Yazar "Kizilaslan, Gonca" seçeneğine göre listele

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    A unified approach to generalized Pascal-like matrices: q-analysis
    (Elsevier Inc., 2023) Akkus, Ilker; Kizilaslan, Gonca; Verde-Star, Luis
    In this paper, we present a general method to construct q-analogues and other generalizations of Pascal-like matrices. Our matrices are obtained as functions of strictly lower triangular matrices and include several types of generalized Pascal-like matrices and matrices related with modified Hermite polynomials of two variables and other polynomial sequences. We find explicit expressions for products, powers, and inverses of the matrices and also some factorization formulas using this method. © 2023 Elsevier Inc.
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    Factorizations of Some Variants of a Statistical Matrix
    (Association of Mathematicians (MATDER), 2024) Kizilaslan, Gonca; Sahin, Harun
    In this article, we define eight orthogonal matrices strongly linked to the well-known Helmert matrix. We derive LU factorizations by providing explicit closed-form formulas for the entries of L and U. Additionally, we factorize matrices by representing them in relation to diagonal matrices. © MatDer.
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    Farey-Pell Sequence, Approximation To Irrationals And Hurwitz's Inequality
    (Int Center Scientific Research & Studies, 2016) Akkus, Ilker; Irmak, Nurettin; Kizilaslan, Gonca
    The purpose of this paper is to give the notion of Farey-Pell sequence. We investigate some identities of the Farey-Pell sequence. Finally, a generalization of Farey-Pell sequence and an approximation to irrationals via Farey-Pell fractions are given
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    Generalization of a statistical matrix and its factorization
    (Taylor & Francis Inc, 2019) Akkus, Ilker; Kizilaslan, Gonca
    We consider a special matrix with integer coefficients and obtain an LU factorization for its member by giving explicit closed-form formulae of the entries of L and U. Our result is applied to give the closed-form formula of the inverse of the considered matrix. We give the relation between the defined matrix and Helmert matrix which has been used for proving the statistical independence of a number of statistics. Also we find the condition numbers of some matrices for some special values of q.
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    The linear algebra of a Pascal-like matrix
    (TAYLOR & FRANCIS LTD, 2020) Zheng, De-Yin; Akkus, Ilker; Kizilaslan, Gonca
    A Pascal-like matrix is constructed whose row entries are the terms of the modified Hermite polynomials of two variables. The multiplication of the two Pascal-like matrices and the power and inverse of the Pascal-like matrix have very similar results to the well-known Binomial Matrix, and the factorization of the Pascal-like matrix has also been given, which is completely similar to the factorization of Binomial Matrix. Furthermore, two simple examples are given to show the application of the power and factorization properties of the Pascal-like matrix. Finally, a generalization of the Pascal-like matrix is given and some combinatorial identities are obtained such as Tepper-like identity.
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    New Curiosity Bivariate Quadratic Quaternionic Polynomials and Their Roots
    (Ovidius Univ Press, 2021) Akkus, Ilker; Kizilaslan, Gonca
    We consider the second-order linear homogeneous quaternion recurrence solutions for some new curiosity bivariate quadratic quaternionic equations.
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    NEW REPRESENTATIONS OF PASCAL MATRIX VIA OPERATIONAL q-CALCULUS
    (Honam Mathematical Soc, 2022) Zheng, De-Yin; Akkus, Ilker; Kizilaslan, Gonca
    In this paper we introduce two type of representations of the Pascal matrix via induced transformations of some q-derivatives as well as their some combinatorial applications.
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    On some Properties of Tribonacci Quaternions
    (Ovidius Univ Press, 2018) Akkus, Ilker; Kizilaslan, Gonca
    In this paper, we give some properties of the Tribonacci and Tribonacci-Lucas quaternions and obtain some identities for them.
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    Pascal-like matrix with double factorial binomial coefficients
    (Indian Nat Sci Acad, 2023) Kizilaslan, Gonca
    We introduce a variation of a Pascal-like matrix which includes double factorial binomial coefficients and show that it satisfies several properties. We find the inverse of the defined matrix and derive explicit representations of the powers of it for the integer, rational and irrational exponents. Finally, we give a generalization of this matrix and obtain some identities.
