Academic literature on the topic 'Fibonacci theory'

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Journal articles on the topic "Fibonacci theory"

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Şentürk, Gülsüm Yeliz, and Nurten Gürses. "Dual quaternion theory over HGC numbers." Journal of Discrete Mathematical Sciences & Cryptography 27, no. 1 (2024): 117–42. http://dx.doi.org/10.47974/jdmsc-1611.

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Knowing the applications of quaternions in various fields, such as robotics, navigation, computer visualization and animation, in this study, we give the theory of dual quaternions considering Hyperbolic-Generalized Complex (HGC) numbers as coefficients via generalized complex and hyperbolic numbers. We account for how HGC number theory can extend dual quaternions to HGC dual quaternions. Some related theoretical results with HGC Fibonacci/Lucas numbers are established, including their dual quaternions. Given HGC Fibonacci/Lucas numbers, their special matrix correspondences have been identifie
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Anderson, Peter G. "Extended Fibonacci Zeckendorf Theory." Fibonacci Quarterly 52, no. 5 (2014): 15–21. http://dx.doi.org/10.1080/00150517.2014.12427852.

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BASU, MANJUSRI, and MONOJIT DAS. "CODING THEORY ON FIBONACCI n-STEP NUMBERS." Discrete Mathematics, Algorithms and Applications 06, no. 02 (2014): 1450017. http://dx.doi.org/10.1142/s1793830914500177.

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We consider the series of Fibonacci n-step numbers and a class of square matrix of order n based on Fibonacci n-step numbers with determinant +1 or -1. Thereby, we introduce a new coding theory called Fibonacci n-step coding theory and establish generalized relation among the code elements for all values of n. For n = 2, the correct ability of the method is 93.33%; for n = 3, the correct ability of the method is 99.80% and for n = 4, the correct ability of the method is 99.998%. In general, the correct ability of the method increases as n increases.
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BASU, MANJUSRI, and BANDHU PRASAD. "CODING THEORY ON h(x) FIBONACCI p-NUMBERS POLYNOMIALS." Discrete Mathematics, Algorithms and Applications 04, no. 03 (2012): 1250030. http://dx.doi.org/10.1142/s1793830912500309.

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In this paper, we introduce h(x) Fibonacci p-numbers polynomials and a new Fibonacci Qp,h(x) matrix for h(x) Fibonacci p-numbers polynomials where p(> 0) is integer and h(x)(> 0) is a polynomial with real coefficients. Thereby, we discuss various properties of Qp,h(x) matrix and the coding theory followed from the Qp,h(x) matrix. We establish the relations among the code matrix elements for p(> 0) is integer and h(x)(> 0). We also show that the relations, among the code matrix elements for h(x) = m (> 0), coincide with the relations among the code matrix elements for coding theo
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BASU, MANJUSRI, and BANDHU PRASAD. "CODING THEORY ON THE (m, t)-EXTENSION OF THE FIBONACCI p-NUMBERS." Discrete Mathematics, Algorithms and Applications 03, no. 02 (2011): 259–67. http://dx.doi.org/10.1142/s1793830911001097.

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In this paper, we define (m, t)-extension of the Fibonacci p-numbers and Golden (p, m, t)-proportions, where p ≥ 0 is integer, m > 0, and t > 0. We establish a relation among golden (p, m, t)-proportion, golden (p, m)-proportion and golden p-proportion. Thereby, we define a new Fibonacci Gp, m, t matrix. Then we show that by proper selection of the initial terms for the (m, t)-extension of the Fibonacci p-numbers, we can apply Fibonacci coding/decoding in Gp, m, t matrix. Also it is obvious that for t = 1, the relations among the code elements for all values of p (non-negative integer) a
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Kumar, Nand Kishor, and Suresh Kumar Sahani. "Generalized K-Fibonacci Sequence of Q- Matrix." Mikailalsys Journal of Advanced Engineering International 2, no. 1 (2025): 55–62. https://doi.org/10.58578/mjaei.v2i1.4811.

