For t an integer, a Pt set is defined as a set of m positive integers with the property that the ... more For t an integer, a Pt set is defined as a set of m positive integers with the property that the product of its any two distinct element increased by t is a perfect square integer. In this study, the certain special P-5, P+5, P-7 and P+7 sets with size three are considered. It is demonstrated that they cannot be extended to P-5, P+5, P-7 and P+7 with size four. Also, some properties of them are proved.Bir t tamsayısı için Pt kümesi, herhangi iki tane farklı elemanının çarpımının t fazlası bir tamkare olma özelliğine sahip m tane pozitif tamsayıdan oluşan bir küme olarak tanımlanır. Bu çalışmada, üç elemanlı bazı P-5, P+5, P-7 ve P+7 kümeleri gözönüne alınıyor. Bu kümelerin dört elemanlı P-5, P+5, P-7 ve P+7 kümelerine genişletilemez olduğu gösteriliyor. Ayrıca, bu kümelerin bazı özellikleri kanıtlanıyor
Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such th... more Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that product of any two of them by adding k is a square. In the present paper, we consider some regular P-k- triples and prove that they can not be extendible to Diophantine quadruple when k = -2 by using fundamental solution of Pell equations. Also, we determine several significant properties about such sets.WOS:0004560917000072-s2.0-8505037341
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2019
On the C *-algebra valued G-metric space related with fixed point theorems There are many fixed p... more On the C *-algebra valued G-metric space related with fixed point theorems There are many fixed point results in the various kinds of metric spaces such as b-metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non-commutative Banach spaces etc. In this work, we consider the one of modern methods as C *-algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C *-algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result.
In modern industrial manufacturing processes, induction motors are broadly utilized as industrial... more In modern industrial manufacturing processes, induction motors are broadly utilized as industrial drives. Online condition monitoring and diagnosis of faults that occur inside and/or outside of the Induction Motor Drive (IMD) system make the motor highly reliable, helping to avoid unscheduled downtimes, which cause more revenue loss and disruption of production. This can be achieved only when the irregularities produced because of the faults are sensed at the moment they occur and diagnosed quickly so that suitable actions to protect the equipment can be taken. This requires intelligent control with a high-performance scheme. Hence, a Field Programmable Gate Array (FPGA) based on neuro-genetic implementation with a Back Propagation Neural network (BPN) is suggested in this article to diagnose the fault more efficiently and almost instantly. It is reported that the classification of the neural network will provide the output within 2 µs although the clone procedure with microcontroll...
Nonlinear phenomena are very important in a variety of scientific fields. Finding solutions of no... more Nonlinear phenomena are very important in a variety of scientific fields. Finding solutions of nonlinear partial differential equations is one of the most difficult problems in mathematics and physics. A precise solution is derived for these non-linear evolution equations (NLEEs), which has been illustrated by the solitary wave solutions for the fifth degree equations, the Sawada-Kotera equation, and then we apply the Backland transformation, which shows a new special precise solution.
Coding Theory - Recent Advances, New Perspectives and Applications [Working Title], 2022
In this work, we use ‘Partial Group’ notion and we do further investigations about partial groups... more In this work, we use ‘Partial Group’ notion and we do further investigations about partial groups. We define ‘Partial Normal Subgroup’ using partial conjugation criteria and we prove few results about partial normal subgroups analogous to normal groups. Also, we define congruence relation for partial groups and via this relation, we state ‘The Quotient of Partial Group or Factor Group’. We give isomorphism theorems for partial groups. Explicitly, this is an analogous concept to group theory and our main is where differences partial groups from groups.
Journal of the Indonesian Mathematical Society, 2020
In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spac... more In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spaces. We get a C*-algebra valued metric space which get values in noncomutative operators. We demonstrate existance and uniqeness of coupled fixed point in a such space. Besides, we support our results by giving numerical examples.
