Araştırma Makalesi
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Genelleştirilmiş Fibonacci ve Lucas polinomlarıyla birlikte sağ devirsel matrisler ve kodlama teorisi

Yıl 2019, , 306 - 322, 15.03.2019
https://doi.org/10.25092/baunfbed.547188

Öz

Bu çalışmada elemanları genelleştirilmiş Fibonacci ve Lucas polinomları olan devirsel matrisler kullanılarak iki yeni kodlama algoritması vereceğiz. Bu amaçla, genelleşirilmiş Fibonacci polinomları, genelleştirilmiş Lucas polimomları  ve geometrik diziler kullanılarak sağ devirsel matrislerin bazı temel özelliklerini çalışacağız.

Kaynakça

  • Catarino, P., The h(x)-Fibonacci Quaternion Polynomials: Some Combinatorial Properties, Advances in Applied Clifford Algebras, 26, 71–79, (2016).
  • Catarino, P., The Modified Pell and the Modified k-Pell Quaternions and Octonions, Advances in Applied Clifford Algebras, 26, 577–590, (2016).
  • Prasad, B., Coding theory on Lucas p numbers, Discrete Mathematics, Algorithms and Applications, 8(4), 17 pages, (2016).
  • Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitions Fractals, 30 (1), 56-66, (2006).
  • Taş, N., Uçar, S., Özgür, N.Y., Pell coding and pell decoding methods with some applications, arXiv:1706.04377 [math.NT].
  • Taş, N., Uçar, S., Özgür, N.Y., Öztunç Ö., A new coding/decoding algorithm using Fibonacci numbers, Discrete Mathematics Algorithms and Applications, 10(2), (2018).
  • Uçar, S., Taş N., Özgür N.Y., A New Application to Coding Theory via Fibonacci and Lucas Numbers, Mathematical Sciences and Applications E-Notes, (Accepted).
  • Catarino, P., A note on certain matrices with -Fibonacci polynomials, Acta Mathematica Universitatis Comenianae, 86(2), (2017).
  • Bueno, A.C.F., Right circulant matrices with ratio of the elements of Fibonacci and geometric sequence, Notes on Number Theory and Discrete Mathematics, 22(3), 79-83, (2016).
  • Gong, Y., Jiang Z., Gao, Y., On Jacobsthal and Jacobsthal-Lucas circulant type matrices, Abstract and Applied Analysis, Article ID 418293, 11pp., (2015).
  • Shen, S. Q., Cen, J. M., Hao, Y., On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Applied Mathematics and Computation, 217(23), 9790–9797, (2011).
  • Ahmed, E., Elgazzar, A.S., On fractional order differential equations model for nonlocal epidemics, Physica A: Statistical Mechanics and its Applications, 379, 607-614, (2007).
  • Bai, Z., Jin, X., Song, L., Strang-type preconditioners for solving linear systems from neutral delay differential equations, Calcolo, 40(1), 21–31, (2003).
  • Nussbaum, R.D., Circulant matrices and differential-delay equations, Journal of Differential Equations, 60(2), 201-217, (1985).
  • Qu, W., Lei, S.L., Vong, S.W., Circulant and skew-circulant splitting iteration for fractional advection-diffusion equations, International Journal of Computer Mathematics, 91(10), 2232-2242, (2014).
  • Wu, J., Zou, X., Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, Journal of Differential Equations, 135(2), 315-357, (1997).
  • Nalli, A., Haukkanen, P., On generalized Fibonacci and Lucas polynomials, Chaos Solitons Fractals, 42(5), 3179-3186, (2009).
  • Kılıç, E., Stanica, P., Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mountain Journal of Mathematics, 41(4), 1247–1264, (2011).
  • Catarino, P., On some idenitities for k-Fibonacci sequence, International Journal of Contemporary Mathematical Sciences, 9(1), 37-42, (2014).
  • Falcon, S., Plaza, A., On the Fibonacci k-numbers, Chaos Solitons Fractals, 32(5), 1615-1624, (2007).
  • Kalman, D., Mena, R., The Fibonacci numbers-exposed, Mathematics Magazine, 76(3), 167-181, (2003).
  • Koshy, T., Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics, Wiley-Interscience, (2001).
  • Şiar, Z., Keskin, R., Some new identites concerning Generalized Fibonacci and Lucas Numbers, Hacettepe Journal of Mathematics and Statistics, 42(3), 211-222, (2013).
  • Uçar, S., On some properties of generalized Fibonacci and Lucas polynomials, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(2), 216-224, (2017).
  • Bueno, A.C.F., Right circulant matrices with geometric progression, International Journal of Applied Mathematical Research, 1(4), 593-603, 2012.
  • Bueno, A.C.F., Right circulant matrices with Fibonacci sequence, International Journal of Mathematics and Computer Science, 2(2), 8–9, (2012).
  • Falcon, S., On the k-Lucas numbers, International Journal of Contemporary Mathematical Sciences, 6, 1039-1050, (2011).
  • Godase, A.D., Dhakne, M.B., On the properties of k-Fibonacci and k-Lucas numbers. International Journal of Applied Mathematics and Mechanics,. 2(1), 100-106, (2014).

Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory

Yıl 2019, , 306 - 322, 15.03.2019
https://doi.org/10.25092/baunfbed.547188

Öz

In the present paper, we consider two new coding algorithms by means of right circulant matrices with elements generalized Fibonacci and Lucas polynomials. To that end, we study basic properties of right circulant matrices using generalized Fibonacci polynomials, generalized Lucas polynomials and geometric sequences.

Kaynakça

  • Catarino, P., The h(x)-Fibonacci Quaternion Polynomials: Some Combinatorial Properties, Advances in Applied Clifford Algebras, 26, 71–79, (2016).
  • Catarino, P., The Modified Pell and the Modified k-Pell Quaternions and Octonions, Advances in Applied Clifford Algebras, 26, 577–590, (2016).
  • Prasad, B., Coding theory on Lucas p numbers, Discrete Mathematics, Algorithms and Applications, 8(4), 17 pages, (2016).
  • Stakhov, A. P., Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitions Fractals, 30 (1), 56-66, (2006).
  • Taş, N., Uçar, S., Özgür, N.Y., Pell coding and pell decoding methods with some applications, arXiv:1706.04377 [math.NT].
  • Taş, N., Uçar, S., Özgür, N.Y., Öztunç Ö., A new coding/decoding algorithm using Fibonacci numbers, Discrete Mathematics Algorithms and Applications, 10(2), (2018).
  • Uçar, S., Taş N., Özgür N.Y., A New Application to Coding Theory via Fibonacci and Lucas Numbers, Mathematical Sciences and Applications E-Notes, (Accepted).
  • Catarino, P., A note on certain matrices with -Fibonacci polynomials, Acta Mathematica Universitatis Comenianae, 86(2), (2017).
  • Bueno, A.C.F., Right circulant matrices with ratio of the elements of Fibonacci and geometric sequence, Notes on Number Theory and Discrete Mathematics, 22(3), 79-83, (2016).
  • Gong, Y., Jiang Z., Gao, Y., On Jacobsthal and Jacobsthal-Lucas circulant type matrices, Abstract and Applied Analysis, Article ID 418293, 11pp., (2015).
  • Shen, S. Q., Cen, J. M., Hao, Y., On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers, Applied Mathematics and Computation, 217(23), 9790–9797, (2011).
  • Ahmed, E., Elgazzar, A.S., On fractional order differential equations model for nonlocal epidemics, Physica A: Statistical Mechanics and its Applications, 379, 607-614, (2007).
  • Bai, Z., Jin, X., Song, L., Strang-type preconditioners for solving linear systems from neutral delay differential equations, Calcolo, 40(1), 21–31, (2003).
  • Nussbaum, R.D., Circulant matrices and differential-delay equations, Journal of Differential Equations, 60(2), 201-217, (1985).
  • Qu, W., Lei, S.L., Vong, S.W., Circulant and skew-circulant splitting iteration for fractional advection-diffusion equations, International Journal of Computer Mathematics, 91(10), 2232-2242, (2014).
  • Wu, J., Zou, X., Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, Journal of Differential Equations, 135(2), 315-357, (1997).
  • Nalli, A., Haukkanen, P., On generalized Fibonacci and Lucas polynomials, Chaos Solitons Fractals, 42(5), 3179-3186, (2009).
  • Kılıç, E., Stanica, P., Factorizations and representations of binary polynomial recurrences by matrix methods, Rocky Mountain Journal of Mathematics, 41(4), 1247–1264, (2011).
  • Catarino, P., On some idenitities for k-Fibonacci sequence, International Journal of Contemporary Mathematical Sciences, 9(1), 37-42, (2014).
  • Falcon, S., Plaza, A., On the Fibonacci k-numbers, Chaos Solitons Fractals, 32(5), 1615-1624, (2007).
  • Kalman, D., Mena, R., The Fibonacci numbers-exposed, Mathematics Magazine, 76(3), 167-181, (2003).
  • Koshy, T., Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics, Wiley-Interscience, (2001).
  • Şiar, Z., Keskin, R., Some new identites concerning Generalized Fibonacci and Lucas Numbers, Hacettepe Journal of Mathematics and Statistics, 42(3), 211-222, (2013).
  • Uçar, S., On some properties of generalized Fibonacci and Lucas polynomials, An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(2), 216-224, (2017).
  • Bueno, A.C.F., Right circulant matrices with geometric progression, International Journal of Applied Mathematical Research, 1(4), 593-603, 2012.
  • Bueno, A.C.F., Right circulant matrices with Fibonacci sequence, International Journal of Mathematics and Computer Science, 2(2), 8–9, (2012).
  • Falcon, S., On the k-Lucas numbers, International Journal of Contemporary Mathematical Sciences, 6, 1039-1050, (2011).
  • Godase, A.D., Dhakne, M.B., On the properties of k-Fibonacci and k-Lucas numbers. International Journal of Applied Mathematics and Mechanics,. 2(1), 100-106, (2014).
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Sümeyra Uçar 0000-0002-6628-526X

