iosr-Jm   Volume-14 ~ Issue-2 ~ Mar-Apr 2018

Abstract: The aim of teacher education (TE) is to produce quality teachers who can facilitate the acquisition of knowledge, skills and attitudes by the students. TE embraces a wider perspective of continued learning within the teaching process and the teacher is an essential facilitator in the implementation process of the curriculum. In education therefore, the importance of the teacher takes second place only after that of the learners so that the quality of the teacher is of great concern to the education system. Like any other professional domain, teaching is based on a wide base of specialized knowledge and it is important to note that the generation, dissemination and application of new knowledge is critical in economic growth..............

Keywords: Teacher Education, Teachers of English Language, English Language Teaching, English Language Teacher Educators, Knowledge Base, Professional Development.

[1]. American Association of Colleges for Teacher Education (AACTE) (2010).21stCetury Knowledge and Skills in Teacher Preparation. New York: Pearson.
[2]. Auerbach, E.R. & Paxton, D. (1997). "It‟s not the English thing" Bringing Reading Research into the ELS Classroom. TESOL Quarterly, 31,237-261.
[3]. Barasa, P. (2005) English Language teaching in Kenya: Policy, Training and Practice. Moi University: Moi University Press.
[4]. Bezzina, C. (2002). Rethinking Teachers‟ Professional Development in Malta: Agenda for the Twenty-First Century.Journal of In-Service Education, Volume28, Number1.
[5]. Borg, S. (2006). The Distinctive Characteristics of Foreign Language Teachers.Language Teaching Research, 10(1),3-31.

Abstract: A single-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. In the derivation of the method, power series is adopted as basis function to obtain the main continuous scheme through collocation and interpolations approach. Taylor method is also used together with new method to generate the non-overlapping numerical results. The newly constructed method is then applied to solve the system of second-order stiff ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error.

Keywords: Power Series, Collocation and Interpolation Method, Hybrid Block Method, Stiff ODEs, System of Second Order ODEs.

[1]. Muhammad R.; Yahaya.Y.A, A sixth order implicit hybrid backward differentiation formulae (HBDF) for block solution of
ordinary differential equations. Amer. J. Math. Statistics.2012 p. 89-94.
[2]. M. Alkasassbeh; Zurni O. Implicit one-step block hybrid third-derivative method for the direct solution of initial value problems of
second –order ordinary differential equations. J. apply.math. 2017, p. 8
[3]. Omar, Z.; Sulaiman, M. Parallel r-point implicit block method for solving higher order ordinary differential equations directly. J.
ICT 2004, 3, 53–66.
[4]. Y. Skwame; J. Sabo; P. Tumba; T. Y. kyagya.Order Ten Implicit One-Step Hybrid Block Method for The Solution of Stiff Secondorder
Ordinary Differential Equations.IJEAS 2017. 2394-3661.
[5]. James, A.; Adesanya, A.; Joshua, S. Continuous block method for the solution of second order initial value problems of ordinary
differential equation. Int. J. Pure Appl. Math.2013, 83, 405–416.

Abstract: The investigation seeks to determine the buckling modes and the static buckling load of a finite imperfect column lying on a cubic nonlinear elastic foundation but with one end simply-supported while the other end is clamped. Perturbation and asymptotic procedures are employed to obtain the asymptotic results. The formulation contains a small non-dimensional parameter upon which asymptotic expansions are initiated. The results which are strictly asymptotic are valid in the limit as the small non-dimensional parameter becomes increasingly small relative to unity.

[1] J.C. Amazigo, B.Budiansky and G.F. Carrier (1971); Asymptotic analysis of the buckling of imperfect columns on nonlinear elastic foundation, Int. J. Solids Struct. 6, 883-900.
[2] J.C. Amzigo and W.B. Fraser (1971); Buckling under external pressure of cylindrical shells with dimple-shaped initial imperfection, Int. J. Solids Struct. 7, 883-900.
[3] H.S. Artem, and L. Aydin (2010); Exact solution and dynamic buckling analysis of a beam column loading, Appl. Math. and Mech., 31(10), 1317-1324.
[4] A.M. Ette (2009); On a lightly damped elastic quadratic model structure modulated by a dynamic load, J. of Nigerian Assoc. of Math. Physics, 14, 21-40.
[5] M. Jabareen and S. Izhak (2009); Dynamic buckling of a beam on a nonlinear elastic foundation under a step loading, J. of Mech. of Materials and Structures, 4(7-8), 1365-1374.

Abstract: In this paper, we construct and draw the graph of some linear box splines using subdivision. The functions were introduced by Prautzsch in [3]. We focus in a particular example of box splines are the B-splines with equidistant knots. Box splines consist of regularly arranged polynomial pieces. A particular interest in linear box spline surfaces that consist of triangular polynomial pieces. The technique involves control points which can be computed iteratively using Matlab from the initial control points of well dened recursion..