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This article explores the generalized K-Fibonacci sequence derived from matrices, extending the classical Fibonacci sequence to matrix representations. The properties and its applications are also described. The interplay of matrix algebra and generalized Fibonacci sequences offers insights into advanced sequence theory.
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Mehraban, Elahe, and Mansour Hashemi. "An Application of the t -Extension of the p -Fibonacci Pascal Matrix in Coding Theory." Advances in Mathematical Physics 2022 (October 10, 2022): 1–14. http://dx.doi.org/10.1155/2022/4619136.

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We consider the t -extension of the p -Fibonacci Pascal matrix. First, we study the k -th power of the t -extension of the p -Fibonacci lower and upper triangular Pascal matrix. Then, we obtain a new code which is named the t -extension of the p -Fibonacci Pascal matrix coding/decoding by using them.
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Balouria, Pallavi, та Meenakshi Chawla. "On λ-Fibonacci statistical convergence of order- α in intuitionistic fuzzy normed spaces (IFNS)". Journal of Interdisciplinary Mathematics 27, № 8 (2024): 1827–35. https://doi.org/10.47974/jim-2047.

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The main goal of this paper is to study and develop the theory of λ-Fibonacci statisticalconvergence of order-α in IFNS. Also λ-Fibonacci statistical Cauchy sequence of order-α and λ-Fibonacci statistical completeness of order-α in IFNS have been defined and studied.
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RIKLUND, ROLF, MATTIAS SEVERIN, and YOUYAN LIU. "THE THUE-MORSE APERIODIC CRYSTAL, A LINK BETWEEN THE FIBONACCI QUASICRYSTAL AND THE PERIODIC CRYSTAL." International Journal of Modern Physics B 01, no. 01 (1987): 121–32. http://dx.doi.org/10.1142/s0217979287000104.

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The electronic spectrum and eigenstates of a one-dimensional aperiodic Thue-Morse crystal isstudied with an on-site tight-binding model. The relation between the constructing elements andthe hierarchical splitting of the bands into subbands is analysed. The eigenstates are shown to be much more similar to those of a periodic crystal than those of a Fibonacci quasicrystal. We thus claim that the Thue-Morse aperiodic crystal is a link between the Fibonacci quasicrystal and theperiodic crystal, and that the study of non-Fibonaccian aperiodic crystals is a promising steptowards the desired unified
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Sharma, Sonal, та Meenakshi Chawla. "Fibonacci statistical convergence of double sequences of order α– in intuitionistic fuzzy normed spaces (IFNS)". Journal of Interdisciplinary Mathematics 27, № 8 (2024): 1817–26. https://doi.org/10.47974/jim-2046.

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The main objective of this work is to study and develop the theory of Fibonacci statistical convergence of double sequences of order α– in IFNS. We examine the Fibonacci statistically Cauchy double sequences of order α– and Fibonacci statistically completeness of double sequences of order α– in IFNS.
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Dissertations / Theses on the topic "Fibonacci theory"

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Flournoy, Cecil Buford Jr. "N-parameter Fibonacci AF C*-Algebras." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1221.

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An n-parameter Fibonacci AF-algebra is determined by a constant incidence matrix K of a special form. The form of the matrix K is defined by a given n-parameter Fibonacci sequence. We compute the K-theory of certain Fibonacci AF-algebra, and relate their K-theory to the K-theory of an AF-algebra defined by incidence matrices that are the transpose of K.
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Meinke, Ashley Marie. "Fibonacci Numbers and Associated Matrices." Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310588704.

