i-manager Publications

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 3 Issue 2 April - June 2014

Article

STEM on Ice: Using figure skating and modeling to apply scientific concepts

Diana Cheng* , Asli Sezen Barrie**

* Assistant Professor, Department of Mathematics, Towson University (Maryland, USA).

** Assistant Professor, Department of Physics, Astronomy and Geosciences, Towson University (Maryland, USA).

Cheng, D., and Sezen-barrie, A. (2014). STEM on Ice: Using figure skating and modeling to apply scientific concepts. i-manager’s Journal on Mathematics, 3(2), 1-6. https://doi.org/10.26634/jmat.3.2.2999

Abstract

In light of recent national efforts to create interdisciplinary STEM activities, a mathematics and physics modeling context for prospective middle school teachers is presented. The activity relates pairs figure skating lifts with the conservation of linear momentum inelastic collision equation. Preservice teachers' work is analyzed in terms of their use of the inquiry process, teacher talk, and use of scientific concepts relevant to the activity.

References

[1]. Aikenhead, G. S. (2006). Science education for everyday life: Evidence-based practice. New York: Teachers College Press.

[2]. Bassett G. &Persky, J. (1994). Rating skating. Journal of the American Statistical Association Vol 89, pp.1075-1079.

[3]. Carroll. M., Rykken, E. & Sorensen, J. (2003). The Canadians should have won!? Mathematics horizons, Vol 10, pp.5-26.

[4]. Judson, E. (2013). Development of an Instrument to Assess and Deliberate on the Integration of Mathematics into Student-Centered Science Learning. School Science and Mathematics, Vol 113(2), pp.56-68.

[5]. Kaiser, G. &Sriraman, B. (2006). A global survey of international perspectives on modelling in education. ZDM, Vol 38(3), pp.302-310.

[6]. Kalchman, M. (2011). Using the math in everyday life to improve student learning. Middle School Journal, Vol43(1), pp.24-31.

[7]. Lee, M. M., Chauvot, J. B., Vowell, J., Culpepper, S. M., &Plankis, B. J. (2013). Stepping into iSMART: Understanding Science–Mathematics Integration for Middle School Science and Mathematics Teachers. School Science and Mathematics, Vol 113(4), pp.159-169.

[8]. Michaels, S. (2013). Connections between practices in NGSS, common core math, and common core ELA. [Power point slides]. Retrieved from http://learningcenter.nsta.org/products/symposia_seminars/Ngss/files/ConnectionsBetween PracticesinNGSSCommonCoreMathandCommonCoreELA_2-12-2013.pdf

[9]. National Governors Association Center for Best Practices, Council of Chief State School Officers.(2010). Common Core State Standards for Mathematics. Washington, DC.

[10]. National Research Council (2013a). A Framework for K–12 Science Education: Practices, Crosscutting Concepts, and Core, Ideas Washington. DC: National Academies Press.

[11]. National Research Council (2013b). Next Generation Science Standards. Washington. DC: National Academies Press.

[12]. Stump, S., Clark, S., Mitchell, M., et. al. (2008). Supporting mathematics in other subject areas. Mathematics teaching in the middle school, Vol14(5), pp.260-266.

[13]. The White House (2008). Educate to Innovate. Retrieved June 20, 2013 from http://www.whitehouse.gov/issues/ education/k-12/educate-innovate

[14]. Wu, S. & Yang, M. (2004). Evaluation of the current decision rule in figure skating and possible improvements. The American Statistician, Vol.58, pp.46-54.

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Article

An Introduction to Learn Mathematical Knot Theory with Knot Polynomial

D. R. Robert Joan*

Assistant Professor, Department of M.Ed, M.E.T College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Joan, D.R.R. (2014). An Introduction To Learn Mathematical Knot Theory With Knot Polynomial. i-manager’s Journal on Mathematics, 3(2), 7-12. https://doi.org/10.26634/jmat.3.2.3000

Abstract

In this article, the author discussed the concept of Mathematical Knot Theory and Knot Polynomial. And finally the author collects different knots which are used in the mathematical knot theory. In Mathematics, a knot is an embedding of a 3 circle in 3-dimensional Euclidean space, R , considered up to continuous deformations (isotopies). A crucial difference between the standard mathematical and conventional notions of a knot is that, mathematical knots are closed-there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term knot is also j n applied to embeddings of S in S , especially in the case j= n-2. The branch of Mathematics that studies about knot is known as Knot Theory.

References

[1]. Adams, C. C. (1994). The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots. New York: W. H. Freeman, pp.280-286.

[2]. Dehn, M. (1914). Die beiden Kleeblattschlingen. Math. Ann, Vol 75, pp.402-413.

