On the structure of periodic complex Horadam orbits
Journal article
Bagdasar, Ovidiu, Larcombe, Peter J. and Anjum, Ashiq 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics..
| Authors | Bagdasar, Ovidiu, Larcombe, Peter J. and Anjum, Ashiq |
|---|---|
| Abstract | Numerous geometric patterns identified in nature, art or science can be generated from recurrent sequences, such as for example certain fractals or Fermat’s spiral. Fibonacci numbers in particular have been used to design search techniques, pseudo random-number generators and data structures. Complex Horadam sequences are a natural extension of Fibonacci sequence to complex numbers, involving four parameters (two initial values and two in the defining recursion), therefore successive sequence terms can be visualized in the complex plane. Here, a classification of the periodic orbits is proposed, based on divisibility relations between orders of generators (roots of the characteristic polynomial). Regular star polygons, bipartite graphs and multisymmetric patterns can be recovered for selected parameter values. Some applications are also suggested. |
Numerous geometric patterns identified in nature, art or science can be generated from recurrent | |
| Keywords | Discrete mathematics; Applied mathematics |
| Year | 2016 |
| Journal | Carpathian Journal of Mathematics. |
| Publisher | North University of Baia Mare (Romania) |
| ISSN | 1584-2851 |
| 1843-4401 | |
| Web address (URL) | http://hdl.handle.net/10545/620860 |
| http://creativecommons.org/licenses/by/4.0/ | |
| hdl:10545/620860 | |
| Publication dates | 16 Jan 2016 |
| Publication process dates | |
| Deposited | 16 Nov 2016, 13:28 |
| Contributors | University of Derby |
| File | File Access Level Open |
| File | File Access Level Open |
| File |
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Larcombe, Peter J. 2017. Horadam sequences: A survey update and extension. Bulletin of the Institute of Combinatorics and its Applications (ICA).On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application.
Larcombe, Peter J. and Fennessey, Eric J. 2017. On sequence-based closed form entries for an exponentiated general $2 \times 2$ matrix: A re-formulation and an application. Bulletin of the Institute of Combinatorics and its Applications (ICA).On the masked periodicity of Horadam sequences: A generator-based approach.
Bagdasar, Ovidiu and Larcombe, Peter J. 2017. On the masked periodicity of Horadam sequences: A generator-based approach. Fibonacci Quarterly.Cloud-based video analytics using convolutional neural networks.
Yaseen, M., Anjum, Ashiq, Farid, Mohsen and Antonopoulos, Nick 2018. Cloud-based video analytics using convolutional neural networks. Software Practice and Experience. https://doi.org/10.1002/spe.2636Deep learning hyper-parameter optimization for video analytics in clouds.
Yaseen, M., Anjum, Ashiq, Rana, Omer and Antonopoulos, Nikolaos 2018. Deep learning hyper-parameter optimization for video analytics in clouds. IEEE Transactions on Systems, Man, and Cybernetics. https://doi.org/10.1109/TSMC.2018.2840341Edge enhanced deep learning system for large-scale video stream analytics.
Ali, Muhammad, Anjum, Ashiq, Yaseen, M. Usman, Zamani, A. Reza, Balouek-Thomert, Daniel, Rana, Omer and Parashar, Manish 2018. Edge enhanced deep learning system for large-scale video stream analytics. IEEE. https://doi.org/10.1109/CFEC.2018.8358733Qualitative case study methodology: Automatic design and correction of ceramic colors.