[1]. C. de Boor, K. H•ollig, and S. Riemenschneider. Box Splines, Springer-Verlag.
[2]. W. Dahmen and C. A. Micchelli. Convexity of multivariate Bernstein polynomials and box spline surfaces. Studia Math., 23:265-287, 1988.
[3]. H. Prautzsch, and W. Boehm. Box Splines.Handbook of Computer Aided Geometric Design,Farin, Hoschek, Kim, eds.
[4]. H. Prautzsch. The location of the control points in the case of box splines. IMA J. Numer. Anal., 6:43-49, 1986.
[5]. H. Prautzsch. On convex Bezier triangles. Mathematical Modelling and Numerical Analysis, 26:23-36, 1992. [6] C. de Boor and R. DeVore. Approximation by smooth multivariate splines. Trans. Amer. Math. Soc., 276: 775-788, 1983.

Abstract: This article investigates performance of Sign test, Wilcoxon Signed Rank test and t-tests with and without transformation on paired samples by considering scenarios where assumptions of parametric test may or may not meet. For example, a paired t-testor a specified mean difference requires the assumption of normality of populations the samples come from. Inreal-life, such an assumption may not meet. Given this reality, atransformed t-test or alternately,non-parametric tests (Sign or Signed rank tests)may be employed. To recommend the best test, it is imperative that we compare the performanceof these tests using Type I error probability and power of the test via Monte Carlo simulation at various sample sizes. Unlike the recent study ([1]), this article simulates paired samples from symmetric normal and uniform distributions, and skewed gamma and exponential distributions with varying levels ofcorrelation and skewness in the paired populations.

Keywords:Paired t-test, Sign-test, Wilcoxon Signed Rank test, correlation, skewness, Type I error rate, Power of a test.

[1]. A. Imam, M. Usman and M. A. Chiawa, On Consistency and Limitation of paired t-test, Sign and Wilcoxon Sign Rank Test, IOSR Journal of Mathematics (IOSA-JM), Volume 10, Issue 1, 2014.
[2]. P. Sprent, Applied Non-parametric Statistical Methods. 2nd Edition. Chapman and Hall, 1993.
[3]. F. Mosteller and J.W. Tukey, Data Analysis and Regression, Addison-Wesley, Reading, MA, 1977.
[4]. A.C. Atkinson, Plots, Transformations and Regression. Oxford University Press, London, 1985.
[5]. G. M. Clarke and D. Cooke, The Nature of Parametric and Non-Parametric tests. A Basic Course in Statistics, 4th edn. Arnold,1998.

Abstract: The Study was carried out to investigate the effect of school location on mathematics students' performance in Gaya Zonal Education Area of Kano State, Nigeria. The expost facto design was used. A systematic random sampling was employed to select the 284 students' out of a population of 669 students' . three (3) hypotheses were tested to determine the effect of school location on mathematics students' performance especially between urban and rural students', between urban and rural girls as well as between urban and rural boys. Significance difference was found in favour urban students irrespective sex. It was recommended that rural schools should be provided with basic human and physical facilities for better results.

Keywords: School location, Performance.

[1]. Awofala, A.O .A & Fatade, A.O (2017) mathematics as a key to sustainable growth and development: implications for curriculum development. Proceedings of the 54th annual national conference of mathematical association of Nigeria (man) pp.489-494.
[2]. Bature,I.J (2006) survey of causes of maths-phobia among secondary school students in ogun state. Journal of education studies, vol 12, issue 1.pp.12
[3]. Ekpoh, U.I EZE, GB. (2015) priciples supervisory techniques and teachers job performance secondary schools in ikwon education zone, cross-river state, Nigeria. British journal of Education , vol.3 no.6 pp31-40
[4]. Ganiyu, S.A (2016). The Effect of School Location on The Performance of senior secondary school students in mathematics in Municipal Area Council Ft. Abuja, Nigeria. Unpublished B.SC(Ed) Thesis. Kano University of Science and Technology, Wudil, Nigeria.
[5]. Ibrahim, M.O & Likita, M. (2017). Impart of Insurgency (Boko Haram) on performance and Retention in Mathematics Among IDP Camps Primary Pupils in Borno State, Nigeria. Proceedings of 54th Annual National Conference of Mathematical Association of Nigeria (Man). PP- 456-459.

