On a result of Bunder involving Horadam sequences: A proof and generalization

Journal article

Larcombe, Peter J. and Bagdasar, Ovidiu 2013. On a result of Bunder involving Horadam sequences: A proof and generalization. Fibonacci Quarterly.
AuthorsLarcombe, Peter J. and Bagdasar, Ovidiu
Abstract

This note introduces, proves, extends empirically and generalizes a short 1975 offering of M.W. Bunder who, in this journal, gave an isolated observation involving Horadam sequences on which work has been conducted for nearly half a century.

KeywordsRecurrent sequences; Horadam sequences; Complex plane
Year2013
JournalFibonacci Quarterly
PublisherFibonacci Association
ISSN0015-0517
Web address (URL)http://hdl.handle.net/10545/620892
http://creativecommons.org/licenses/by/4.0/
hdl:10545/620892
Publication dates03 May 2013
Publication process dates
Deposited17 Nov 2016, 12:42
ContributorsUniversity of Derby
File
File Access Level
Open
File
File Access Level
Open
Permalink -

https://repository.derby.ac.uk/item/952v5/on-a-result-of-bunder-involving-horadam-sequences-a-proof-and-generalization

Log in to edit

Download files

  • 54
    total views
  • 0
    total downloads
  • 2
    views this month
  • 0
    downloads this month

Export as

Related outputs

Deep Learning-Driven Anomaly Detection for IoMT-Based Smart Healthcare Systems
Bagdasar, O. 2024. Deep Learning-Driven Anomaly Detection for IoMT-Based Smart Healthcare Systems. Computer Modeling in Engineering & Sciences . 141 (3), pp. 2121-2141. https://doi.org/10.32604/cmes.2024.054380
Numerical analyses of acoustic vibrational resonance in a Helmholtz resonator
Omoteso, K., Bagdasar, O., Roy-Layinde, T. O. and Diala, U. 2024. Numerical analyses of acoustic vibrational resonance in a Helmholtz resonator. Nonlinear Dynamics . pp. 1-21. https://doi.org/10.1007/s11071-024-10534-w
A New Algorithm for Variational Inequality Problems in CAT(0) Spaces
Kalsoom, A., Rashid, M., Ovidiu Bagdasar and Un Nisa, Z. 2024. A New Algorithm for Variational Inequality Problems in CAT(0) Spaces. Mathematics. 12 (14), pp. 1-20. https://doi.org/10.3390/math12142193
On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle
Andrica, D. and Ovidiu Bagdasar 2024. On Some Properties of the Equilateral Triangles with Vertices Located on the Support Sides of a Triangle. Axioms. 13 (7), pp. 1-15. https://doi.org/10.3390/axioms13070478
On the Dynamic Geometry of Kasner Polygons with Complex Parameter
Dorin Andrica and Ovidiu Bagdasar 2024. On the Dynamic Geometry of Kasner Polygons with Complex Parameter. International Conference on Difference Equations and Applications. Springer. https://doi.org/10.1007/978-3-031-51049-6_4
Inertial Krasnosel’skiĭ-Mann iterative algorithm with step-size parameters involving nonexpansive mappings with applications to solve image restoration problems
Artsawang, N., Baiya, S., Ungchittrakool, K., Bagdasar, O., Plubtieng, S. and Thammasiri, P. 2024. Inertial Krasnosel’skiĭ-Mann iterative algorithm with step-size parameters involving nonexpansive mappings with applications to solve image restoration problems. Carpathian Journal of Mathematics.. 40 (2), pp. 243- 261. https://doi.org/10.37193/CJM.2024.02.02
On the Dynamic Geometry of Kasner Triangles with Complex Parameter
