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i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Mathematical Modeling of Higher Overtone Vibrational Frequencies in Dichlorine Monoxide
Some Types of Generalized Closed and Generalized Star Closed Sets in Topological Ordered Spaces
Optimizing Capsule Endoscopy Detection: A Deep Learning Approach with L-Softmax and Laplacian-SGD
Kernel Ideals in Semigroups
Modeling the Dynamics of Covid-19 with the Inclusion of Treatment, Vaccination and Natural Cure
Calculation of Combined Vibrational Frequencies in Cl₂O using Lie Algebraic Method

Most Cited

Volume 8 Issue 4 October - December 2019

Research Paper

Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab

Mohammad *

Nizwa College of Applied Sciences, University of Technology and Applied Sciences, Oman.

Shahzad, M. (2019). Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab. i-manager's Journal on Mathematics, 8(4), 1-9. https://doi.org/10.26634/jmat.8.4.17548

Abstract

The present study deals with the synchronization of chaotic systems of different orders. The author investigates the reduced-order synchronization (ROS) problem for a circular restricted three body problem (CRTBP)-Lorenz chaotic systems that are of different orders. The study of ROS has been carried out via a robust generalized active control technique together with the effect of both unknown model uncertainties and external disturbances. Also for the chosen master-slave combination, a comparison of computational study between Mathematica and Matlab has been presented in order to observe the variations. Furthermore, it is discussed that ROS is a special case for multi-switching synchronization of different orders of chaotic systems.

References

[1]. Aghababa, M. P., & Aghababa, H. P. (2012). Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties. Nonlinear Dynamics, 67(4), 2689-2701. https://doi.org/10.1007/s11071-011-0181-5

[2]. Ahmad, I., Saaban, A. B., Ibrahim, A. B., & Shahzad, M. (2015). Global chaos synchronization of new chaotic system using linear active control. Complexity, 21(1), 379-386. https://doi.org/10.1002/cplx.21573

[3]. Ahmad, I., Saaban, A. B., Ibrahim, A. B., Shahzad, M., & Naveed, N. (2016). The synchronization of chaotic systems with different dimensions by a robust generalized active control. Optik, 127(11), 4859-4871. https://doi.org/10.1016/j.ijleo.2015. 12.134

[4]. Al-sawalha, M. M., & Noorani, M. S. M. (2011). Adaptive increasing-order synchronization and anti-synchronization of chaotic systems with uncertain parameters. Chinese Physics Letters, 28(11), 1-3. https://doi.org/10.1088/0256-307X/28/11/ 110507

[5]. Castro-Ramírez, J., Martínez-Guerra, R., & Cruz-Victoria, J. C. (2015). A new reduced-order observer for the synchronization of nonlinear chaotic systems: an application to secure communications. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(10), 1-7. https://doi.org/10.1063/1.4934650

[6]. Femat, R., & Solís-Perales, G. (2002). Synchronization of chaotic systems with different order. Physical Review E, 65(3), 036226.

[7]. Ho, M. C., Hung, Y. C., Liu, Z. Y., & Jiang, I. M. (2006). Reduced-order synchronization of chaotic systems with parameters unknown. Physics Letters A, 348(3-6), 251-259. https://doi.org/10.1016/j.physleta.2005.08.076

[8]. Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130-141. https://doi. org/10.1175/1520-0469(1963)020%3C0130:DNF%3E2.0.CO;2

[9]. Njah, A. N. (2011). Synchronization via active control of parametrically and externally excited Φ6 Van der Pol and Duffing oscillators and application to secure communications. Journal of Vibration and Control, 17(4), 493-504. https://doi.org/ 10.1177%2F1077546309357024

[10]. Njah, A. N., & Vincent, U. E. (2009). Synchronization and anti-synchronization of chaos in an extended Bonhöffer–van der Pol oscillator using active control. Journal of Sound and Vibration, 319(1-2), 41-49. https://doi.org/10.1016/j.jsv.2008.05. 036

[11]. Ojo, K. S., Njah, A. N., Olusola, O. I., & Omeike, M. O. (2014). Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique. Nonlinear Dynamics, 77(3), 583-595.

