i-manager's Journal on Mathematics (JMAT)


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.

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.

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.

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.

Research Paper

Reliability Analysis Of A Waste Water Treatment Plant With Inspection

Prof Syed Mohd 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.