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MELO, MARIA ISABEL AFONSO. "GOLDEN RATIO AND FIBONACCI NUMBERS: FROM THEORY TO PRACTICE THROUGH PHOTOGRAPHY." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33080@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR<br>PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL<br>Este trabalho teve o intuito de conciliar o ensino de matemática com práticas muito presentes no cotidiano dos alunos nos dias atuais: o uso da tecnologia e a comunicação através da fotografia. Com esse objetivo, foram selecionados conteúdos matemáticos que historicamente estão relacionados com a beleza e harmonia: a razão áurea e a sequência de Fibonacci. Tais enfoques permitem associações diretas em outros ca
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Silva, Bruno Astrolino e. "Números de Fibonacci e números de Lucas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03032017-143706/.

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Neste trabalho, exploramos os números de Fibonacci e de Lucas. A maioria dos resultados históricos sobre esses números são apresentados e provados. Ao longo do texto, um grande número de identidades a respeito dos números de Fibonacci e de Lucas são mostradas válidas para todos os inteiros. Sequências generalizadas de Fibonacci, a relação entre os números de Fibonacci e de Lucas com as raízes da equação x2 -x -1 = 0 e a conexão entre os números de Fibonacci e de Lucas com uma classe de matrizes em M2(R) são também exploradas.<br>In this work we explore the Fibonacci and Lucas numbers. The majo
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Siani, Serena. "A problem in the Theory of Groups and a question related to Fibonacci-Like sequences." Doctoral thesis, Universita degli studi di Salerno, 2016. http://hdl.handle.net/10556/2180.

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2013 - 2014<br>This thesis is composed of four chapters, two of which, Chapter 3 and Chapter 4, contain original results. In Chapter 1 we recall some basic notions and establish some of the notation and terminology which will be used in the sequel. For example, we recall some useful results about the class X of groups which are isomorphic to their non-abelian subgroups. Every group of this class is in_nite and 2-generated. This class of groups has been studied by H. Smith and J. Wiegold( [34]). They proved that every insoluble X-group is centre- by-simple and they gave a complete characteriza
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Зинченко, Д. В. "Отпечаток Бога в математике и природе". Thesis, Сумский государственный университет, 2014. http://essuir.sumdu.edu.ua/handle/123456789/38774.

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Если верить Библии, то существует некий творец, который создал вселенную и положил начало жизни человека, природы… У каждого из нас есть отпечатки пальцев, именно они делают нас индивидуальными с самого рождения. Касаясь к чему либо, мы оставляем свой неповторимый след. И не исключено, что при творении мира сего Бог тоже оставил отпечаток своих пальцев.
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Bethlehem, Tobias. "Theory of 3-4 Heap." Thesis, University of Canterbury. Computer Science and Software Engineering, 2008. http://hdl.handle.net/10092/1930.

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As an alternative to the Fibonacci heap, and a variation of the 2-3 heap data structure by Tadao Takaoka, this research presents the 3-4 heap data structure. The aim is to prove that the 3-4 heap, like its counter-part 2-3 heap, also supports n insert, n delete-min, and m decrease-key operations, in O(m + nlog n) time. Many performance tests were carried out during this research comparing the 3-4 heap against the 2-3 heap and for a narrow set of circumstances the 3-4 heap outperformed the 2-3 heap. The 2-3 heap has got a structure based on dimensions which are rigid using ternary linking an
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Silva, Júnior Normando. "Aplicações para o princípio de indução matemática." Universidade Federal de Goiás, 2014. http://repositorio.bc.ufg.br/tede/handle/tede/7508.

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Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-23T18:24:17Z No. of bitstreams: 2 Dissertação - Normando Silva Junior - 2014.pdf: 1908561 bytes, checksum: 892d0c609dce5de60fb3458349a15243 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2017-07-07T20:23:37Z (GMT) No. of bitstreams: 2 Dissertação - Normando Silva Junior - 2014.pdf: 1908561 bytes, checksum: 892d0c609dce5de60fb3458349a15243 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br
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Belmont, Daniele Ferreira de Sousa. "Teoria das ondas de elliott: uma aplicação ao mercado de ações da bm&fbovespa." Universidade Federal da Paraí­ba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/5048.