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    Quaternions: Quantum calculus approach with applications
    (Academic Publication Council, 2019) Akkus, Ilker; Kizilaslan, Gonca
    In this paper we introduce two types of quaternion sequences with components including quantum integers. We also introduce quantum quaternion polynomials. Moreover, we give some properties and identities for these quantum quaternions and polynomials. Finally, we give time evolution and rotation applications for some specific quaternion sequences. The applications can be converted into quantum integer forms under suitable conditions with similar considerations.
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    Sequential quaternions: Nestedness and applications
    (World Scientific Publ Co Pte Ltd, 2023) Kizilaslan, Gonca; Akkus, Ilker
    In this paper, we define a function Q which gives the sequence of partial sums of the Fibonacci quaternion sequence (Q(n)). We provide an identity about Q(k) which is the sequence obtained by applying Q to (Q(n)) k-times.
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    Some New Quaternionic Quadratics with Zeros in Terms of Second Order Quaternion Recurrences
    (Springer Basel Ag, 2019) Akkus, Ilker; Kizilaslan, Gonca
    In this paper a comprehensive analysis of the Horadam quaternion zeros for some new types of bivariate quadratic quaternion polynomial equations is presented.
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    The altered Hermite matrix: implications and ramifications
    (Amer Inst Mathematical Sciences-Aims, 2024) Kizilaslan, Gonca
    Matrix theory is essential for addressing practical problems and executing computational tasks. Matrices related to Hermite polynomials are essential due to their applications in quantum relations, and spectral properties make them a valuable tool for both theoretical research and practical applications. From a different perspective, we introduced a variant of the Hermite matrix that incorporates triple factorials and demonstrated that this matrix satisfies various properties. By utilizing effective matrix algebra techniques, various algebraic properties of this matrix have been determined, including the product formula, inverse matrix and eigenvalues. Additionally, we extended this matrix to a more generalized form and derived several identities.
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    THE LINEAR ALGEBRA OF A GENERALIZED TRIBONACCI MATRIX
    (Ankara Univ, Fac Sci, 2023) Kizilaslan, Gonca
    In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k-th power. We also give a relation between the matrix and a matrix exponential of a special matrix.
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    The linear algebra of a generalized Tribonacci matrix
    (2023) Kizilaslan, Gonca
    In this paper, we consider a generalization of a regular Tribonacci matrix for two variables and show that it can be factorized by some special matrices. We produce several new interesting identities and find an explicit formula for the inverse and k?th power. We also give a relation between the matrix and a matrix exponential of a special matrix.
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    Torsion homology growth for noncongruence subgroups of Bianchi groups
    (WORLD SCIENTIFIC PUBL CO PTE LTD, 2020) Kizilaslan, Gonca; Sengun, Mehmet Haluk
    We carry out numerical experiments to investigate the growth of torsion in their first homology of noncongruence subgroups of Bianchi groups. The data we collect suggest that the torsion homology growth conjecture of Bergeron and Venkatesh for congruence subgroups may apply to the noncongruence case as well.
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    Unrestricted Tribonacci and Tribonacci-Lucas quaternions
    (Bulgarian Acad Science, 2023) Kizilaslan, Gonca; Karabulut, Leyla
    We define a generalization of Tribonacci and Tribonacci-Lucas quaternions with arbitrary Tribonacci numbers and Tribonacci-Lucas numbers coefficients, respectively. We get generating functions and Binet's formulas for these quaternions. Furthermore, several sum formulas and a matrix representation are obtained.
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    A variant of the reciprocal super Catalan matrix
    (De Gruyter Poland Sp Zoo, 2015) Kilic, Emrah; Akkus, Ilker; Kizilaslan, Gonca
    Recently Prodinger [8] considered the reciprocal super Catalan matrix and gave explicit formula for its LU-decomposition, the LU-decomposition of its inverse, and obtained some related matrices. For all results, q-analogues were also presented. In this paper, we define and study a variant of the reciprocal super Catalan matrix with two additional parameters. Explicit formula for its LU-decomposition, LU-decomposition of its inverse and the Cholesky decomposition are obtained. For all results, q-analogues are also presented.