[3]. Gordon, C., & Luecke, J. (1989). Knots are Determined by their Complements. Amer. Math. Soc. Vol 2, pp.371-415.

[4]. Hass, J. (1998). Algorithms for recognizing knots and 3-manifolds Chaos, pp.569–581, doi:10.1016/S0960-0779(97)00109- 4.

[5]. Hoste, J. (2005). The enumeration and classification of knots and links. Handbook of Knot Theory.

[6]. Hoste, J., Thistlethwaite, M., & Weeks, J. (1998). The First Knots. Math. Intell, Vol 20, pp.33-48.

[7]. Lickorish, W. B. (1997). An Introduction to Knot Theory. Graduate Texts in Mathematics, Springer-Verlag, ISBN 0-387- 98254-X.

[8]. Livingston, C. (1993). Knot Theory. Washington, DC: Math. Assoc. Amer.

[9]. Rolfsen, D. (1976). Knots and Links, Publish on Perish, ISBN 0-914098-16-0.

[10]. Schubert, H. (1949). Die eindeutige Zerlegbarkeit eines Knotens in Primknoten. Heidelberger Akad. Wiss. Math.-Nat. Kl. Vol 3, pp.57–104.

[11]. Sossinsky, A. (2002). Knots, mathematics with a twist. Harvard University Press, ISBN 0-674-00944-4.

[12]. Thomson, S. W. (1867). On Vortex Atoms, Proceedings of the Royal Society of Edinburgh, pp.94–105.

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Research Paper

The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity

James Edward Osler II*

Associate Professor, Department of Curriculum and Instruction, North Carolina Central University.

Osler, J. E., II. (2014). The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity. i-manager’s Journal on Mathematics, 3(2), 13-21. https://doi.org/10.26634/jmat.3.2.3001

Abstract

This monograph provides a logical and epistemological rational for the Post Hoc testing of the instrumentation used in the transformative process of qualitative data into quantitative outcomes through the Tri–Squared Test introduced in the Journal on Mathematics and expounded upon in the Journal on Educational Psychology. An advanced Post Hoc statistical measure using the Del Differential Operator and Matrix Algebra is used to determine the Construct Validity of researcher designed instruments using the Tri–Squared research design parameters. This additional novel approach to advanced data analysis adds additional value to Tri–Squared as an innovative mixed methods approach to investigative inquiry.

References

[1]. Apostol, T. M. (1967). Calculus, Second edition, Volume one: One-variable calculus, with an introduction to linear algebra. Waltham, MA: Blaisdell.

[2]. Kant, I. (2007). Critique of pure reason (based on Max Müller's translation). P. Classics a Division of Pearson PLC. New York, NY.

[3]. James Edward Osler (2012). Introducing: Trichotomy–Squared – A Novel Mixed Methods Test and Research Procedure Designed to Analyze, Transform, and Compare Qualitative and Quantitative Data for Education Scientists Who are Administrators, Practitioners, Teachers, and Technologists. i-manager's Journal on Mathematics, 1(3), Jul - Sep 2012 Print ISSN 2277-5129, E-ISSN 2277-5137, pp. 23-32.

[4]. James Edward Osler and Carl Waden(2012). Using Innovative Technical Solutions As An Intervention For At Risk Students: A Meta–Cognitive Statistical Analysis To Determine The Impact Of Ninth Grade Freshman Academies, Centers, And Center Models Upon Minority Student Retention And Achievement. i-manager's Journal on School Educational Technology, 8(2), Sep-Nov 2012, Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 11-23.

[5]. James Edward Osler (2013). The Psychometrics Of Educational Science: Designing Trichotomous Inventive Investigative Instruments For Qualitative And Quantitative Inquiry. i-manager's Journal on School Educational Technology, 8(3), Dec-Feb 2013, Print ISSN: 0973-2217, E-ISSN: 2230-7133, pp. 15-22.

[6]. James Edward Osler (2013). The Psychological Efficacy Of Education As A Science Through Personal, Professional, And Contextual Inquiry Of The Affective Learning Domain. i-manager's Journal on Educational Psychology. 6(4) Feb-April 2013 Print ISSN 0973-8827, E-ISSN 2230-7141, pp. 36-41.

[7]. James Edward Osler II (2013). Algorithmic Triangulation Metrics for Innovative Data Transformation: Defining The Application Process of The Tri–Squared Test. i-manager's Journal on Mathematics, 2(2) Apr - Jun 2013 Print ISSN 2277-5129, EISSN 2277-5137, pp. 10-16.

