• On A new class of hyperbolic fibonacci functions via some special polynomials 

  Köme, Sure; Yazlık, Yasin (2023-06-08)

  In recent years, many researchers have studied hyperbolic Fibonacci functions and some special polynomials, which are important areas of mathematics. In this study, we give an extension of the Euler polynomials in order ...
• Some properties of the conditional dual lucas octonions 

  Köme, Sure (2023-07-10)

  The study of higher-dimensional algebraic structures has gained significant attention in recent years. Octonions, a normed division algebra with eight dimensions, have applications in fields such as quantum logic, special ...
• On the generalized fibonacci matrix hybrinomials 

  Köme, Sure; Yazan, Sefa (2022-11-10)

  Complex numbers, hyperbolic numbers, and dual numbers are well-known number systems in the literature. The hybrid numbers, which have significantly increased interest in recent years, are the generalization of complex ...
• Some properties of generalized bivariate bihyperbolic polynomials 

  Köme, Sure; Ergezer, Sinem (2023-11-11)

  Understanding the properties and applications of bihyperbolic polynomials sheds light on many mathematical problems. For this reason, bihyperbolic polynomials can play an important role in various fields of mathematics. ...
• Special type of bernoulli polynomials and hyperbolic fibonacci functions 

  Köme, Sure; Yazlık, Yasin (2023-07-11)

  Bernoulli numbers and Bernoulli polynomials have been studied by many researchers recently, as they are widely used in mathematics, engineering and other disciplines. Hyperbolic functions are frequently observed in the ...
• Quantum mechanics approach for appropriately chosen hamiltonian 

  Kaya, Ahmet (2022-06-30)

  In this paper, Dirac notations are operated to find the Hamiltonian matrix with the eigenvector basis for two and three-state cases, and its tensor product version with a change of basis.
• On a new family of the generalized gauss k-pell-lucas numbers and their polynomials 

  Özimamoğlu, Hayrullah; Kaya, Ahmet (2022-06-16)

  In this paper, we generalize the known Gauss Pell-Lucas numbers, and call such numbers as the generalized Gauss k-Pell-Lucas numbers. We obtain relations between the family of the generalized Gauss k-Pell-Lucas numbers ...
• Leonardo octonions 

  Özimamoğlu, Hayrullah (2022-06-16)

  In this paper, we introduce a new class of octonions. We define the Leonardo octonions. Then, we obtain some algebraic properties of the Leonardo octonions such as the generating function, Binet formula, some summation ...
• F_4 üzerindeki optimal ve hemen hemen optimal toeplitz toplamsal kodların inşası 

  Özimamoğlu, Hayrullah; Şahin, Murat (2019-03-28)

  Giriş: Dört elemanlı bir cisim w^2=w+1 olmak üzere F_4={0,1,w,w^2 } ile gösterilsin. n uzunluğunda F_4 üzerindeki bir C toplamsal kodu, F_4^n toplamsal grubunun bir alt grubudur. C toplamsal kodunun üreteç matrisi, ...
• Construction of the binary simplex codes and the first order reed-muller codes 

  Özimamoğlu, Hayrullah; Şahin, Murat (2018-06-27)

  GF(q) denote the finite field with q elements. An [n,k,d] linear code C over GF(q) is a k-dimensional subspace of GF(q) ^n with minimum (Hamming) distance d. The vectors in C are codewords of C. Specially, codes over ...
• Classification of optimal additive toeplitz codes over GF(4) 

  Özimamoğlu, Hayrullah; Şahin, Murat (2018-06-27)

  We denote GF_4={0,1,w,w^2} where w^2=w+1. An additive code C over GF_4 of length n is an additive subgroup of GF_4^n . C contains 2^k codewords for some 0<=k<= 2n, and can be defined by a kxn generator matrix, with entries ...
• K-Autocorrelation and Its applications 

  Şahin, Murat; Özimamoğlu, Hayrullah (2017-05-11)

  The standart autocorrelation is used to measure the similarities between a binary sequence and its any shifted form. It has applications in communication systems and cryptography. Let a =(a_0,a_1,a_2,...,a_n-1) be a ...
• On a new class of the generalized gauss k-pell numbers and their polynomials 

  Kaya, Ahmet; Özimamoğlu, Hayrullah (2022-10-12)

  In this article, we generalize the well-known Gauss Pell numbers and refer to them as generalized Gauss k-Pell numbers. There are relationships discovered between the class of generalized Gauss k-Pell numbers and the ...
• Additive Toeplitz codes over F4 

  Şahin, Murat; Özimamoğlu, Hayrullah (2020)

  In this paper, we introduce additive Toeplitz codes over F4. The additive Toeplitz codes are a generalization of additive circulant codes over F4. We find many optimal additive Toeplitz codes (OATC) over F4. These ...
• K-autocorrelation and its applications 

  Özimamoğlu, Hayrullah; Şahin, Murat; Ölmez, Oktay (2019)

  The standard autocorrelation measures similarities between a binary sequence and its any shifted form. In this paper, we introduce the concept of the k-autocorrelation of a binary sequence as a generalization of the ...
• Bivariate biperiodic fibonacci hybrinomials 

  Köme, Sure; Kumtas, Zeynep (2022-06-21)

  The Hybrid numbers are generalization of complex, hyperbolic and dual numbers. In recent years, studies related with Hybrid numbers have increased significantly. Also, there are many studies interesting generalizations and ...
• Wilker-type inequalities for k-Fibonacci hyperbolic functions 

  Köme, Sure (Turkish Journal of Mathematics and Computer Science, 2022)

  In this paper, we introduce the Wilker-Anglesio’s inequality and parameterized Wilker inequality for the k-Fibonacci hyperbolic functions using classical analytical techniques
• Factorizations of some lower triangular matrices and related combinatorial identities 

  Köme, Cahit (Notes on Number Theory and Discrete Mathematics, 2021-10)

  In this study, we investigate the connection between second order recurrence matrix and several combinatorial matrices such as generalized r-eliminated Pascal matrix, Stirling matrix of the first and of the second kind ...
• Some combinatorial identities via k-order Fibonacci matrices 

  Köme, Cahit (Miskolc Mathematical Notes, 2022-06)

  Matrix factorizations have been widely used in recent years, especially in engineering problems, to facilitate performance-requiring computations. In this paper, we investigate some interesting relationships between some ...
• Cholesky factorization of the generalized symmetric k-Fibonacci matrix 

  Köme, Cahit (Gazi University, 2022-02)

  Matrix methods are a useful tool while dealing with many problems stemming from linear recurrence relations. In this paper, we discuss factorizations and inverse factorizations of two kinds of generalized k-Fibonacci ...

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