For 𝑡 an integer, a 𝑃𝑡 set is defined as a set of 𝑚 positive integers with the property that the ... more For 𝑡 an integer, a 𝑃𝑡 set is defined as a set of 𝑚 positive integers with the property that the product of its any two distinct element increased by 𝑡 is a perfect square integer. In this study, the certain special 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 sets with size three are considered. It is demonstrated that they cannot be extended to 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 with size four. Also, some properties of them are proved.
The aim of this paper is to determine and investigate the continued fractions expansions of wd fo... more The aim of this paper is to determine and investigate the continued fractions expansions of wd for the real quadratic number fields Q( √ d) for which the period has constant elements that are completely equal to 2 (except the last digit of period) in the symetric part of the period of integral basis element where d ≡ 2, 3 mod 4 is a square free positive integer. Moreover, we give new explicit formulas for the fundamental unit d and Yokoi’s d-invariants nd and md in relation to continued fraction expansion of such form of wd. These new formulas are not known in the literature of real quadratic fields. Such types of real quadratic fields are classified as new results.
The aim of this paper is to establish a new Coupled Fixed Point Theorems for C∗-algebra valued b-... more The aim of this paper is to establish a new Coupled Fixed Point Theorems for C∗-algebra valued b-metric spaces. As an application of our result, we discuss the existence and uniqueness results for Couple Fixed Point Theorem in C∗-algebra valued b-metric spaces. We also give conclusion to demonstrate our result.
Indonesian Journal of Electrical Engineering and Computer Science, 2021
Nowadays, with the advences in ICT and rapid development of mobile internet; media information sh... more Nowadays, with the advences in ICT and rapid development of mobile internet; media information shared on the various communication networks requires the existence of adequate security measures. Cryptography becoming an effective way to meet these requirements and for maintain the confidentiality. However, communicating with encrypted messages requires secret key exchange, which is a part of a complex protocol. In this paper, we propose a new method for exchanging key based on Diffie-Hellman protocol and image registration with fast fourier transform, the principle of this method consists to concealing the key in a set of transformed images. Therefore, image registration allows finding transformations between images, which become a tool for recovering the key by the receiver.
In Number Theory, the notion of the quadratic fields is difficult task. There are many different ... more In Number Theory, the notion of the quadratic fields is difficult task. There are many different approaches such as genus theory, composition of binary quadratic forms, and class field theory as a developmental tool for quadratic fields. Moreover, many books and papers on the number theory apply many different methods like continued fraction expansions, class number, regulators in the class group, etc. . . Recently, class number which is very difficult to calculate is used in the cryptology and security. In this paper, we determine the real quadratic fields coincide with positive square free integers d including specific continued fraction expansion of integral basis element in the case of d ≡ 2, 3 (mod 4) or d ≡ 1 (mod 4), where `(d) is the period length of continued fraction expansion. Besides, we deal with determining the fundamental unit and Yokoi’s d-invariants nd and md in the relation to continued fraction expansion of wd, we also give several numerical tables to support our ...
The aim of this paper is to construct a relation between tribonacci numbers and generalized tribo... more The aim of this paper is to construct a relation between tribonacci numbers and generalized tribonacci numbers. Besides, certain conditions are obtained to generalize the representation of a positive integer [Formula: see text] which is determined in [S. Badidja and A. Boudaoud, Representation of positive integers as a sum of distinct tribonacci numbers, J. Math. Statistic. 13 (2017) 57–61] for a [Formula: see text]-generalized Fibonacci numbers [Formula: see text]. Lastly, some applications to cryptography are given by using [Formula: see text].
The primary purpose of this paper is to classify real quadratic fields Q(√d) which include the fo... more The primary purpose of this paper is to classify real quadratic fields Q(√d) which include the form of specific continued fraction expansion of integral basis element 𝑤𝑑 for arbitrary period length l = l(𝑑) where d ≡ 2,3(mod4) is a square free positive integers. Furthermore, the present paper deals with determining new certain parametric formulas of fundamental unit and Yokoi’s d-invariants nd , md for such real quadratic fields. All results are also supported by several numerical tabular forms.