Bagdasar, Ovidiu, Birlutiu, Adriana, Chen, Minsi and Popa, Ioan-Lucian 2017. Qualitative case study methodology: Automatic design and correction of ceramic colors. IEEE. https://doi.org/10.1109/ICSTCC.2017.8107118Representing variant calling format as directed acyclic graphs to enable the use of cloud computing for efficient and cost effective genome analysis
Aizad, Sanna, Anjum, Ashiq and Sakellariou, Rizos 2017. Representing variant calling format as directed acyclic graphs to enable the use of cloud computing for efficient and cost effective genome analysis. IEEE. https://doi.org/10.1109/CCGRID.2017.116Blockchain standards for compliance and trust
Anjum, Ashiq, Sporny, Manu and Sill, Alan 2017. Blockchain standards for compliance and trust. IEEE Cloud Computing. https://doi.org/10.1109/MCC.2017.3791019Big data analytics in healthcare: A cloud based framework for generating insights
Anjum, Ashiq, Aizad, Sanna, Arshad, Bilal, Subhani, Moeez, Davies-Tagg, Dominic, Abdullah, Tariq and Antonopoulos, Nikolaos 2017. Big data analytics in healthcare: A cloud based framework for generating insights. in: Springer.Clinical and genomics data integration using meta-dimensional approach
Subhani, Moeez, Anjum, Ashiq, Koop, Andreas and Antonopoulos, Nikolaos 2016. Clinical and genomics data integration using meta-dimensional approach. Association for Computing Machinery. https://doi.org/10.1145/2996890.3007896Deadline constrained video analysis via in-transit computational environments
Zamani, Ali Reza, Zou, Mengsong, Diaz-Montes, Javier, Petri, Ioan, Rana, Omer, Anjum, Ashiq and Parashar, Manish 2017. Deadline constrained video analysis via in-transit computational environments. IEEE Transactions on Services Computing. https://doi.org/10.1109/TSC.2017.2653116Data Intensive and Network Aware (DIANA) grid scheduling
McClatchey, Richard, Anjum, Ashiq, Stockinger, Heinz, Ali, Arshad, Willers, Ian and Thomas, Michael 2007. Data Intensive and Network Aware (DIANA) grid scheduling. Journal of Grid Computing. https://doi.org/10.1007/s10723-006-9059-zIntelligent grid enabled services for neuroimaging analysis
McClatchey, Richard, Habib, Irfan, Anjum, Ashiq, Munir, Kamran, Branson, Andrew, Bloodsworth, Peter and Kiani, Saad Liaquat 2013. Intelligent grid enabled services for neuroimaging analysis. Neurocomputing. https://doi.org/10.1016/j.neucom.2013.01.042Cloud-based scalable object detection and classification in video streams
Yaseen, M., Anjum, Ashiq, Rana, Omer and Hill, Richard 2017. Cloud-based scalable object detection and classification in video streams. Future Generation Computer Systems. https://doi.org/10.1016/j.future.2017.02.003Modeling and analysis of a deep learning pipeline for cloud based video analytics.
Yaseen, M., Anjum, Ashiq and Antonopoulos, Nikolaos 2017. Modeling and analysis of a deep learning pipeline for cloud based video analytics. https://doi.org/10.1145/3148055.3148081Conditions governing cross-family member equality in a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2014. Conditions governing cross-family member equality in a particular class of polynomial families. Fibonacci Quarterly.On certain series expansions of the sine function: Catalan numbers and convergence
Larcombe, Peter J., O'Neill, Sam T. and Fennessey, Eric J. 2014. On certain series expansions of the sine function: Catalan numbers and convergence. Fibonacci Quarterly.Traffic monitoring using video analytics in clouds
Abdullah, Tariq, Anjum, Ashiq, Tariq, M. Fahim, Baltaci, Yusuf and Antonopoulos, Nikolaos 2014. Traffic monitoring using video analytics in clouds. IEEE. https://doi.org/10.1109/UCC.2014.12On the number of complex horadam sequences with a fixed period
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the number of complex horadam sequences with a fixed period. Fibonacci Quarterly.On the characterization of periodic complex Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2013. On the characterization of periodic complex Horadam sequences. Fibonacci Quarterly.Big-Data analytics and cloud computing: Theory, algorithms and applications
Hill, Richard, Trovati, Marcello, Liu, Lu, Anjum, Ashiq and Zhu, Shao Ying 2015. Big-Data analytics and cloud computing: Theory, algorithms and applications. Springer.On a result of Bunder involving Horadam sequences: A proof and generalization
Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.On a result of Bunder involving horadam sequences: A new proof
Larcombe, Peter J., Bagdasar, Ovidiu and Fennessey, Eric J. 2014. On a result of Bunder involving horadam sequences: A new proof. Fibonacci Quarterly.Influence discovery in semantic networks: An initial approach