Dorin Andrica and Ovidiu Bagdasar 2023. On the Dynamic Geometry of Kasner Triangles with Complex Parameter. International Conference on Mathematics and Computations. Springer. https://doi.org/10.1007/978-981-99-0447-1_17
Remarks on the Coefficients of Inverse Cyclotomic Polynomials
Andrica, D. and Ovidiu Bagdasar 2023. Remarks on the Coefficients of Inverse Cyclotomic Polynomials. Mathematics. 11 (17), pp. 1-16. https://doi.org/10.3390/math11173622
Modeling and Analyzing Logic Vulnerabilities of E-Commerce Systems at the Design Phase
Wangyang Yu, Lu Liu, Xiaoming Wang, Ovidiu Bagdasar and John Panneerselvam 2023. Modeling and Analyzing Logic Vulnerabilities of E-Commerce Systems at the Design Phase. IEEE Transactions on Systems, Man, and Cybernetics: Systems. https://doi.org/10.1109/tsmc.2023.3299605
Escape Rooms for Secondary Mathematics Education: Design and Experiments
Andrews, J. and Bagdasar, O. 2023. Escape Rooms for Secondary Mathematics Education: Design and Experiments. Open Education Studies . 5 (1), pp. 1-17. https://doi.org/10.1515/edu-2022-0194
On some links between the generalised Lucas pseudoprimes of level k
Andrica, Dorin, Bagdasar, O. and Rassias, Michael Th. 2023. On some links between the generalised Lucas pseudoprimes of level k. Analele Universitatii "Ovidius" Constanta - Seria Matematica. Vol 31 (Issue 1), pp. 23-46. https://doi.org/10.2478/auom-2023-0002
On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators
Bagdasar, O., Chen, M, Drăgan, V., Ivanov, I.G. and Popa, I.-L. 2023. On Horadam Sequences with Dense Orbits and Pseudo-Random Number Generators. Mathematics. 11 (5), pp. 1-16. https://doi.org/10.3390/math11051244
On a Hilbert-type integral inequality in the whole plane with the equivalent forms
B. C. Yang, D. Andrica, Bagdasar, O. and M. Th. Rassias 2023. On a Hilbert-type integral inequality in the whole plane with the equivalent forms. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. (57), pp. 1-16. https://doi.org/10.1007/s13398-023-01388-9
Critical Comparison of Data Imputation Techniques at IoT Edge
Erhan, L., Di Mauro, M., Bagdasar, O. and Liotta, A. David Camacho, Prof. Domenico Rosaci, Prof. Giuseppe M. L. Sarné and Mario Versaci (ed.) 2022. Critical Comparison of Data Imputation Techniques at IoT Edge. Springer.
Mobility Analysis during the 2020 Pandemic in a Touristic city: the Case of Cagliari
Ferrara, Enrico, Uras, Marco, Atzori, Luigi, Bagdasar, Ovidiu and Liotta, Antonio 2021. Mobility Analysis during the 2020 Pandemic in a Touristic city: the Case of Cagliari. IEEE. https://doi.org/10.1109/ieeeconf49204.2021.9604867
Relations Between Entropy and Accuracy Trends in Complex Artificial Neural Networks
Cavallaro, Lucia, Grassia, Marco, Fiumara, Giacomo, Mangioni, Giuseppe, De Meo, Pasquale, Carchiolo, Vincenza, Bagdasar, Ovidiu and Liotta, Antonio 2022. Relations Between Entropy and Accuracy Trends in Complex Artificial Neural Networks. in: Complex Networks & Their Applications X Springer.
DYNAMIC GEOMETRY OF KASNER TRIANGLES WITH A FIXED WEIGHT
Andrica, D., Bagdasar, O. and Marinescu, D.Ş. 2022. DYNAMIC GEOMETRY OF KASNER TRIANGLES WITH A FIXED WEIGHT. INTERNATIONAL JOURNAL OF GEOMETRY. Vol 11 (Issue 2), pp. 101 - 110.
