conic sections given according to a simple function as the axis of reflection y = g(x) is studied. Some kinds of reflections are explored. If simple functions are one-to-one, how are the conical sections reflected when in this case? The case in which the domain of given conic section Ax 2 + Bxy + Cy 2...

In this paper, the symmetrical situation is of conic sections given according to a simple function as the axis of reflection y = g(x) is studied. Some kinds of reflections are explored. If simple functions are one-to-one, how are the conical sections reflected when in this case? The case in which the domain of given conic section Ax 2 + Bxy + Cy 2...

In this book; The first grades of the universities are; For Social Sciences The subjects which will form the basis of Mathematics-I-, General Mathematics, Mathematics-I-, Analysis-I- courses were given. Various examples of these issues were solved. Although there are many sample solutions; bookless book tracking is not recommended. Despite the rigo...

GENERAL MATHEMATICS-I- & MATHEMATICS-I-

General Mathematics

ON MAIN AXES OF CONIC SECTIONS REFLECTION

The new result in involutive matrices

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 op...

In this study, the symmetrical state is of simple function given according a simple function y g x = the axis of reflection. Some kind of reflections are explored. The special conditions under which the reflecting function is one-to-one are studied. If the reflecting function is one-to-one, it is determined how the results will emerge. We know simp...

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 not...

1] Rafael Bru,, Maria T. Gassó,, Isabel Giménez, and José A. Scott, The Hadamard Product of a NonsingularGeneral H-Matrix and Its Inverse Transpose Is Diagonally Dominant, Hindawi Publishing Corporation Journalof Applied Mathematics Volume, Article ID 264680, (2015), 6 pages. [2] Keles, H., The Rational Matrices, New Trends in Nanotechnology and No...

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. All of these geometric figures may be obtained by the intersection a double cone with a plane....

Mathematics creates the systematic thinking of every human being who carries his or her thoughts and allows them to use it. Even with the numbers, discover your future and bring your plan together.

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

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 rela...

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...