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Made available in DSpace on 2015-05-08T14:45:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1848162 bytes, checksum: 8d8c6d6ea96038f73be05f042425a488 (MD5) Previous issue date: 2010-09-17<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>The prices of securities traded on stock exchanges, as well as any other commodity in the financial market fluctuate naturally with the demand for these products. These oscillations, along with the asymmetry of information about the prices of these products generate volatility processes. Charles Dow in the early twentieth century created s
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Hanley, Jodi Ann. "Egyptian fractions." CSUSB ScholarWorks, 2002. https://scholarworks.lib.csusb.edu/etd-project/2323.

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Egyptian fractions are what we know as unit fractions that are of the form 1/n - with the exception, by the Egyptians, of 2/3. Egyptian fractions have actually played an important part in mathematics history with its primary roots in number theory. This paper will trace the history of Egyptian fractions by starting at the time of the Egyptians, working our way to Fibonacci, a geologist named Farey, continued fractions, Diophantine equations, and unsolved problems in number theory.
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Books on the topic "Fibonacci theory"

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Vajda, Steven. Fibonacci and Lucas numbers, and the golden section: Theory and applications. Ellis Horwood, 1989.

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Howard, Frederic T. Applications of Fibonacci Numbers: Volume 9: Proceedings of The Tenth International Research Conference on Fibonacci Numbers and Their Applications. Springer Netherlands, 2004.

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Vajda, S. Fibonacci & Lucas numbers, and the golden section: Theory and applications. E. Horwood Ltd., 1989.

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International Conference on Fibonacci Numbers and Their Applications (6th 1994 Washington State University). Applications of Fibonacci numbers: Proceedings of "the sixth International Research Conference on Fibonacci Numbers and Their Applications", Washington State University, Pullman, Washington, U.S.A., July 18-22, 1994. Kluwer Academic, 1996.

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International Conference on Fibonacci Numbers and Their Applications (8th 1998 Rochester Institute of Technology). Applications of fibonacci numbers: Volume 8 : proceedings of 'The Eighth International Research Conference on Fibonacci Numbers and Their Applications', Rochester Institute of Technology, Rochester, New York, U.S.A., June 22-26, 1998. Springer, 1999.

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International Conference on Fibonacci Numbers and Their Applications (7th 1996 Technische Universität Graz). Applications of Fibonacci numbers: Proceedings of 'The Seventh International Confererence on Fibonacci Numbers and their Applications',Technische Universität, Graz, Austria, July 15-19, 1996. Kluwer Academic, 1998.

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Anthony, Olsen Scott, ed. The mathematics of harmony: From Euclid to contemporary mathematics and computer science. World Scientific, 2009.

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Benjamin, Arthur. Discrete mathematics. The Teaching Company, 2009.

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Florian, Luca, ed. Analytic number theory: Exploring the anatomy of integers. American Mathematical Society, 2012.

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Bergum, G. E. Applications of Fibonacci Numbers. Springer Verlag, 2013.

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Book chapters on the topic "Fibonacci theory"

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Vorobiew, Nicolai N. "Fibonacci Numbers and Search Theory." In Fibonacci Numbers. Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8107-4_6.

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Stachowiak, Grzegorz. "Fibonacci Correction Networks." In Algorithm Theory - SWAT 2000. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-44985-x_45.

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Křížek, Michal, Lawrence Somer, and Alena Šolcová. "Fibonacci and Lucas Numbers." In From Great Discoveries in Number Theory to Applications. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-83899-7_7.

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Bicknell-Johnson, Marjorie. "On Purple Parrots, Fibonacci Numbers, and Color Theory." In Applications of Fibonacci Numbers. Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-0-306-48517-6_6.

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Prajapati, U. M., and K. K. Raval. "A Few Results on Fibonacci Cordial Labeling." In Recent Advancements in Graph Theory. CRC Press, 2020. http://dx.doi.org/10.1201/9781003038436-10.

