iosr-Jm   Volume-13 ~ Issue-4 ~ Jul-Aug 2017

Abstract: This paper is an introduction for solving Delay Differential Equations (DDEs) using market equilibrium. By market we mean the conditions under which producers sell and consumers buy a certain commodity. The term market is used when only one commodity is being bought and sold and the word multimarket is used when more than one commodity is involved. The price, demand and supply of any one good affects the prices etc. of any other goods and vice-versa. DDEs discussed in this paper are linear. The most fundamental
Functional Differential Equations(FDEs) is the linear first order Delay Differential Equations (DDEs). Both DDEs and FDEs are used as modeling tools in models in Economics. We discuss the solution of constant coefficient DDEs by the "Method Of Characteristics" (MOC..............

Keywords:Delay differential equations, Demand function, Equivalent systems, Market equilibrium, Method of characteristics, Method of steps, Stability of the equilibrium, Supply function

[1] ASl, F.M. and Ulsoy, A.G., Analysis of a system of Linear Delay Differential Equations, Journal of Dynamic Systems, Measurement
and Control,2003, V.125, PP215-223.
[2] Bender, A.E., and Neuwirth, L.P. Traffic Flow : Laplace Transforms, American Mathematical Monthly, Vol.80, (1973), 417-423.
[3] Driver, R.D., Sasser, D.W and Slater, M.L., The Equationy'(t)=ay(t)+by(t-𝜏) with 'small' Delay, American Mathematical Monthly,
Vol.80, 1973, pp 990-995.
[4] Falbo, C.E. Complete Solutions to Certain Functional Differential Equations, Proceedings systemic, Cybernetics, informatics, 1998,
Vol.4, pp.157-161.
[5] Flabo, C.E., Idempotent Differential Equation, Journal of interdisciplinary Mathematics, Vol.6, No.3, pp279-289, October 2003.

Abstract: In this paper some properties of fgspr-continuous functions are studied. It is shown that the class of all fgspr-irresolute functions implies the class of all fgspr*-continuous functions and the class of all
fgspr*-continuous functions implies the class of all fgspr-continuous functions.

Keywords: fgspr-continuous, fgspr-irresolute and fgspr*-continuous.

[1] K. K Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J.Math.Anal.Appl., 82(1)(1981), 14 – 32.
[2] G. Balasubramanian and P. Sundaram, On some generalizations of fuzzy continuous functions, Fuzzy Sets and Systems, 86(1)(1997), 93 – 100.
[3] C. L. Chang, Fuzzy Topological Spaces, J.Math.Anal.Appl., 24(1968), 182 – 190.
[4] Y. Gnanambal and K. Balachandran, On GPR-Continuous Functions in Topological spaces, Indian J.pure.appl.Math., 30(6)(1999), 581-593.
[5] Govindappa Navalagi, A. S. Chandrashekarappa and S. V. Gurushantanavar, On GSPR – Closed Sets in Topological Spaces, Int.J.Math.Comp.Appl., Vol 2, No. 1 – 2(2010), 51 – 58.

Abstract: Despite practical work being accorded a pivotal role in science classrooms, the poor quality of conducting practical work in biology classroom leads students to develop certain undesirable attitude towards practical work. Even though there has been lengthy research into students' attitudes to science there is little research specifically into their attitudes to practical work. The purpose of this study was to examine students' attitude toward practical work and the extent to which such attitude influence students' achievement in biology. A sequential explanatory mixed methods design............

Keywords: practical work, perceived achievement, interest factor, importance factor, difficult factor

[1]. Chilisa, B., & Preece, J. (2005). Research methods for adult educators in Africa. Pearson education South Africa, ISBN 9282011186.
[2]. Creswell, J. W., Plano Clark, V. L., Gutmann, M., & Hanson, W. (2003). Advanced mixed methods research designs. Thousand Oaks, CA: Sage.
[3]. Hofstein, A., & Lunetta, V. N. (2004). The laboratory in science education: Foundations for the twenty‐first century. Science Education, 88(1), 28-54.
[4]. Hofstein, A., & Mamlok-Naaman, R. (2011). High-school students' attitudes toward and interest in learning chemistry. Educación Química, 22 (2), 90-102.
[5]. Jenkins, E. W., & Nelson, N. W. (2005). Important but not for me: Students' attitudes towards secondary school science in England. Research in science and Technological.

Abstract: West African countries are lagging behind in the global trends in mathematics and science achievement. Globally, governments and educational stakeholders are interested in international comparisons' of student achievement, using assessment instruments such as Trends in International Mathematics and Science Study (TIMSS), PERIL, SACMEQ, WASSCE, and Programme for International Student Assessment (PISA). The reluctance of West African countries to join in these global efforts at finding means of improving the generally deteriorating performance in mathematics and science points...........

Keywords: Performance in mathematics and science, TIMSS, Assessment and Research.

[1]. Anamuah-Mensah, J. and Mereku, D.K. (2004). Ghanaian JSS Students'
[2]. Mathematics Achievement in TIMSS 2003. Implications for item construction for the BECE mathematics.
[3]. Appiah, J. K. (n.d ). The significance of international comparison of student achievement. Retrieved from http://www.iaea.info/documents
[4]. Clarke, M. (2011). Framework for building an effective student assessment system. READ/SABER Working Paper. Retrieved from http://files.eric.ed.gov/fulltext/ED553178.pdf
[5]. Fredua-Kwarteng, T. (2005). Ghana Flunks at Mathematics and Science: Analysis (1) and (2).