Weak Pseudoprimality Associated with the Generalized Lucas Sequences
Andrica, D., Bagdasar, O. and Rassias, M.T. 2022. Weak Pseudoprimality Associated with the Generalized Lucas Sequences. in: Nicholas J. Daras and Themistocles M. Rassias (ed.) Approximation and Computation in Science and Engineering Springer. pp. 53-75
Modelling equilibrium for a multi-criteria selfish routing network equilibrium flow problem
O'Neill, S., Bagdasar, O., Berry, S., Popovici, N. and Raja, R. 2022. Modelling equilibrium for a multi-criteria selfish routing network equilibrium flow problem. Mathematics and Computers in Simulation. Vol 201 (November 2022), pp. 658 - 669. https://doi.org/10.1016/j.matcom.2021.06.001
O(t−β) -Synchronization and Asymptotic Synchronization of Delayed Fractional Order Neural Networks
Pratap, A., Raja, R., Cao, J., Huang, C., Alzabut, J. and Bagdasar, O. 2022. O(t−β) -Synchronization and Asymptotic Synchronization of Delayed Fractional Order Neural Networks. Acta Mathematica Scientia. Vol 42 (Issue 4), p. 1273–1292. https://doi.org/10.1007/s10473-022-0402-7
An equivalent property of a Hilbert-type integral inequality and its applications
Bagdasar, O., Andrica, D., Yang, B. and Rassias, M.Th. 2022. An equivalent property of a Hilbert-type integral inequality and its applications. Applicable Analysis and Discrete Mathematics. Volume 16 (2), pp. 548-563. https://doi.org/10.2298/AADM220514025Y
On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter
Bagdasar, O. and Andrica, D. 2022. On the Dynamic Geometry of Kasner Quadrilaterals with Complex Parameter. Mathematics. 10 (18). https://doi.org/10.3390/math10183334
Reflections On What Mathematics Is and Isn't: Halmos, Keyser, and Others
Larcombe, P. 2022. Reflections On What Mathematics Is and Isn't: Halmos, Keyser, and Others. Palestine Journal of Mathematics. 11 (3), pp. 664-699.
Mathematician? Feeling Old? A Discussion
Larcombe, P. 2022. Mathematician? Feeling Old? A Discussion. Palestine Journal of Mathematics. 11, pp. 19-36.
Social network analysis: the use of graph distances to compare artificial and criminal networks
Ficara, Annamaria, Curreri, Francesco, Cavallaro, Lucia, De Meo, Pasquale, Fiumara, Giacomo, Bagdasar, Ovidiu and Liotta, Antonio 2021. Social network analysis: the use of graph distances to compare artificial and criminal networks. Journal of Smart Environments and Green Computing. https://doi.org/10.20517/jsegc.2021.08
Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games
Drăgan, Vasile, Ivanov, Ivan Ganchev, Popa, Ioan-Lucian and Bagdasar, Ovidiu 2021. Closed-Loop Nash Equilibrium in the Class of Piecewise Constant Strategies in a Linear State Feedback Form for Stochastic LQ Games. Mathematics. 9 (21), p. 2713. https://doi.org/10.3390/math9212713
A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems
O’Neill, Sam, Wrigley, Paul and Bagdasar, Ovidiu 2021. A mixed-integer linear programming formulation for the modular layout of three-dimensional connected systems. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.09.019
Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria
Arockia, Stephen, Raja, R, Alzabut, J, Zhu, Quanxin, Niezabitowski, M and Bagdasar, Ovidiu 2021. Mixed Time-Delayed Nonlinear Multi-agent Dynamic Systems for Asymptotic Stability and Non-fragile Synchronization Criteria. Neural Processing Letters. https://doi.org/10.1007/s11063-021-10619-2
Criminal networks analysis in missing data scenarios through graph distances
Ficara, A., Cavallaro, L., Curreri, F., Fiumara, G., de Meo, P., Bagdasar, O., Song, W. and Liotta, A. 2021. Criminal networks analysis in missing data scenarios through graph distances. Public Library of Science (PLoS). https://doi.org/10.1371/journal.pone.0255067
Internet of Planets (IoP): A New Era of the Internet
Kang, Byungseok, Malute, Francis, Bagdasar, Ovidiu and Hong, Choongseon 2021. Internet of Planets (IoP): A New Era of the Internet. IT Professional. 23 (3), pp. 76-81. https://doi.org/10.1109/mitp.2021.3068763
On Generalized Lucas Pseudoprimality of Level k