[12]. Shahzad, M. (2015). The improved results with Mathematica and effects of external uncertainty and disturbances on synchronization using a robust adaptive sliding mode controller: a comparative study. Nonlinear Dynamics, 79(3), 2037- 2054. https://doi.org/10.1007/s11071-014-1793-3

[13]. Shahzad, M., & Ahmad, I. (2013). Experimental study of synchronization & Anti-synchronization for spin orbit problem of Enceladus. International Journal of Control Science and Engineering, 3(2), 41-47. https://doi.org/10.5923/j.control. 20130302.02

[14]. Shahzad, M., Ahmad, I., Saaban, A. B., & Ibrahim, A. B. (2016). Improved time response of stabilization in synchronization of chaotic oscillators using Mathematica. Systems, 4(2), 1-21. https://doi.org/10.3390/systems4020025

[15]. Sparrow, C. (1982). The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer.

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[18]. Vincent, U. E., & Ucar, A. (2007). Synchronization and anti-synchronization of chaos in permanent magnet reluctance machine. Far East Journal of Dynamical System, 9, 211–221.

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Research Paper

On I_θ−Convergence and Some Properties in Fuzzy n-Normed Spaces

Muhammed Recai Turkmen *

Faculty of Education, Afyon Kocatepe University, Afyonkarahisar, Turkey.

Turkmen, M. R. (2019). On I_θ−Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager's Journal on Mathematics, 8(4), 10-18. https://doi.org/10.26634/jmat.8.4.17572

Abstract

In this study, firstly lacunary convergence and lacunary ideal convergence is introduced in fuzzy n-normed spaces. Later, the relation between lacunary convergence and lacunary ideal convergence is investigated in fuzzy n-normed spaces. Finally, we have introduced the concept of FI_θ - limit point, FI_θ- cluster point, Fθ - Cauchy sequence and FI_θ- Cauchy sequence in fuzzy n-normed space.

References

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Research Paper

Mathematical Analysis of One Ammensal and Two Mutualistic Species

N. V. S. R. C. Murty Gamini* , Paparao A. V.**

* Department of Science & Humanities, BVC Institute of Technology & Science, Amalapuram, Andhra Pradesh, India.

** Department of Mathematics, JNTUK University College of Engineering, Vizianagaram, Andhra Pradesh, India.

Gamini, N. V. S. R. C. M., and Paparao, A. V. (2019). Mathematical Analysis of One Ammensal and Two Mutualistic Species. i-manager's Journal on Mathematics, 8(4), 19-31. https://doi.org/10.26634/jmat.8.4.17131

Abstract

In this paper we studied the dynamics of one ammensal and two mutualistic species. A distributed time lag is induced in the interaction of ammensal and two mutual species. Local and global stability analysis is discussed at co-existing state. Numerical simulation with different delay kernel strengths are illustrated and proved that delay kernels play a significant role in the growth of two mutual species populations.

References

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[2]. Cushing, J. M. (1977). Integro-Differential equations and delay models in population dynamics. Verlag, Heidelberg: Springer.

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[6]. May, R. M. (1973). Stability and complexity in model Eco-Systems. (Vol. 1). Princeton: Princeton University Press.

[7]. Narayan, L. K., & Rao, K. K. (2016). Stability Analysis of a Three Species Syn-Ecological Model with Prey-Predator and Amensalism. Bulleten of Calcutta Mathematical Society, 108(1), 63-76.

[8]. Narayan, L. K., & Rao, K. K. (2017). Dynamical System of Ammensal Relationship of Human's on Plants and Birds with Time Delay. Bulletin of Calcutta Mathematical Society, 109(6), 485-500.

[9]. Narayan, L. K., & Rao, K. K. (2017). Stability Analysis of Three Species Food Chain Model with Ammensalism and Mutualism. In Proceedings of the 11th International Conference MSAST 2017 (IMBIC) Kolkata, 6, 125-135.