Trovati, Marcello and Bagdasar, Ovidiu 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/UKSim.2014.48Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570Concise computer mathematics: tutorials on theory and problems
Bagdasar, Ovidiu 2013. Concise computer mathematics: tutorials on theory and problems. Springer.On the characterization of periodic generalized Horadam sequences
Bagdasar, Ovidiu and Larcombe, Peter J. 2014. On the characterization of periodic generalized Horadam sequences. Journal of Difference Equations and Applications. https://doi.org/10.1080/10236198.2014.891022Local maximum points of explicitly quasiconvex functions
Bagdasar, Ovidiu and Popovici, Nicolae 2014. Local maximum points of explicitly quasiconvex functions. Optimization Letters. https://doi.org/10.1007/s11590-014-0781-3A Horadam-based pseudo-random number generator
Bagdasar, Ovidiu and Chen, Minsi 2014. A Horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/UKSim.2014.55Alwyn Francis Horadam, 1923-2016: A personal tribute to the man and his sequence
Larcombe, Peter J. 2016. Alwyn Francis Horadam, 1923-2016: A personal tribute to the man and his sequence. Bulletin of the Institute of Combinatorics and its Applications (ICA).A scaled power product recurrence examined using matrix methods
Larcombe, Peter J. and Fennessey, Eric J. 2016. A scaled power product recurrence examined using matrix methods. Bulletin of the Institute of Combinatorics and its Applications (ICA).On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach
Larcombe, Peter J. 2016. On the evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations using a hypergeometric approach. Fibonacci Quarterly.On a scaled balanced-power product recurrence
Larcombe, Peter J. and Fennessey, Eric J. 2016. On a scaled balanced-power product recurrence. Fibonacci Quarterly.A short monograph on exposition and the emotive nature of research and publishing
Larcombe, Peter J. 2016. A short monograph on exposition and the emotive nature of research and publishing. Mathematics Today.A polynomial based construction of periodic Horadam sequences
Larcombe, Peter J. and Fennessey, Eric J. 2016. A polynomial based construction of periodic Horadam sequences. Utilitas Mathematica.A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix power
Larcombe, Peter J. 2016. A new formulation of a result by McLaughlin for an arbitrary dimension 2 matrix power. Bulletin of the Institute of Combinatorics and its Applications (ICA).On the jacobsthal, horadam and geometric mean sequences
Larcombe, Peter J. and Rabago, Julius, F. T. 2016. On the jacobsthal, horadam and geometric mean sequences. Bulletin of the Institute of Combinatorics and its Applications (ICA).A note on the invariance of the general $2 \times 2$ matrix anti-diagonals ratio with increasing matrix power: Four proofs
Larcombe, Peter J. 2015. A note on the invariance of the general $2 \times 2$ matrix anti-diagonals ratio with increasing matrix power: Four proofs. Fibonacci Quarterly.Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations
Larcombe, Peter J. 2015. Closed form evaluations of some series comprising sums of exponentiated multiples of two-term and three-term Catalan number linear combinations. Fibonacci Quarterly.Closed form evaluations of some series involving Catalan numbers
Larcombe, Peter J. 2014. Closed form evaluations of some series involving Catalan numbers. Bulletin of the Institute of Combinatorics and its Applications (ICA).A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2015. A condition for anti-diagonals product invariance across powers of $2 \times 2$ matrix sets characterizing a particular class of polynomial families. Fibonacci Quarterly.On the phenomenon of masked periodic Horadam sequences
Larcombe, Peter J. and Fennessey, Eric J. 2015. On the phenomenon of masked periodic Horadam sequences. Utilitas Mathematica.On horadam sequence periodicity: A new approach
Larcombe, Peter J. and Fennessey, Eric J. 2015. On horadam sequence periodicity: A new approach. Bulletin of the Institute of Combinatorics and its Applications (ICA).A non-linear identity for a particular class of polynomial families
Larcombe, Peter J. and Fennessey, Eric J. 2014. A non-linear identity for a particular class of polynomial families. Fibonacci Quarterly.On cyclicity and density of some Catalan polynomial sequences
Larcombe, Peter J. and Fennessey, Eric J. 2014. On cyclicity and density of some Catalan polynomial sequences. Bulletin of the Institute of Combinatorics and its Applications (ICA).Some factorisation and divisibility properties of Catalan polynomials