Andrica, Dorin and Bagdasar, Ovidiu 2021. On Generalized Lucas Pseudoprimality of Level k. Mathematics. 9 (8), p. 838. https://doi.org/10.3390/math9080838
On k-partitions of multisets with equal sums
Andrica, Dorin and Bagdasar, Ovidiu 2021. On k-partitions of multisets with equal sums. The Ramanujan Journal. 55 (2), pp. 421-435. https://doi.org/10.1007/s11139-021-00418-7
Graph and network theory for the analysis of criminal networks
Cavallaro, L., Bagdasar, O., de Meo, P., Liotta, A. and Fiumara, G. 2021. Graph and network theory for the analysis of criminal networks. Springer, Cham. https://doi.org/10.1007/978-3-030-67197-6_8
An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control
Dianavinnarasi, J., Raja, R., Alzabut, J., Niezabitowski, M., Selvam, G. and Bagdasar, O. 2021. An LMI Approach-Based Mathematical Model to Control Aedes aegypti Mosquitoes Population via Biological Control. Mathematical Problems in Engineering. 2021, pp. 1-18. https://doi.org/10.1155/2021/5565949
Controlling Wolbachia transmission and invasion dynamics among aedes aegypti population via impulsive control strategy
Dianavinnarasi, Joseph, Raja, Ramachandran, Alzabut, Jehad, Niezabitowski, Michał and Bagdasar, Ovidiu 2021. Controlling Wolbachia transmission and invasion dynamics among aedes aegypti population via impulsive control strategy. Symmetry. 13 (3), p. 434. https://doi.org/10.3390/sym13030434
Application of caputo–fabrizio operator to suppress the aedes aegypti mosquitoes via wolbachia: an LMI approach
Dianavinnarasi, J., Raja, R., Alzabut, J., Cao, J., Niezabitowski, M. and Bagdasar, O. 2021. Application of caputo–fabrizio operator to suppress the aedes aegypti mosquitoes via wolbachia: an LMI approach. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.02.002
Pseudoprimality related to the generalized Lucas sequences
Andrica, Dorin and Bagdasar, Ovidiu 2021. Pseudoprimality related to the generalized Lucas sequences. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2021.03.003
On some new arithmetic properties of the generalized Lucas sequences
Andrica, Dorin and Bagdasar, Ovidiu 2021. On some new arithmetic properties of the generalized Lucas sequences. Mediterranean Journal of Mathematics. 18 (2). https://doi.org/10.1007/s00009-020-01653-w
The number of partitions of a set and Superelliptic Diophantine equations
Andrica, Dorin, Bagdasar, Ovidiu and Ţurcaş, George Cătălin 2020. The number of partitions of a set and Superelliptic Diophantine equations. in: Springer Optimization and Its Applications Springer.
Graph Comparison and Artificial Models for Simulating Real Criminal Networks
Cavallaro, L., Ficara, A., Curreri, F., Fiumara, G., De Meo, P., Bagdasar, O. and Liotta, A. Prof. Rosa M. Benito, Prof. Chantal Cherifi, Prof. Hocine Cherifi, Prof. Esteban Moro, Prof. Luis Mateus Rocha and Prof. Marta Sales-Pardo (ed.) Graph Comparison and Artificial Models for Simulating Real Criminal Networks.
On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms
Yang, B., Andrica, D., Bagdasar, O. and Rassias, M.T. 2021. On Two Kinds of the Hardy-Type Integral Inequalities in the Whole Plane with the Equivalent Forms. in: Ioannis N. Parasidis, Efthimios Providas and Themistocles M. Rassias (ed.) Mathematical Analysis in Interdisciplinary Research Springer. pp. 1025 - 1048
On some new results for the generalised Lucas sequences
Andrica, D., Bagdasar, O. and Turcaş, G.C. 2021. On some new results for the generalised Lucas sequences. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. Volume 29 (Issue 1), pp. 17 - 36. https://doi.org/10.2478/auom-2021-0002
On 'Two Cultures' and Tackling the 'Writing Versus Mathematics' Dichotomy
Larcombe, P. 2021. On 'Two Cultures' and Tackling the 'Writing Versus Mathematics' Dichotomy. Palestine Journal of Mathematics. 10 (2), pp. 480-486.
Write, and Write Well - Speak, and Speak Well: The Gospel According to Halmos and Rota
Larcombe, P. 2021. Write, and Write Well - Speak, and Speak Well: The Gospel According to Halmos and Rota. Palestine Journal of Mathematics. 10 (1), pp. 86-101.
