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.