iosr-Jm   Volume-6 ~ Issue-1

Abstract: A unified approach is attempted to bring the descriptive statistics in to a more refined frame work. Different measure of central tendencies such as arithmetic mean, median, mode, geometric mean and harmonic mean are derived from a generalized notion of a measure of central tendency developed through an optimality criteria. This generalized notion is extended to introduce the concept of an interval of central tendency. Retaining the spirit of this notion, measure of central tendency may be called point of central tendency. The same notion is further extended to obtain confidence interval for population mean in a finite population model and confidence interval for probability of success in Bernoulli population.

Key words: Point of central tendency, Interval of central tendency, Metric space, Confidence coefficient.

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Abstract: In this action research study, where the subjects are our undergraduate grade mathematics students, w e try to investigate the impact of direct 'inquisition' instruction on their communication and achievement. We will strategically implement the addition of 'replication' study into each concept of limit over a four-month time period and thus conclusion can be making for the rest of the Mathemat ics . The students practiced using inquiry in verbal discussions, review activities, and in mathematical problem explanations. We discovered that a majority of students improved their overall understanding of mathematical concepts based on an analysis of the data we collected. We also found that in general, students felt that knowing the definition of mathematical words are important and that it increased their achievement when they understood the concept as a whole. In addition, students will be more exact in their communication after receiving inquiry instructions. As a result of this research, we plan to continue to implement inquisition into daily lessons and keep replication communication as a focus of the mathematics class.

Keywords: Concept of Limits,   definition of Limit

[1]. Chris Rasmussen: An inquiry oriented Approach to undergraduate mathematics. The Journal ofMathematical Behavior, Vol. 26,
Nov.3, (2007).
[2]. Borasi, R. & Rose, B. (1989). Journal writing and mathematics instruction. EducationalStudies in Mathematics, 20(4), 347-365.
[3]. Zaslavsky, O. & Shir, K. (2005). Students' conceptions of a mathematical definition.Journal for Research in Mathematics
Education, 36(4), 317-346.
[4]. Zimmerman, C. (1997). Do reading and interactive vocabulary instruction make a difference? An empirical study. TESOL
Quarterly, 31(1), 121-140.

Abstract: The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the convection cells changes when the parameters involved in the study vary with the porous structure bringing out considerable influence.

Keywords - Darcy-Brinkman porous layer, Ferromagnetic fluid, Magnetization, Second sound, Stability.

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[8] S. Aniss, M. Belhaq and M. Souhar, Effects of magnetic modulation on the stability of a magnetic liquid layer heated from above, J. Heat Transfer, 123(3), 2001, 428-433.

[9] A. Abraham, Rayleigh-Bénard convection in a micropolar ferromagnetic fluid, Int. J. Engg. Sci., 40(4), 2002, 449-460.

[10] S. Maruthamanik

Abstract: In this paper we studied m-projectively flat, m-projectively conservative, 𝜑-m-projectively flat LP-Sasakian manifold. It has also been proved that quasi m- projectively flat LP-Sasakian manifold is locally isometric to the unit sphere 𝑆𝑛(1) if and only if �𝑛 is m-projectively flat.

Keywords – Einstein manifold, m-projectively flat, m-projectively conservative, quasi m-projectively flat, 𝜑-m-projectively flat

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[9] A. A. Shaikh and U. C. De, On 3-dimensional LP-Sasakian manifolds, Soochow J. of Math., 26 (4) (2000), 359-368.

[10] J. P. Singh, On an Einstein m-projective P-Sasakian manifolds, (2008) (to appear in Bull. Cal. Math. Soc.).