Embedded Data Imputation for Environmental Intelligent Sensing: A Case Study
Erhan, Laura, Di Mauro, Mario, Anjum, Ashiq, Bagdasar, Ovidiu, Song, Wei and Liotta, Antonio 2021. Embedded Data Imputation for Environmental Intelligent Sensing: A Case Study. Sensors. 21 (23), p. 7774. https://doi.org/10.3390/s21237774
Smart anomaly detection in sensor systems: A multi-perspective review
Erhan, L., Ndubuaku, M., Di Mauro, M., Song, W., Chen, M., Fortino, G., Bagdasar, O. and Liotta, A. 2020. Smart anomaly detection in sensor systems: A multi-perspective review. Elsevier. https://doi.org/10.1016/j.inffus.2020.10.001
WiFi probes sniffing: an artificial intelligence based approach for MAC addresses de-randomization
Uras, Marco, Cossu, Raimondo, Ferrara, Enrico, Bagdasar, Ovidiu, Liotta, Antonio and Atzori, Luigi 2020. WiFi probes sniffing: an artificial intelligence based approach for MAC addresses de-randomization. IEEE. https://doi.org/10.1109/camad50429.2020.9209257
Recurrent sequences: Key results, applications, and problems
Andrica, Dorin and Bagdasar, Ovidiu 2020. Recurrent sequences: Key results, applications, and problems. Springer International Publishing.
CloudIoT-based Jukebox Platform: a music player for mobile users in Café
Kang, Byungseok, Lee, Joohyun, Bagdasar, Ovidiu and Choo, Hyunseung 2020. CloudIoT-based Jukebox Platform: a music player for mobile users in Café. Journal of Internet Technology. https://doi.org/10.3966/160792642020092105012
Artificial Neural Networks Training Acceleration Through Network Science Strategies
Lucia Cavallaro, Ovidiu Bagdasar, Pasquale De Meo, Giacomo Fiumara and Antonio Liotta 2020. Artificial Neural Networks Training Acceleration Through Network Science Strategies. in: Springer Science and Business Media LLC.
Stability of discrete-time fractional-order time-delayed neural networks in complex field
Pratap, Anbalagan, Raja, Ramachandran, Cao, Jinde, Huang, Chuangxia, Niezabitowski, Michal and Bagdasar, Ovidiu 2020. Stability of discrete-time fractional-order time-delayed neural networks in complex field. Mathematical Methods in the Applied Sciences. https://doi.org/10.1002/mma.6745
Disrupting resilient criminal networks through data analysis: The case of sicilian mafia
Cavallaro, L., Ficara, A., de Meo, P., Fiumara, G., Catanese, S., Bagdasar, O. and Liotta, A. 2020. Disrupting resilient criminal networks through data analysis: The case of sicilian mafia. Public Library of Science (PLoS). https://doi.org/10.1371/journal.pone.0236476
Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem
Pratap, A., Raja, R., Agarwal, Ravi. P., Cao, J. and Bagdasar, Ovidiu 2020. Multi-weighted complex structure on fractional order coupled neural networks with linear coupling delay: a robust synchronization problem. Neural Processing Letters. https://doi.org/10.1007/s11063-019-10188-5
Traffic assignment: on the interplay between optimization and equilibrium problems
Bagdasar, Ovidiu, Popovici, Nicolae and Berry, Stuart 2020. Traffic assignment: on the interplay between optimization and equilibrium problems. Optimization. https://doi.org/10.1080/02331934.2019.1711082
A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation
Chartbupapan, Watcharin, Bagdasar, Ovidiu and Mukdasai, Kanit 2020. A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation. Mathematics. 8 (1), p. 82. https://doi.org/10.3390/math8010082
An Online Learning Approach to a Multi-player N-armed Functional Bandit
Sam O’Neill, Ovidiu Bagdasar and Antonio Liotta 2020. An Online Learning Approach to a Multi-player N-armed Functional Bandit. in: Numerical Computations: Theory and Algorithms Springer. pp. 438 - 445
On Cyclotomic Polynomial Coefficients
Andrica, D. and Bagdasar, O. 2020. On Cyclotomic Polynomial Coefficients. Malaysian Journal of Mathematical Sciences. 14 (3), pp. 289 - 402.