Purpose of this paper is to determine some regular non-extendible D(n) triples for some fixed int... more Purpose of this paper is to determine some regular non-extendible D(n) triples for some fixed integer n. Besides, paper includes a number of algebraic properties for such diophantine sets with size three.
International Journal of Nonlinear Analysis and Applications, 2019
The system of double equations with three unknowns given by d+ay+bx+cx^2 = z^2 , y+z=x^2 is analy... more The system of double equations with three unknowns given by d+ay+bx+cx^2 = z^2 , y+z=x^2 is analysed for its infinitely many non-zero distinct integer solutions. Different sets of integer solutions have been presented. A few interesting relations among the solutions are given.
Notes on Number Theory and Discrete Mathematics, 2019
We obtain infinitely many non-zero integer triples (x, y, z) satisfying the nonhomogeneous bi-qua... more We obtain infinitely many non-zero integer triples (x, y, z) satisfying the nonhomogeneous bi-quadratic equation with three unknowns 2 2 4 11() 3() 10. x y x y z − + + = Various interesting properties among the values of x, y, z are presented. Some relations between the solutions and special numbers are exhibited.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2019
Some results on a special type of real quadratic fields In this paper, we determine the real quad... more Some results on a special type of real quadratic fields In this paper, we determine the real quadratic fields Q(√ d) coincide with positive square-free integers d including the continued fraction expansion form of w d = a0; 7, 7,. .. , 7 −1 , a . Furthermore, we deal with determining fundamental units and Yokoi's d-invariants n d and m d in the relation to continued fraction expansion of w d where (d) is a period length of w d for the such type of real quadratic number fields Q(√ d). The present paper improve the theory of fundamental unit which generates the unit group of real quadratic fields and also determine the special form of continued fraction expansion of integral basis element in real quadratic fields.
For t an integer, a Pt set is defined as a set of m positive integers with the property that the ... more For t an integer, a Pt set is defined as a set of m positive integers with the property that the product of its any two distinct element increased by t is a perfect square integer. In this study, the certain special P-5, P+5, P-7 and P+7 sets with size three are considered. It is demonstrated that they cannot be extended to P-5, P+5, P-7 and P+7 with size four. Also, some properties of them are proved.Bir t tamsayısı için Pt kümesi, herhangi iki tane farklı elemanının çarpımının t fazlası bir tamkare olma özelliğine sahip m tane pozitif tamsayıdan oluşan bir küme olarak tanımlanır. Bu çalışmada, üç elemanlı bazı P-5, P+5, P-7 ve P+7 kümeleri gözönüne alınıyor. Bu kümelerin dört elemanlı P-5, P+5, P-7 ve P+7 kümelerine genişletilemez olduğu gösteriliyor. Ayrıca, bu kümelerin bazı özellikleri kanıtlanıyor
Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such th... more Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that product of any two of them by adding k is a square. In the present paper, we consider some regular P-k- triples and prove that they can not be extendible to Diophantine quadruple when k = -2 by using fundamental solution of Pell equations. Also, we determine several significant properties about such sets.WOS:0004560917000072-s2.0-8505037341
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2019
On the C *-algebra valued G-metric space related with fixed point theorems There are many fixed p... more On the C *-algebra valued G-metric space related with fixed point theorems There are many fixed point results in the various kinds of metric spaces such as b-metric spaces, quaternion metric spaces, G-metric spaces, uniform spaces, non-commutative Banach spaces etc. In this work, we consider the one of modern methods as C *-algebra G-metric space with fixed point theory to solve problems above mentioned. We prove the fixed point theorems for a mapping under the contractive conditions in C *-algebra G-metric space. Besides, we establish the not only existence but also uniqueness theorem of fixed point in the such space. Also, we provide several examples to put support behind our main result.