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Lindner, Marko, and Hagen Söding. "Finite sections of the Fibonacci Hamiltonian." In The Diversity and Beauty of Applied Operator Theory. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-75996-8_20.

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Temlyakov, V. N. "Universality of the fibonacci cubature formulas." In Methods of Approximation Theory in Complex Analysis and Mathematical Physics. Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/bfb0117486.

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Rosenberger, Gerhard. "A Note on Fibonacci and Related Numbers in the Theory of 2 × 2 Matrices." In Fibonacci Numbers and Their Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4311-7_18.

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Khan, Vakeel A., Kamal M. A. S. Alshlool, and Sameera A. A. Abdullah. "A Study of Fibonacci Difference I–Convergent Sequence Spaces." In Sequence Space Theory with Applications. Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003178200-6.

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Lahr, Joseph. "Fibonacci and Lucas Numbers and the Morgan-Voyce Polynomials in Ladder Networks and in Electric Line Theory." In Fibonacci Numbers and Their Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4311-7_11.

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Conference papers on the topic "Fibonacci theory"

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Wang, Hsin-Po, and Chi-Wei Chin. "On Counting Subsequences and Higher-Order Fibonacci Numbers." In 2024 IEEE International Symposium on Information Theory (ISIT). IEEE, 2024. http://dx.doi.org/10.1109/isit57864.2024.10619178.

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Esmaeili, Mostafa, Morteza Esmaeili, and T. Aaron Gulliver. "High rate fibonacci polynomial codes." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6033886.

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Davies, B., and L. Morini. "Mathematical Theory For Supercell Approximations Of Fibonacci Quasicrystals." In 2023 Seventeenth International Congress on Artificial Materials for Novel Wave Phenomena (Metamaterials). IEEE, 2023. http://dx.doi.org/10.1109/metamaterials58257.2023.10289207.

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Kushnerov, Alexander, Tsorng-Juu Peter Liang, and Alexandre Yakovlev. "Multiphase ternary Fibonacci 2D switched capacitor converters." In 2017 European Conference on Circuit Theory and Design (ECCTD). IEEE, 2017. http://dx.doi.org/10.1109/ecctd.2017.8093316.

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Rostami, Ali, Samiye Matloub, and F. Janabi Sharifi. "Analysis of one-dimensional Fibonacci-class quasicrystals using perturbation theory." In 2009 International Symposium on Optomechatronic Technologies (ISOT 2009). IEEE, 2009. http://dx.doi.org/10.1109/isot.2009.5326071.

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Blaum, Mario, and Ksenija Lakovic. "Variable Span Fibonacci Modulation Codes with Limited Byte Error Propagation." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557601.

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Allasasmeh, Younis, and Stefano Gregori. "A performance comparison of dickson and fibonacci charge pumps." In 2009 European Conference on Circuit Theory and Design (ECCTD 2009). IEEE, 2009. http://dx.doi.org/10.1109/ecctd.2009.5275049.

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Ying Zhang. "A cryptographic algorithm based on pq-generalized Fibonacci matrix." In 2010 IEEE International Conference on Information Theory and Information Security (ICITIS). IEEE, 2010. http://dx.doi.org/10.1109/icitis.2010.5689571.

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Hussein, Hisham H., Wassim Alexan, Mohamed ElBeltagy, and Amr Aboshousha. "Visual Data Security Incorporating Fibonacci Sequence, S-Box, and Chaos Theory." In 2022 International Conference on Smart Systems and Power Management (IC2SPM). IEEE, 2022. http://dx.doi.org/10.1109/ic2spm56638.2022.9989013.

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Patsakis, Constantinos, and Evangelos Fountas. "Extending Fibonacci LSB data hiding technique to more integer bases." In 2010 3rd International Conference on Advanced Computer Theory and Engineering (ICACTE 2010). IEEE, 2010. http://dx.doi.org/10.1109/icacte.2010.5579623.

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