[10]. Paparao A. V., & Gamini, N. V. S. R. C. M. (2018). Dynamical Behaviour of Prey Predators Model with Time Delay. International Journal of Mathematics And its Applications, 6(3), 27-37.

[11]. Paparao, A. V., & Narayan, K. L. (2017). Dynamics of a prey predator and competitor model with time delay. International Journal of Ecology & Development, 32(1), 75-86.

[12]. Paparao, A. V., & Narayan, K. L. (2017). A prey, predator and a competitor to the predator model with time delay. International Journal of Research in Science & Engineering, 27-38.

[13]. Paparao, A. V., Narayan. K. L., & Rao, K. K. (2019). Amensalism Model: A Mathematical Study. International Journal of Ecological Economics & Statistics (IJEES), 40(3), 75-87.

[14]. Rao, V. S. H., & Rao, P. R. S. (2009). Dynamic models and control of biological systems. Verlag, New York: Springer.

[15]. Voltera, V. (1931). Leçons sur la théorie mathématique de la Lutte pour la vie (Lessons on the Mathematical Theory of Struggle for Life). Paris: Gauthier Villars.

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Research Paper

Variable Control Charts Based on Pareto – Rayleigh Distribution

I. Narasimha Rao * , M. S. Ravikumar, R. R. L. Kantam *

* Online Tutor Course Hero Pvt Ltd., Rajahmundry, Andhra Pradesh, India.

Department of Community Medicine, Konaseema Institute of Medical Sciences & Research Foundation/ General Hospital, Andhra Pradesh, India.

* Department of Statistics, Acharya Nagarjuna University, Guntur-Andhra Pradesh, India.

Rao, I. N., Ravikumar, M. S., and Kantam, R. R. L. (2019). Variable Control Charts Based on Pareto – Rayleigh Distribution. i-manager's Journal on Mathematics, 8(4), 32-40. https://doi.org/10.26634/jmat.8.4.17100

Abstract

A special case of the well-known T – X family of distributions proposed by Alzaatreh et al. (2012) called Pareto – Rayleigh (P – R) distribution is considered. Control limits chart for averages and range of samples were drawn from Pareto – Rayleigh Distribution. The variable control chart limits for mean and range of samples are drawn from Pareto – Rayleigh distribution and is constructed by using Skewness Corrected (SC) control chart technique based on the Moments, Bowley's, Kelly's, and Moor's coefficient of skewness. The results have been illustrated with an example.

References

[1]. Alzaatreh, A., Famoye, F., & Lee, C. (2012). Gamma-Pareto distribution and its applications. Journal of Modern Applied Statistical Methods, 11(1), 78-94. https://doi.org/10.22237/jmasm/1335845160

[2]. Boyapati, S. R., & Kantam, R. R. L. (2012a). Extreme value charts and analysis of means based on half logistic distribution. International Journal of Quality & Reliability Management, 29(5), 501-511. https://doi.org/10.1108/02656711211230490

[3]. Boyapati, S. R., & Kantam, R. R. L. (2012b). Mean and range charts for skewed distributions – a comparison based on half logistic distribution. Pakistan Journal of Statistics, 28(4), 437-444.

[4]. Chan, L. K., & Cui, H. J. (2003). Skewness correction X and R charts for skewed distributions. Naval Research Logistics (NRL), 50(6), 555-573. https://doi.org/10.1002/nav.10077

[5]. Edgeman, R. L. (1989). Inverse Gaussian control charts. Australian Journal of Statistics, 31(1), 78-84. https://doi.org/10. 1111/j.1467-842X.1989.tb00500.x

[6]. Kantam, R. R. L. & Priya, M. Ch. (2010). Extreme order statistics- control charts. ANU Journal of Physical Sciences. 2(1), 48-55.

[7]. Kantam, R. R. L., & Priya, M. Ch. (2011). Time Control Charts Using Order Statistics. Inter Stat.