In modern industrial manufacturing processes, induction motors are broadly utilized as industrial... more In modern industrial manufacturing processes, induction motors are broadly utilized as industrial drives. Online condition monitoring and diagnosis of faults that occur inside and/or outside of the Induction Motor Drive (IMD) system make the motor highly reliable, helping to avoid unscheduled downtimes, which cause more revenue loss and disruption of production. This can be achieved only when the irregularities produced because of the faults are sensed at the moment they occur and diagnosed quickly so that suitable actions to protect the equipment can be taken. This requires intelligent control with a high-performance scheme. Hence, a Field Programmable Gate Array (FPGA) based on neuro-genetic implementation with a Back Propagation Neural network (BPN) is suggested in this article to diagnose the fault more efficiently and almost instantly. It is reported that the classification of the neural network will provide the output within 2 µs although the clone procedure with microcontroll...
Nonlinear phenomena are very important in a variety of scientific fields. Finding solutions of no... more Nonlinear phenomena are very important in a variety of scientific fields. Finding solutions of nonlinear partial differential equations is one of the most difficult problems in mathematics and physics. A precise solution is derived for these non-linear evolution equations (NLEEs), which has been illustrated by the solitary wave solutions for the fifth degree equations, the Sawada-Kotera equation, and then we apply the Backland transformation, which shows a new special precise solution.
Coding Theory - Recent Advances, New Perspectives and Applications [Working Title], 2022
In this work, we use ‘Partial Group’ notion and we do further investigations about partial groups... more In this work, we use ‘Partial Group’ notion and we do further investigations about partial groups. We define ‘Partial Normal Subgroup’ using partial conjugation criteria and we prove few results about partial normal subgroups analogous to normal groups. Also, we define congruence relation for partial groups and via this relation, we state ‘The Quotient of Partial Group or Factor Group’. We give isomorphism theorems for partial groups. Explicitly, this is an analogous concept to group theory and our main is where differences partial groups from groups.
Journal of the Indonesian Mathematical Society, 2020
In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spac... more In the present paper, we introduce the coupled xed point theorem in C*-algebra valued metric spaces. We get a C*-algebra valued metric space which get values in noncomutative operators. We demonstrate existance and uniqeness of coupled fixed point in a such space. Besides, we support our results by giving numerical examples.
For 𝑡 an integer, a 𝑃𝑡 set is defined as a set of 𝑚 positive integers with the property that the ... more For 𝑡 an integer, a 𝑃𝑡 set is defined as a set of 𝑚 positive integers with the property that the product of its any two distinct element increased by 𝑡 is a perfect square integer. In this study, the certain special 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 sets with size three are considered. It is demonstrated that they cannot be extended to 𝑃−5, 𝑃+5, 𝑃−7 and 𝑃+7 with size four. Also, some properties of them are proved.
The aim of this paper is to determine and investigate the continued fractions expansions of wd fo... more The aim of this paper is to determine and investigate the continued fractions expansions of wd for the real quadratic number fields Q( √ d) for which the period has constant elements that are completely equal to 2 (except the last digit of period) in the symetric part of the period of integral basis element where d ≡ 2, 3 mod 4 is a square free positive integer. Moreover, we give new explicit formulas for the fundamental unit d and Yokoi’s d-invariants nd and md in relation to continued fraction expansion of such form of wd. These new formulas are not known in the literature of real quadratic fields. Such types of real quadratic fields are classified as new results.
The aim of this paper is to establish a new Coupled Fixed Point Theorems for C∗-algebra valued b-... more The aim of this paper is to establish a new Coupled Fixed Point Theorems for C∗-algebra valued b-metric spaces. As an application of our result, we discuss the existence and uniqueness results for Couple Fixed Point Theorem in C∗-algebra valued b-metric spaces. We also give conclusion to demonstrate our result.
Indonesian Journal of Electrical Engineering and Computer Science, 2021
Nowadays, with the advences in ICT and rapid development of mobile internet; media information sh... more Nowadays, with the advences in ICT and rapid development of mobile internet; media information shared on the various communication networks requires the existence of adequate security measures. Cryptography becoming an effective way to meet these requirements and for maintain the confidentiality. However, communicating with encrypted messages requires secret key exchange, which is a part of a complex protocol. In this paper, we propose a new method for exchanging key based on Diffie-Hellman protocol and image registration with fast fourier transform, the principle of this method consists to concealing the key in a set of transformed images. Therefore, image registration allows finding transformations between images, which become a tool for recovering the key by the receiver.