[8]. Rust, J. & Golombok, S. (1989). Modern psychometrics: The science of psychological assessment(2nd ed.). Florence, KY, US: Taylor & Frances/Routledge.

[9]. Sensagent: Retrieved, May 9, 2012: http://dictionary.sensagent.com/trichotomy+(mathematics)/en-en/

[10]. Singh, S. (1997). Fermat's enigma: The epic quest to solve the world's greatest mathematical problem. A. Books a Division of Random House. New York, NY.

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Research Paper

Synchronization of Circular Restricted Three Body Problem with Liu Hyper Chaotic System using a Robust Adaptive Sliding Mode Controller

Ayub Khan* , 0**

* Professor, Department of Mathematics, Jamia Millia Islamia, New Delhi, India.

** Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

Khan, A., and Shahzad, M. (2014). Synchronization of Circular Restricted Three Body Problem with Liu Hyper Chaotic System using a Robust Adaptive Sliding Mode Controller. i-manager’s Journal on Mathematics, 3(2), 22-29. https://doi.org/10.26634/jmat.3.2.3002

Abstract

In this computational study, the authors synchronize the Circular Restricted Three Body Problem (CRTBP) with Liu Hyper Chaotic System (LHCS) using a Robust Adaptive Sliding Mode Controller (RASMC) together with uncertainties, external disturbances and fully unknown parameters. A simple suitable sliding surface, which includes synchronization errors, is constructed and appropriate update laws are used to tackle the uncertainties, external disturbances and unknown parameters. All simulations to achieve the synchronization for the proposed technique for the two non-identical systems under consideration are being done using Mathematica.

References

[1]. Pecora, L. M. & Carroll, T. L. (1990). Synchronization in Chaotic Systems, Phys. Rev. Lett. Vol 64, pp.821- 824.

[2]. Xiang, W. & Huangpu, Y. (2010). Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simulat, Vol 15, pp.3241–3247.

[3]. Rafikov, M. & Balthazar, J. M. (2008). On control and synchronization in chaotic and hyperchaotic systems via linear feedback control, Commun Nonlinear Sci Numer Simulat, Vol 13, pp.1246–1255.

[4]. Bowong, S. (2007). Adaptive synchronization between two different chaotic dynamical systems, Commun Nonlinear Sci Numer Simulat, Vol 12, pp.976–985.

[5]. Chen, H., Sheu, G., Lin, Y. & Chen, C. (2009). Chaos synchronization between two different chaotic systems via nonlinear feedback control, Nonlinear Anal, Vol 70, pp.4393–4401.

[6]. Yassen, M. T. (2007). Controlling, synchronization and tracking chaotic Liu system using active backstepping design, Phys Lett A, Vol 360, pp.582–587.

[7]. Wang, F. & Liu, C. (2007). Synchronization of unified chaotic system based on passive control, Physica D, Vol 225, pp.55–60.

[8]. Yau, H. & Shieh, C. (2008). Chaos synchronization using fuzzy logic controller, Nonlinear Anal: RWA Vol 9, pp.1800–1810.

[9]. Chang, W. (2009). PID control for chaotic synchronization using particle swarm optimization, Chaos Soliton Fract, Vol 39, pp.910–917.

[10]. Sun, Y. (2009). Chaos synchronization of uncertain Genesio–Tesi chaotic systems with dead zone nonlinearity, Phys Lett A, Vol 373, pp.3273–3276.

[11]. Jianwen, F., Ling, H., Chen, X., Austin, F. & Geng, W. (2010). Synchronizing the noise-perturbed Genesio chaotic system by sliding mode control, Commun Nonlinear Sci Numer Simulat, Vol 15, pp.2546–2551.

[12]. Feki, M. (2009). Sliding mode control and synchronization of chaotic systems with parametric uncertainties, Chaos Soliton Fract, Vol 41, pp.1390–1400.

[13]. Lin, C., Peng, Y. & Lin, M. (2009). CMAC-based adaptive backstepping synchronization of uncertain chaotic systems, Chaos Soliton Fract ,Vol 42, pp.981–988.

[14]. Ahmadi, A. A. & Majd, V. J. (2009). Robust synchronization of a class of uncertain chaotic systems, Chaos Soliton Fract, Vol 42, pp.1092–1096.

[15]. Asheghan, M. M. & Beheshti, M. T. H. (2009). An LMI approach to robust synchronization of a class of chaotic systems with gain variations, Chaos Soliton Fract, Vol 42, pp.1106–1111.

[16]. Zhang, H. & Ma, X. (2004). Synchronization of uncertain chaotic systems with parameters perturbation via active control, Chaos Soliton Fract, Vol 21, pp.39–47.