Nihal Yılmaz Özgür Bu kişi benim 0000-0002-4535-4019

Yayımlanma Tarihi 15 Mart 2019
Gönderilme Tarihi 7 Ocak 2019
Yayımlandığı Sayı Yıl 2019

Kaynak Göster

APA Uçar, S., & Yılmaz Özgür, N. (2019). Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(1), 306-322. https://doi.org/10.25092/baunfbed.547188
AMA Uçar S, Yılmaz Özgür N. Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory. BAUN Fen. Bil. Enst. Dergisi. Mart 2019;21(1):306-322. doi:10.25092/baunfbed.547188
Chicago Uçar, Sümeyra, ve Nihal Yılmaz Özgür. “Right Circulant Matrices With Generalized Fibonacci and Lucas Polynomials and Coding Theory”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21, sy. 1 (Mart 2019): 306-22. https://doi.org/10.25092/baunfbed.547188.
EndNote Uçar S, Yılmaz Özgür N (01 Mart 2019) Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21 1 306–322.
IEEE S. Uçar ve N. Yılmaz Özgür, “Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory”, BAUN Fen. Bil. Enst. Dergisi, c. 21, sy. 1, ss. 306–322, 2019, doi: 10.25092/baunfbed.547188.
ISNAD Uçar, Sümeyra - Yılmaz Özgür, Nihal. “Right Circulant Matrices With Generalized Fibonacci and Lucas Polynomials and Coding Theory”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 21/1 (Mart 2019), 306-322. https://doi.org/10.25092/baunfbed.547188.
JAMA Uçar S, Yılmaz Özgür N. Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory. BAUN Fen. Bil. Enst. Dergisi. 2019;21:306–322.
MLA Uçar, Sümeyra ve Nihal Yılmaz Özgür. “Right Circulant Matrices With Generalized Fibonacci and Lucas Polynomials and Coding Theory”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 21, sy. 1, 2019, ss. 306-22, doi:10.25092/baunfbed.547188.
Vancouver Uçar S, Yılmaz Özgür N. Right circulant matrices with generalized Fibonacci and Lucas polynomials and coding theory. BAUN Fen. Bil. Enst. Dergisi. 2019;21(1):306-22.