DETN: Delay-Efficient Tolerant Network for Internet of Planet
Byungseok Kang, Francis Malute, Ovidiu Bagdasar and Hyunseung Choo 2020. DETN: Delay-Efficient Tolerant Network for Internet of Planet. IEEE Sensors Journal. 21 (2). https://doi.org/10.1109/jsen.2020.3020585
Efficient resampling for fraud detection during anonymised credit card transactions with unbalanced datasets
Mrozek, Petr, Panneerselvam, J. and Bagdasar, Ovidiu 2020. Efficient resampling for fraud detection during anonymised credit card transactions with unbalanced datasets. IEEE. https://doi.org/10.1109/ucc48980.2020.00067
Social Network Analysis of Sicilian Mafia Interconnections
Ficara, A., Cavallaro, L., De Meo, P., Fiumara, G., Catanese, S., Bagdasar, O. and Liotta, A. Hocine Cherifi, Sabrina Gaito, José Fernendo Mendes, Esteban Moro and Prof. Luis Mateus Rocha (ed.) 2020. Social Network Analysis of Sicilian Mafia Interconnections. Springer.
Remarks on a family of complex polynomials
Andrica, Dorin and Bagdasar, Ovidiu 2019. Remarks on a family of complex polynomials. Applicable Analysis and Discrete Mathematics. https://doi.org/10.2298/aadm180827022a
GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems
Xu, Xiaolong, Yuan, Hao, Matthew, Peter, Ray, Jeffrey, Bagdasar, Ovidiu and Trovati, Marcello 2019. GORTS: genetic algorithm based on one-by-one revision of two sides for dynamic travelling salesman problems. Soft Computing. https://doi.org/10.1007/s00500-019-04335-2
Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations
Pratap, A., Raja, R., Cao, J., Lim, C.P. and Bagdasar, Ovidiu 2019. Stability and pinning synchronization analysis of fractional order delayed Cohen–Grossberg neural networks with discontinuous activations. Applied Mathematics and Computation. 359, pp. 241-260. https://doi.org/10.1016/j.amc.2019.04.062
A new formula for the coefficients of Gaussian polynomials
Andrica, D. and Bagdasar, O. 2019. A new formula for the coefficients of Gaussian polynomials. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. https://doi.org/10.2478/auom-2019-0031
Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, O., Cao, J. and Rajchakit, G. 2019. Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays. Asian Journal of Control. https://doi.org/10.1002/asjc.2075
Mathematicians can also write, right?
Larcombe, Peter J 2019. Mathematicians can also write, right? Mathematics Today.
Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays
Pratap, A., Dianavinnarasi, J., Raja, R., Rajchakit, G., Cao, J. and Bagdasar, Ovidiu 2019. Mittag-Leffler state estimator design and synchronization analysis for fractional order BAM neural networks with time delays. International Journal of Adaptive Control and Signal Processing. https://doi.org/10.1002/acs.2983
A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations.
Larcombe, Peter J. and O'Neill, Sam T. 2018. A generating function approach to the automated evaluation of sums of exponentiated multiples of generalized Catalan number linear combinations. Fibonacci Quarterly.
Message from the workshop chairs
Yu, W., Liu, L., Fang, X. and Bagdasar, O. 2019. Message from the workshop chairs. 2019 IEEE SmartWorld. IEEE. https://doi.org/10.1109/smartworld-uic-atc-scalcom-iop-sci.2019.00036
Assessing Domain Specificity in the Measurement of Mathematics Calculation Anxiety
Hunt, Thomas E., Bagdasar, Ovidiu, Sheffield, David and Schofield, M. 2019. Assessing Domain Specificity in the Measurement of Mathematics Calculation Anxiety. Education Research International. 2019, pp. 1-7. https://doi.org/10.1155/2019/7412193
On some results concerning the polygonal polynomials
Andrica, D. and Bagdasar, O. 2019. On some results concerning the polygonal polynomials. Carpathian Journal of Mathematics. Vol 35 (Issue 1), pp. 1-12. https://doi.org/10.37193/cjm.2019.01.01
New proofs of linear recurrence identities for terms of the Horadam sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2019. New proofs of linear recurrence identities for terms of the Horadam sequence. Palestine Journal of Mathematics.
