Author

# Efruz Özlem Mersin

Bio: Efruz Özlem Mersin is an academic researcher. The author has contributed to research in topics: Mathematics & Recurrence relation. The author has an hindex of 1, co-authored 2 publications receiving 3 citations.

##### Papers

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TL;DR: This paper applies Sturm Theorem to the generalized Frank matrix which is a special form of the Hessenberg matrix and examines its eigenvalues by using Sturm property and illustrates the results with an example.

Abstract: One of the popular test matrices for eigenvalue routines is Frank matrix due to its well-conditioned and poorly conditioned eigenvalues. All eigenvalues of Frank matrix are real, positive and different. Sturm Theorem is very useful tool for computing eigenvalues of tridiagonal symmetric matrices. We apply Sturm Theorem to generalized Frank matrix which is a special form of Hessenberg matrix and we examine its eigenvalues using Sturm property in the present paper. Moreover, we give an example to illustrate our results.

3 citations

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01 May 2020

TL;DR: A new generalization of Frank matrix is introduced and its algebraic structure, determinant, inverse, LU decomposition and characteristic polynomial are examined.

Abstract: In this paper, we first introduce a new generalization of Frank matrix. Then, we examine its algebraic structure, determinant, inverse, LU decomposition and characteristic polynomial.

1 citations

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TL;DR: In this paper , hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as recurrence relations, summation formulas, and generating functions are presented.

Abstract: In this paper, hyper-Fibonacci and hyper-Lucas polynomials are defined and some of their algebraic and combinatorial properties such as the recurrence relations, summation formulas, and generating functions are presented. In addition, some relationships between the hyper-Fibonacci and hyper-Lucas polynomials are given.

1 citations

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21 Nov 2022-Eskişehir technical university journal of science and technology a- applied sciences and engineering

TL;DR: In this paper , the authors define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano and examine some properties of their properties such as the recurrence relation, summation formula and generating function.

Abstract: The aim of this paper is to define hyper-Leonardo hybrinomials as a generalization of the Leonardo Pisano hybrinomials and to examine some of their properties such as the recurrence relation, summation formula and generating function. Another aim is to introduce hyper hybrid-Leonardo numbers.

1 citations

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30 Mar 2023-Communications Faculty of Sciences University of Ankara. Series A1: mathematics and statistics

TL;DR: In this article , the authors define hybrinomials related to hyper-Leonardo numbers, and introduce hybrid hyper Leonardo numbers, which are related to the hyperbrinomial.

Abstract: In this paper, we define hybrinomials related to hyper-Leonardo numbers. We study some of their properties such as the recurrence relation and summation formulas. In addition, we introduce hybrid hyper Leonardo numbers.

##### Cited by

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TL;DR: This paper applies Sturm Theorem to the generalized Frank matrix which is a special form of the Hessenberg matrix and examines its eigenvalues by using Sturm property and illustrates the results with an example.

Abstract: One of the popular test matrices for eigenvalue routines is Frank matrix due to its well-conditioned and poorly conditioned eigenvalues. All eigenvalues of Frank matrix are real, positive and different. Sturm Theorem is very useful tool for computing eigenvalues of tridiagonal symmetric matrices. We apply Sturm Theorem to generalized Frank matrix which is a special form of Hessenberg matrix and we examine its eigenvalues using Sturm property in the present paper. Moreover, we give an example to illustrate our results.

3 citations

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01 Jan 2009

TL;DR: In this paper, a methode speciale pour the resolution des equations algebriques determinees, auxquelles conduit l'integration des equations differentielles lineaires, dont il est ici question.

Abstract: On connait les equations differentielles que Lagrange et Laplace ont trouvees pour determiner les variations seculaires des elemens des orbites des planetes, la belle methode que ces illustres geometres ont employee pour integrer ces equations, et les consequences capitales qu’ils en ont deduites relativement a la stabilite du systeme du inonde. On sait que Lagrange a represente par des equations differentielles de la meme forme les petites oscillations d’un systeme de points materiels assujettis a des liaisons quelconques, et qu’il y a applique les memes procedes d’integration dont il avait fail usage dans ses recherches sur les mouvemens des corps celesles. D’autres problemes, moins generaux, de mecanique et de physique, dependent aussi d’equations du meme genre. L’elude que j’ai faite de ces importantes questions et de l’analyse qui s’y rapporte m’a fait decouvrir quelques propositions nouvelles que je developpe dans ce memoire. Le resultat principal de mes recherches sur ce sujet est une methode speciale pour la resolution des equations algebriques determinees, auxquelles conduit l’integration des equations differentielles lineaires dont il est ici question.

1 citations

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TL;DR: In this paper , hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined and some algebraic and combinatoric properties of these numbers are examined, such as recurrence relations, summation formulas and generation functions.

Abstract: Hybrid numbers which are accepted as a generalization of complex, hyperbolic and dual numbers, have attracted the attention of many researchers recently. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic and combinatoric properties of these hybrinomials are examined such as the recurrence relations, summation formulas and generation functions. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.

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TL;DR: In this article , a recurrence relation for the characteristic polynomial for matrix $ \mathcal{A}_{min} = \left[a_{min\left(i, j\right)}\right]_{i,j = 1}^n $, where $ a_s $'s are the elements of a real sequence $ \left\lbrace a_ s\right\rbrace $.

Abstract: In the present paper, we study Min matrix $ \mathcal{A}_{min} = \left[a_{min\left(i, j\right)}\right]_{i, j = 1}^n $, where $ a_s $'s are the elements of a real sequence $ \left\lbrace a_s\right\rbrace $. We first obtain a recurrence relation for the characteristic polynomial for matrix $ \mathcal{A}_{min} $, and some relations between the coefficients of its characteristic polynomial. Next, we show that the sequence of the characteristic polynomials of the $ i \times i \left(i \leq n\right) $ Min matrices satisfies the Sturm sequence properties according to different required conditions of the sequence $ \left\lbrace a_s\right\rbrace $. Using Sturm's Theorem, we get some results about the eigenvalues, such as the number of eigenvalues in an interval. Thus, we obtain the number of positive and negative eigenvalues of Min matrix $ \mathcal{A}_{min} $. Finally, we give an example to illustrate our results.