In Number Theory, the notion of the quadratic fields is difficult task. There are many different ... more In Number Theory, the notion of the quadratic fields is difficult task. There are many different approaches such as genus theory, composition of binary quadratic forms, and class field theory as a developmental tool for quadratic fields. Moreover, many books and papers on the number theory apply many different methods like continued fraction expansions, class number, regulators in the class group, etc. . . Recently, class number which is very difficult to calculate is used in the cryptology and security. In this paper, we determine the real quadratic fields coincide with positive square free integers d including specific continued fraction expansion of integral basis element in the case of d ≡ 2, 3 (mod 4) or d ≡ 1 (mod 4), where `(d) is the period length of continued fraction expansion. Besides, we deal with determining the fundamental unit and Yokoi’s d-invariants nd and md in the relation to continued fraction expansion of wd, we also give several numerical tables to support our ...
The aim of this paper is to construct a relation between tribonacci numbers and generalized tribo... more The aim of this paper is to construct a relation between tribonacci numbers and generalized tribonacci numbers. Besides, certain conditions are obtained to generalize the representation of a positive integer [Formula: see text] which is determined in [S. Badidja and A. Boudaoud, Representation of positive integers as a sum of distinct tribonacci numbers, J. Math. Statistic. 13 (2017) 57–61] for a [Formula: see text]-generalized Fibonacci numbers [Formula: see text]. Lastly, some applications to cryptography are given by using [Formula: see text].
The primary purpose of this paper is to classify real quadratic fields Q(√d) which include the fo... more The primary purpose of this paper is to classify real quadratic fields Q(√d) which include the form of specific continued fraction expansion of integral basis element 𝑤𝑑 for arbitrary period length l = l(𝑑) where d ≡ 2,3(mod4) is a square free positive integers. Furthermore, the present paper deals with determining new certain parametric formulas of fundamental unit and Yokoi’s d-invariants nd , md for such real quadratic fields. All results are also supported by several numerical tabular forms.
Purpose of this paper is to determine some regular non-extendible D(n) triples for some fixed int... more Purpose of this paper is to determine some regular non-extendible D(n) triples for some fixed integer n. Besides, paper includes a number of algebraic properties for such diophantine sets with size three.
International Journal of Nonlinear Analysis and Applications, 2019
The system of double equations with three unknowns given by d+ay+bx+cx^2 = z^2 , y+z=x^2 is analy... more The system of double equations with three unknowns given by d+ay+bx+cx^2 = z^2 , y+z=x^2 is analysed for its infinitely many non-zero distinct integer solutions. Different sets of integer solutions have been presented. A few interesting relations among the solutions are given.
Notes on Number Theory and Discrete Mathematics, 2019
We obtain infinitely many non-zero integer triples (x, y, z) satisfying the nonhomogeneous bi-qua... more We obtain infinitely many non-zero integer triples (x, y, z) satisfying the nonhomogeneous bi-quadratic equation with three unknowns 2 2 4 11() 3() 10. x y x y z − + + = Various interesting properties among the values of x, y, z are presented. Some relations between the solutions and special numbers are exhibited.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2019
Some results on a special type of real quadratic fields In this paper, we determine the real quad... more Some results on a special type of real quadratic fields In this paper, we determine the real quadratic fields Q(√ d) coincide with positive square-free integers d including the continued fraction expansion form of w d = a0; 7, 7,. .. , 7 −1 , a . Furthermore, we deal with determining fundamental units and Yokoi's d-invariants n d and m d in the relation to continued fraction expansion of w d where (d) is a period length of w d for the such type of real quadratic number fields Q(√ d). The present paper improve the theory of fundamental unit which generates the unit group of real quadratic fields and also determine the special form of continued fraction expansion of integral basis element in real quadratic fields.
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