On the notion of mathematical genius: rhetoric and reality.
Larcombe, Peter J. 2019. On the notion of mathematical genius: rhetoric and reality. Palestine Journal of Mathematics.
On generalised multi-index non-linear recursion identities for terms of the Horadam sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2019. On generalised multi-index non-linear recursion identities for terms of the Horadam sequence. Palestine Journal of Mathematics.
A note on two rational invariants for a particular 2 x 2 matrix.
Larcombe, Peter J. and Fennessey, Eric J. 2018. A note on two rational invariants for a particular 2 x 2 matrix. Palestine Journal of Mathematics.
A new non-linear recurrence identity class for Horadam sequence terms.
Larcombe, Peter J. and Fennessey, Eric J. 2018. A new non-linear recurrence identity class for Horadam sequence terms. Palestine Journal of Mathematics.
On two derivative sequences from scaled geometric mean sequence terms.
Larcombe, Peter J., Rabago, Julius, F. T. and Fennessey, Eric J. 2018. On two derivative sequences from scaled geometric mean sequence terms. Palestine Journal of Mathematics.
A new tri-diagonal matrix invariance property.
Larcombe, Peter J. and Fennessey, Eric J. 2017. A new tri-diagonal matrix invariance property. Palestine Journal of Mathematics.
A few thoughts on the aesthetics of mathematics in research and teaching.
Larcombe, Peter J. 2018. A few thoughts on the aesthetics of mathematics in research and teaching. Palestine Journal of Mathematics.
On an arithmetic triangle of numbers arising from inverses of analytic functions.
Bagdasaryan, Armen G. and Bagdasar, Ovidiu 2018. On an arithmetic triangle of numbers arising from inverses of analytic functions. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.003
On some new arithmetic functions involving prime divisors and perfect powers.
Bagdasar, Ovidiu and Tatt, Ralph-Joseph 2018. On some new arithmetic functions involving prime divisors and perfect powers. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.002
Some remarks on 3-partitions of multisets.
Andrica, Dorin and Bagdasar, Ovidiu 2018. Some remarks on 3-partitions of multisets. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.11.001
Traffic assignment: methods and simulations for an alternative formulation of the fixed demand problem
Bagdasar, Ovidiu, Berry, Stuart, O’Neill, Sam, Popovici, Nicolae and Raja, Ramachandran 2018. Traffic assignment: methods and simulations for an alternative formulation of the fixed demand problem. Mathematics and Computers in Simulation. https://doi.org/10.1016/j.matcom.2018.08.004
On some results concerning generalized arithmetic triangles.
Bagdasaryan, Armen G. and Bagdasar, Ovidiu 2018. On some results concerning generalized arithmetic triangles. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.012
On the ratios and geometric boundaries of complex Horadam sequences.
Bagdasar, Ovidiu, Hedderwick, Eve and Popa, Ioan-Lucian 2018. On the ratios and geometric boundaries of complex Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.011
ENDM Proceedings for TREPAM'17: Preface
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2018. ENDM Proceedings for TREPAM'17: Preface. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2018.05.001
Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.
Pratap, A., Raja, R., Sowmiya, C., Bagdasar, Ovidiu, Cao, Jinde and Rajchakit, Grienggrai 2018. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. Neural Networks. https://doi.org/10.1016/j.neunet.2018.03.012
Unifying local-global type properties in vector optimization.
Bagdasar, Ovidiu and Popovici, Nicolae 2018. Unifying local-global type properties in vector optimization. Journal of Global Optimization. https://doi.org/10.1007/s10898-018-0656-8
Case studies: Using heuristics.
Lowndes, Val, Bagdasar, Ovidiu and Berry, Stuart 2017. Case studies: Using heuristics. in: Springer.
Further use of heuristic methods.