[17]. Cai, N., Jing, Y. & Zhang, S. (2010). Modified projective synchronization of chaotic systems with disturbances via active sliding mode control, Commun Nonlinear Sci Numer Simulat, Vol 15, pp.1613–1620.

[18]. Kebriaei, H. & Yazdanpanah, M. J. (2010). Robust adaptive synchronization of different uncertain chaotic systems subject to input nonlinearity, Commun Nonlinear Sci Numer Simulat, Vol 15, pp.430–441.

[19]. Chen, C. (2009). Quadratic optimal neural fuzzy control for synchronization of uncertain chaotic systems, Expert Syst Appl, Vol 36, pp.11827–11835.

[20]. Li, W. & Chang, K. (2009). Robust synchronization of drive-response chaotic systems via adaptive sliding mode control, Chaos Soliton Fract, Vol 39, pp.2086–2092.

[21]. Wang, H., Han, Z., Xie, Q. & Zhang, W. (2009). Finite-time chaos synchronization of unified chaotic system with uncertain parameters, Commun Nonlinear Sci Numer Simulat, Vol 14, pp.2239–2247

[22]. Zhang, G., Liu, Z. & Zhang, J. (2008). Adaptive synchronization of a class of continuous chaotic systems with uncertain parameters, Phys Lett A, Vol 372, pp.447–450.

[23]. Ma, J., Zhang, A., Xia, Y. & Zhang, L. (2010). Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems, Appl Math Comput ,Vol 215, pp.3318–3326

[24]. El-Gohary A. (2006). Optimal synchronization of Rossler system with complete uncertain parameters, Chaos Soliton Fract, Vol 27, pp.345–355.

[25]. Hwang, E., Hyun, C., Kim, E. & Park, M. (2009). Fuzzy model based adaptive synchronization of uncertain chaotic systems: robust tracking control approach, Phys Lett A, Vol 373, pp.1935–1939.

[26]. Yassen, M.T. (2005). Adaptive synchronization of two different uncertain chaotic systems, Phys Lett A, Vol 337, pp.335–341.

[27]. Chen, X. & Lu, J. (2007). Adaptive synchronization of different chaotic systems with fully unknown parameters, Phys Lett A, Vol 364, pp.123–128.

[28]. Salarieh, H. & Shahrokhi, M. (2008). Adaptive synchronization of two different chaotic systems with time varying unknown parameters, Chaos Soliton Fract, Vol 37, pp.125–136.

[29]. Yan, J., Hung, M., Chiang, T. & Yang, Y. (2006). Robust synchronization of chaotic systems via adaptive sliding mode control, Phys Lett A, Vol 356, pp.220–225.

[30]. Aghababa, M. P. & Heydari, A. (2012). Chaos synchronization between two different chaotic systems with uncertainties, external disturbances, unknown parameters and input nonlinearities, Applied Mathematical Modelling. Vol 36, pp.1639–1652.

[31]. Aghababa, M. P. & Akbari, M. E. (2012). A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances, Applied Mathematics and Computation, Vol 218, pp. 5757–5768.

[32]. Pourmahmood, M., Khanmohammadi, S. & Alizadeh, G. (2011). Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller, Commun Nonlinear Sci Numer Simulat, Vol 16, pp.2853–2868.

[33]. Wang C. & Ge S. S. (2001). Adaptive synchronization of uncertain chaotic systems via backstepping design, Chaos Soliton Fract, Vol 12, pp.1199–1206.

[34]. Khan, A. & Shahzad, M. (2013). Synchronization of Circular Restricted Three Body Problem with Lorenz Hyper Chaotic System using a Robust Adaptive Sliding Mode Controller, Complexity, Vol 18, pp.58-64.

[35]. Mohammad Shahzad (2014). Synchronization of Three Dimensional Cancer Model with Lorenz System Using A Robust Adaptive Sliding Mode Controller. i-manager's Journal on Mathematics, 3 (1), Jan-Mar 2014, Print ISSN 2277-5129, E-ISSN 2277-5137, pp. 27-34.

[36]. Szebehely, V. (1967). Theory of Orbits. Academic Press, San Diego.

[37]. Wang F. Q. & Liu C. X. (2006). Hyper chaos evolved from the Liu chaotic system. Chin. Phys. Vol 15, pp.963- 968.

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Research Paper

Reliability Analysis Of A Waste Water Treatment Plant With Inspection

Dr. Syed Mohammed Rizwan* , Joseph V Thanikal**

* Professor and HOD, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Sultanate of Oman.