Jarvis, Frazer A., Larcombe, Peter J. and Fennessey, Eric J. 2014. Some factorisation and divisibility properties of Catalan polynomials. Bulletin of the Institute of Combinatorics and its Applications (ICA).Generalised Catalan polynomials and their properties
Larcombe, Peter J., Jarvis, Frazer A. and Fennessey, Eric J. 2014. Generalised Catalan polynomials and their properties. Bulletin of the Institute of Combinatorics and its Applications (ICA).The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs
Larcombe, Peter J., Kirschenhofer, Peter and Fennessey, Eric J. 2014. The Asymptotic Form of the Sum $\sum_{i=0}^{n} i^{p} { n+i \choose i }$: Two Proofs. Utilitas Mathematica.A cloud resource management model for the creation and orchestration of social communities
Ikram, Ahsan, Anjum, Ashiq and Bessis, Nik 2015. A cloud resource management model for the creation and orchestration of social communities. Simulation Modelling Practice and Theory. https://doi.org/10.1016/j.simpat.2014.05.003Federated broker system for pervasive context provisioning
Kiani, Saad Liaquat, Anjum, Ashiq, Knappmeyer, Michael, Bessis, Nik and Antonopoulos, Nikolaos 2013. Federated broker system for pervasive context provisioning. Journal of Systems and Software. https://doi.org/10.1016/j.jss.2012.11.050Adapting scientific workflow structures using multi-objective optimization strategies
Habib, Irfan, Anjum, Ashiq, Mcclatchey, Richard and Rana, Omer 2013. Adapting scientific workflow structures using multi-objective optimization strategies. ACM Transactions on Autonomous and Adaptive Systems. https://doi.org/10.1145/2451248.2451252Video stream analysis in clouds: An object detection and classification framework for high performance video analytics
Anjum, Ashiq, Abdullah, Tariq, Tariq, M. Fahim, Baltaci, Yusuf and Antonopoulos, Nikolaos 2016. Video stream analysis in clouds: An object detection and classification framework for high performance video analytics. IEEE Transactions on Cloud Computing. https://doi.org/10.1109/TCC.2016.2517653Towards cloud based big data analytics for smart future cities
Khan, Zaheer, Anjum, Ashiq, Tahir, Muhammad Atif and Soomro, Kamran Ahmed 2015. Towards cloud based big data analytics for smart future cities. Journal of Cloud Computing. https://doi.org/10.1186/s13677-015-0026-8Spatial frequency based video stream analysis for object classification and recognition in clouds
Yaseen, M., Anjum, Ashiq and Antonopoulos, Nikolaos 2016. Spatial frequency based video stream analysis for object classification and recognition in clouds. IEEE.High performance video processing in cloud data centres
Yaseen, M., Zafar, Muhammad Sarim, Anjum, Ashiq and Hill, Richard 2016. High performance video processing in cloud data centres. IEEE. https://doi.org/10.1109/SOSE.2016.56On some functions involving the lcm and gcd of integer tuples
Bagdasar, Ovidiu 2014. On some functions involving the lcm and gcd of integer tuples. Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics. https://doi.org/10.5937/SPSUNP1402091BAn Inter-Cloud Meta-Scheduling (ICMS) simulation framework: architecture and evaluation
Sotiriadis, Stelios, Bessis, Nik, Anjum, Ashiq and Buyya, Rajkumar 2015. An Inter-Cloud Meta-Scheduling (ICMS) simulation framework: architecture and evaluation. IEEE Transactions on Services Computing. https://doi.org/10.1109/TSC.2015.2399312Glueing grids and clouds together: a service-oriented approach
Anjum, Ashiq, Hill, Richard, McClatchey, Richard, Bessis, Nik and Branson, Andrew 2012. Glueing grids and clouds together: a service-oriented approach. International Journal of Web and Grid Services. https://doi.org/10.1504/IJWGS.2012.049169Energy conservation in mobile devices and applications: a case for context parsing, processing and distribution in clouds
Kiani, Saad Liaquat, Anjum, Ashiq, Bessis, Nik, Hill, Richard and Knappmeyer, Michael 2013. Energy conservation in mobile devices and applications: a case for context parsing, processing and distribution in clouds. Mobile Information Systems.Approaching the Internet of things (IoT): a modelling, analysis and abstraction framework
Ikram, Ahsan, Anjum, Ashiq, Hill, Richard, Antonopoulos, Nikolaos, Liu, Lu and Sotiriadis, Stelios 2013. Approaching the Internet of things (IoT): a modelling, analysis and abstraction framework. Concurrency and Computation: Practice and Experience. https://doi.org/10.1002/cpe.3131Performance simulation of a context provisioning middleware based on empirical measurements
Reetz, Eike Steffen, Knappmeyer, Michael, Kiani, Saad Liaquat, Anjum, Ashiq, Bessis, Nik and Tönjes, Ralf 2012. Performance simulation of a context provisioning middleware based on empirical measurements. https://doi.org/10.1016/j.simpat.2012.03.002