Lowndes, Val, Berry, Stuart, Parkes, Chris, Bagdasar, Ovidiu and Popovici, Nicolae 2017. Further use of heuristic methods. in: Springer.
On the geometry of certain periodic non-homogeneous Horadam sequences.
Bagdasar, Ovidiu and Popa, Ioan-Lucian 2016. On the geometry of certain periodic non-homogeneous Horadam sequences. Electronic Notes in Discrete Mathematics. https://doi.org/10.1016/j.endm.2016.11.002
A closed form formulation for the general term of a scaled triple power product recurrence sequence.
Larcombe, Peter J. and Fennessey, Eric J. 2017. A closed form formulation for the general term of a scaled triple power product recurrence sequence. Fibonacci Quarterly.
New results and conjectures on 2-partitions of multisets.
Bagdasar, Ovidiu and Andrica, Dorin 2017. New results and conjectures on 2-partitions of multisets. Proceedings of the 7th International Conference on Modeling, Simulation, and Applied Optimization (ICMSAO). https://doi.org/10.1109/ICMSAO.2017.7934928
Opinions, opinions, opinions ...
Larcombe, Peter J. 2017. Opinions, opinions, opinions ... Mathematics Today.
Mathematics as a mirror of painting.
Larcombe, Peter J. 2017. Mathematics as a mirror of painting. Mathematics Today.
Horadam sequences: A survey update and extension.
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).
Qualitative case study methodology: Automatic design and correction of ceramic colors
Bagdasar, O., Birluţiu, A., Chen, M. and Popa, I.-L. 2017. Qualitative case study methodology: Automatic design and correction of ceramic colors. IEEE. https://doi.org/10.1109/icstcc.2017.8107118
New results and conjectures on 2-partitions of multisets
Bagdasar, O. and Andrica, D. 2017. New results and conjectures on 2-partitions of multisets. 7th International Conference on Modeling, Simulation, and Applied Optimization, ICMSAO 2017. IEEE Computer Society. https://doi.org/10.1109/icmsao.2017.7934928
ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH
Bagdasar, Ovidiu D., Larcombe, Peter J. and Bagdasar, O. 2017. ON THE MASKED PERIODICITY OF HORADAM SEQUENCES: A GENERATOR-BASED APPROACH. Fibonacci Quarterly.
LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS
Bagdasar, Ovidiu, Popovici, Nicolae and Bagdasar, O. 2017. LOCAL MAXIMIZERS OF GENERALIZED CONVEX VECTOR-VALUED FUNCTIONS. Journal of Nonlinear and Convex Analysis.
Conditions 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.
On 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.
Influence discovery in semantic networks: An initial approach
Trovati, M. and Bagdasar, O. 2014. Influence discovery in semantic networks: An initial approach. IEEE. https://doi.org/10.1109/uksim.2014.48
Complementary iInequalities involving the Stolarsky Mean
Bagdasar, Ovidiu 2010. Complementary iInequalities involving the Stolarsky Mean. Journal of Inequalities and Applications. https://doi.org/10.1155/2010/492570
Concise 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/10.1080/10236198.2014.891022
Local 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/s11590-014-0781-3
A horadam-based pseudo-random number generator
Bagdasar, O.D., Chen, M. and Bagdasar, O. 2014. A horadam-based pseudo-random number generator. IEEE. https://doi.org/10.1109/uksim.2014.55
Alwyn 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.
On the structure of periodic complex Horadam orbits
Bagdasar, Ovidiu D., Larcombe, Peter J., Anjum, Ashiq and Bagdasar, O. 2016. On the structure of periodic complex Horadam orbits. Carpathian Journal of Mathematics.
Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems
Popa, I.-L., Ceauşu, T., Bagdasar, O. and Agarwal, R.P. 2016. Characterizations of Generalized Exponential Trichotomies for Linear Discrete-time Systems. Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica. 27 (2), pp. 153-166. https://doi.org/10.2478/auom-2019-0025
On 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/SPSUNP1402091B
ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF
Larcombe, Peter J., Bagdasar, O. and Fennessey, Eric J. 2014. ON A RESULT OF BUNDER INVOLVING HORADAM SEQUENCES: A NEW PROOF. Fibonacci Quarterly. pp. 175-177.