Abstract: Let G = (V, E) be a graph with p vertices and q edges. The Vertex Magic Pyramidal labeling of a graph G with p vertices and q edges is an assignment of integers from 1,2,3,...,𝑝𝑞 to the vertices and edges of G where 𝑝𝑞 is the qth Pyramidal number so that at each vertex the sum of that vertex label and the labels of the edges incident with that vertex is a constant and the constant must be a Pyramidal number. In this paper we prove that the Cycles, Stars, Peterson graph, Complete bipartite graphs are Vertex Magic Pyramidal graphs. By a graph we mean a finite, undirected graph without multiple edges or loops. For graph theoretic terminology, we refer to Harary [2] and Bondy and Murty [4]. For number theoretic terminology, we refer to M. Apostal [1] and Niven and Herbert S. Zuckerman [5].

Keywords: Pyramidal number, Vertex magic pyramidal, Magic strength.

[1]. Awofala, A.O .A & Fatade, A.O (2017) mathematics as a key to sustainable growth and development: implications for curriculum development. Proceedings of the 54th annual national conference of mathematical association of Nigeria (man) pp.489-494.
[2]. Bature,I.J (2006) survey of causes of maths-phobia among secondary school students in ogun state. Journal of education studies, vol 12, issue 1.pp.12
[3]. Ekpoh, U.I EZE, GB. (2015) priciples supervisory techniques and teachers job performance secondary schools in ikwon education zone, cross-river state, Nigeria. British journal of Education , vol.3 no.6 pp31-40
[4]. Ganiyu, S.A (2016). The Effect of School Location on The Performance of senior secondary school students in mathematics in Municipal Area Council Ft. Abuja, Nigeria. Unpublished B.SC(Ed) Thesis. Kano University of Science and Technology, Wudil, Nigeria.
[5]. Ibrahim, M.O & Likita, M. (2017). Impart of Insurgency (Boko Haram) on performance and Retention in Mathematics Among IDP Camps Primary Pupils in Borno State, Nigeria. Proceedings of 54th Annual National Conference of Mathematical Association of Nigeria (Man). PP- 456-459.

Abstract: The numerical optimization of general nonlinear multivariable objective functions requires efficient and robust techniques. Effectiveness is vital in light of the fact that these issues require an iterative arrangement strategy, and experimentation ends up noticeably unfeasible for more than three or four factors. Power (the capacity to accomplish an answer) is attractive on the grounds that a general nonlinear capacity is capricious in its conduct; there might be relative maxima or minima, saddle focuses, locales of convexity, concavity, et cetera. In a few areas the improvement calculation may advance gradually toward the ideal, requiring over the top PC time. Luckily, we can draw on broad involvement in testing nonlinear programming calculations for unconstrained capacities to assess different methodologies proposed for the enhancement of such capacities. This paper learns about procedures for tackling unconstrained enhancement issue

Keywords: Techniques, unconstrained optimization, nonlinear multivariable

[1] Avriel, M. Nonlinear Programming. Prentice-Hall, Englewood Cliffs, New Jersey (1976). Broyden, C. G. "The Convergence of a Class of Double-Rank Minimization Algorithms." J Znst Math Appl6: 76-90 (1970).
[2] Dembo, R. S.; S. C. Eisenstat; and T. Steihang. "Inexact Newton Methods." SIAM J Num Anal 19: 400-408 (1982). Dennis, J. E.; and R. B. Schnabel. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, New Jersey (1996)
[3] Levenberg, K. "A Method for the Solution of Certain Problems in Least Squares." Q Appl Math 2: 164-168 (1944).
[4] Kelley, C. T. Iterative Methods for Optimization. SIAM, Philadelphia (1999).
[5] Li, J.; and R. R. Rhinehart. "Heuristic Random Optimization." Comput Chem Engin 22: 427-444 (1998)..

Abstract: In this paper, the generalized n-dimensional quadratic functional equation of the form.......

Keywords: Banach Sapce, Fixed Point, Fuzzy Normed Space, Hyers-Ulam Stability, Quadratic Functional Equation.

[1] J. H. Bae, On the stability of n-dimensional Quadratic Functional Equation, Comm. Korean Math. Soc. 16(1), (2001), 103-111.
[2] J. H. Bae and K. W. Jun, On the Generalized Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation, Bull. Korean Math. Soc. 38(2), (2001),
325-336.
[3] G. Balasubramaniyan, V.Govindan and C.Muthamilarasi. General Solution and Stability of Quadratic Functional Equation. Int. J. Math. Appl.,5 (2 A),
(2017). 13- 26.
[4] I. S. Chang and H. M. Kim, Hyers-Ulam-Rassias Stability of a Quadratic Functional Equation, Kyungpook Math.J., 42(1), (2002), 71-86.
[5] I. S. Chang, E. H. Lee and H. M. Kim, On Hyers-Ulam-rassias Stability of a Quadratic Functional Equation, Math. Inequal. Appl., 6(1), (2003), 87-95..