[8]. Kantam, R. R. L., Rao, A. V., & Rao, G. S. (2006). Control charts for the log-logistic distribution. Economic Quality Control, 21(1), 77-86. https://doi.org/10.1515/EQC.2006.77

[9]. Kantam, R. R. L., & Sriram, B. (2001). Variable control charts based on Gamma distribution. IAPQR Transactions, 26(2), 63- 78.

[10]. Montgomery, D. C. (2007). Introduction to Statistical Quality Control (6 Ed.). John Wiley & Sons.

[11]. Rao, G. S., & Kantam, R. R. L. (2010). Acceptance sampling plans from truncated life tests based on the log-logistic distributions for percentiles. Economic Quality Control, 25(2), 153-167.

[12]. Rao, R. S., & Kantam, R. R. L. (2008). Variable Control Charts for Process Mean with Reference to Double Exponential Distribution. Acta Ciencia Indica, 34(4), 1925-1930.

[13]. Rao, R. S., Kantam, R. R. L., & Prasad, G. (2015). Modified Maximum Likelihood Estimation in Pareto-Rayleigh distribution. In Conference Proceedings of National Seminar on Recent Developments in Applied Statistics Golden Research Thoughts (pp. 140-152).

[14]. Rao, R. S., Mamidi, P. L., & Kumar, M. R. (2016). Skewness Corrected Control charts for two Inverted Models. Journal of Chemical and Pharmaceutical Sciences, 51 - 55.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

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Most Cited

Volume 8 Issue 4 October - December 2019

Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab

Mohammad *

Nizwa College of Applied Sciences, University of Technology and Applied Sciences, Oman.

Shahzad, M. (2019). Reduced Order Synchronization: A Comparison of Simulation between Mathematica & Matlab. i-manager's Journal on Mathematics, 8(4), 1-9. https://doi.org/10.26634/jmat.8.4.17548

Abstract

References

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On Iθ −Convergence and Some Properties in Fuzzy n-Normed Spaces

Muhammed Recai Turkmen *

Faculty of Education, Afyon Kocatepe University, Afyonkarahisar, Turkey.

Turkmen, M. R. (2019). On Iθ −Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager's Journal on Mathematics, 8(4), 10-18. https://doi.org/10.26634/jmat.8.4.17572

Abstract

References

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Mathematical Analysis of One Ammensal and Two Mutualistic Species

N. V. S. R. C. Murty Gamini* , Paparao A. V.**

* Department of Science & Humanities, BVC Institute of Technology & Science, Amalapuram, Andhra Pradesh, India. ** Department of Mathematics, JNTUK University College of Engineering, Vizianagaram, Andhra Pradesh, India.

Gamini, N. V. S. R. C. M., and Paparao, A. V. (2019). Mathematical Analysis of One Ammensal and Two Mutualistic Species. i-manager's Journal on Mathematics, 8(4), 19-31. https://doi.org/10.26634/jmat.8.4.17131

Abstract

References

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Variable Control Charts Based on Pareto – Rayleigh Distribution

I. Narasimha Rao * , M. S. Ravikumar**, R. R. L. Kantam ***

Rao, I. N., Ravikumar, M. S., and Kantam, R. R. L. (2019). Variable Control Charts Based on Pareto – Rayleigh Distribution. i-manager's Journal on Mathematics, 8(4), 32-40. https://doi.org/10.26634/jmat.8.4.17100

Abstract

References

Full Article (HTML)

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On I_θ−Convergence and Some Properties in Fuzzy n-Normed Spaces

Turkmen, M. R. (2019). On I_θ−Convergence and Some Properties in Fuzzy n-Normed Spaces. i-manager's Journal on Mathematics, 8(4), 10-18. https://doi.org/10.26634/jmat.8.4.17572

* Department of Science & Humanities, BVC Institute of Technology & Science, Amalapuram, Andhra Pradesh, India.

** Department of Mathematics, JNTUK University College of Engineering, Vizianagaram, Andhra Pradesh, India.

I. Narasimha Rao * , M. S. Ravikumar, R. R. L. Kantam *