** Research professor, Caledonian (University) College of Engineering, Sultanate of Oman.

Rizwan, S.M., and Thanikal, J.V. (2014). Reliability Models in Waste Water Treatment Plant with Inspection. i-manager’s Journal on Mathematics, 3(2), 30-35. https://doi.org/10.26634/jmat.3.2.3003

Abstract

The paper presents a methodology of estimating various reliability indices for analyzing a wastewater treatment plant. The continuous operation of the plant is of utmost importance and therefore its reliability analysis under different stipulated conditions helps in understanding the overall plant performance. Relevant data for a specific waste water treatment plant have been used to validate the methodology. Here, the plant failure is categorized into minor or major reasons of failures and the type of failure is detected by inspection only. Semi-Markov process and regenerative point techniques are used in the entire analysis.

References

[1]. Krishna B. Misra (2008). Handbook of Performability Engineering, Springer, pp.789-803.

[2]. Dekker R. Schouten, FD & Wildeman R, (1997). A review of Multi-Component Maintenance models with economic dependence. Mathematical Methods of Operational Research, Vol 45(3). pp.411-435.

[4]. Syed Mohd Rizwan and GulshanTaneja, (2012). Maintenance / Reliability models in technological systems. Caledonian Journal of Engineering, Vol 8 (2), pp.1-3.

[5]. S M Rizwan, Joseph V Thanikal & Michel Torijos, (2013). Reliability Analysis of a Domestic Waste Water Treatment Plant in France. in Proc. of International Conference on Harnessing Technology, 2-3 Dec, Sultanate of Oman.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 13 Issue 2

Most Read

Most Cited

Volume 3 Issue 2 April - June 2014

STEM on Ice: Using figure skating and modeling to apply scientific concepts

Diana Cheng* , Asli Sezen Barrie**

* Assistant Professor, Department of Mathematics, Towson University (Maryland, USA). ** Assistant Professor, Department of Physics, Astronomy and Geosciences, Towson University (Maryland, USA).

Cheng, D., and Sezen-barrie, A. (2014). STEM on Ice: Using figure skating and modeling to apply scientific concepts. i-manager’s Journal on Mathematics, 3(2), 1-6. https://doi.org/10.26634/jmat.3.2.2999

Abstract

References

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An Introduction to Learn Mathematical Knot Theory with Knot Polynomial

D. R. Robert Joan*

Assistant Professor, Department of M.Ed, M.E.T College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Joan, D.R.R. (2014). An Introduction To Learn Mathematical Knot Theory With Knot Polynomial. i-manager’s Journal on Mathematics, 3(2), 7-12. https://doi.org/10.26634/jmat.3.2.3000

Abstract

References

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The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity

James Edward Osler II*

Associate Professor, Department of Curriculum and Instruction, North Carolina Central University.

Osler, J. E., II. (2014). The Trimetric Tri–Squared Test: An Advanced Post Hoc Exact Test Designed to Statistically Determine Construct Validity. i-manager’s Journal on Mathematics, 3(2), 13-21. https://doi.org/10.26634/jmat.3.2.3001

Abstract

References

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Synchronization of Circular Restricted Three Body Problem with Liu Hyper Chaotic System using a Robust Adaptive Sliding Mode Controller

Ayub Khan* , 0**

* Professor, Department of Mathematics, Jamia Millia Islamia, New Delhi, India. ** Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

Khan, A., and Shahzad, M. (2014). Synchronization of Circular Restricted Three Body Problem with Liu Hyper Chaotic System using a Robust Adaptive Sliding Mode Controller. i-manager’s Journal on Mathematics, 3(2), 22-29. https://doi.org/10.26634/jmat.3.2.3002

Abstract

References

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Reliability Analysis Of A Waste Water Treatment Plant With Inspection

Dr. Syed Mohammed Rizwan* , Joseph V Thanikal**

* Professor and HOD, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Sultanate of Oman. ** Research professor, Caledonian (University) College of Engineering, Sultanate of Oman.

Rizwan, S.M., and Thanikal, J.V. (2014). Reliability Models in Waste Water Treatment Plant with Inspection. i-manager’s Journal on Mathematics, 3(2), 30-35. https://doi.org/10.26634/jmat.3.2.3003

Abstract

References

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* Assistant Professor, Department of Mathematics, Towson University (Maryland, USA).

** Assistant Professor, Department of Physics, Astronomy and Geosciences, Towson University (Maryland, USA).

* Professor, Department of Mathematics, Jamia Millia Islamia, New Delhi, India.

** Assistant Professor, Department of General Requirements, College of Applied Sciences, Nizwa, Oman.

* Professor and HOD, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Sultanate of Oman.

** Research professor, Caledonian (University) College of Engineering, Sultanate of Oman.