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.
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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).

Abstract: This paper presents an initial value problem with boundary integral conditions for the partial differential equation. Modification of adomian decomposition method is introduced for solving problem. Finally, simulation results for some examples illustrate the comparison of the analytical and numerical solutions. The results are presented using the MathCAD 12 and Matlab software package.

Keywords:Modified decomposition method, partial differential equation, boundary integral condition problem..

[1]. P. Pue-on, N. Viriyapong, Modified Adomian Decomposition Method for Solving Particular Third-Order Ordinary Differential
Equations, Applied Mathematical Sciences, Vol. 6, (2012), 1463 - 1469.
[2]. G. Adomian, A review of the decomposition method and some recent results for nonlinear equation, Math Comput Model,
13(7) (1992) 17.
[3]. A.M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl Math Comput, 111(1)
(2000), 53-69.
[4]. A.M. Wazwaz, A reliable modification of Adomian decomposition method, Appl Math Comput, 102, (1999), pp. 77–86.
[5]. M.M. Hosseini, H Nasabzadeh, Modified Adomian decomposition method for specific second order ordinary differential equations,
Appl. Math. Comput, 186 (2007), 117-123.

Abstract: The present paper deals with a new fixed point theorem in Menger space. This is in line with research in fixed point theory using any kind of coincidentally commuting mappings and integral functions. Examples have also been given in support of our result.

Keywords:Menger space, t-norm, common fixed point, compatible maps, occasionally weak compatible maps, any kind of coincidentally commuting maps.

[1]. Jain, A. and Chaudhary, B., On common fixed point theorems for semi-compatible and occasionally weakly compatible mappings
in Menger space, International Journal of Research and Reviews in Applied Sciences, Vol. 14 (3), (2013), 662-670.
[2]. Jain, A. and Singh, B., Common fixed point theorem in Menger Spaces, The Aligarh Bull. of Math. 25 (1), (2006), 23-31.
[3]. Kutukcu, S., A fixed point theorem in Menger spaces, International Mathematical Forum 1(32), (2006), 1543-1554.
[4]. Menger, K., Statistical metrics, Proc. Nat. Acad. Sci. USA. 28(1942), 535 -537.
[5]. Mishra, S.N., Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36(2), (1991), 283-289.

Abstract: Logistic regression model is one of the popular mathematical models for analysis of binary data with applications in health, behavioural and statistical sciences. The main mathematical concept under the logistic regression model is the logit or the natural logarithm of an odds ratio. It is one of the most commonly used models to account for confounders in medical literature. This research sought to evaluate the impact of automatic backward model selection criterion on the bias of the parameters for large sample size. This study used a data set simulated in R-package using different kinds............

[1] Abdelrahman A.l., 2010. Applying Logistic Regression Model to the Second Primary Cancer Data. Ain Shams University. Egypt.
[2] Agresti, A. (2007). An introduction to Categorical Data Analysis (2nd ed). Wiley-Interscience.
[3] Al-Ghamdi A.S (2002). Using Logistic regression to estimate the influence of accident factors on accident severity. Accident
Analysis & Prevention.
[4] Al-Ghamdi A.S., 2001 Using Logistic regression to estimate the influence of accident factors on accident severity
[5] Allison, Paul D. (2014) "Measures of fit for logistic regression." Paper 1485-2014 presented at the SAS Global Forum, Washington,
DC.

Abstract: This work focuses on the unsteady MHD free convection Aligned magnetic flow of a viscous fluid past a inclined porous plate embedded with porous medium in presence of chemical reaction. In obtaining the solution, the terms regarding radiation effect, temperature gradient dependent heat source are taken into account of energy equation and chemical reaction parameter is taken into account of concentration equation. The Permeability of the porous medium and the suction velocity...............

Keywords: Aligned Magnetic, Chemical Reaction, MHD, Radiation.

[1] Chamkha. A J. Hydro-magnetic combined heat and mass transfer by natural convection from a permeable surface embedded in a
fluid saturated porous medium, Int. J. Num.Methods for heat and fluid flow, 10 (5), 2000, 455-476.
[2] Chamkha. A J and Khaled. A R.Hydro-magnetic combined heat and mass transfer by natural convection from a permeable surface
embedded in fluid saturated porous medium, International Journal of Numerical methods for Heat and Fluid Flow, 10 (5), 2000
[3] Chamkha. A J.MHD flow of a uniformly stretched vertical permeable surface in the presence of heat generation/absorption and a
chemical reaction, Int.Commun. Heat mass transfer, 30 (3), 2003, 413- 422.
[4] Kandasamy. R, Periasamy. K and Prabhu. K.K.S.Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching
surface with heat source and thermal stratification effects, Int. J. Heat Mass Transfer, 48, 2005, 4557–4561.
[5] Postelnicu. A. Influence of chemical reaction on heat and mass transfer by natural convection from vertical surfaces in porous
media considering Soret and Dufour effects, Heat and Mass Transfer, 43, 2007, 595–602.

Abstract: In this paper an inventory model is developed and analyzed with exponential demand under the condition of permissible delay in payments. Deterioration rate is taken to be a constant fraction of the on hand inventory. In deterioration the realistic assumption of life period is taken into account. Shortages are allowed and they are taken as completely backlogged. Interest is earned on the unit cost of generated sales revenue which is to be deposited in an interest bearing account. Interest charges are paid on the stock held beyond the permissible period, Three different cases depending upon the permissible period are discussed.

Keywords: inventory, permissible, perishability. Exponential.

[1]. Aggarwal, S. P. and Jaggi, C, K. (1995)Ordering policies of deteriorating items under permissible delay in payments.Jour of Opl. Res. Soc., 46 : 658-662.
[2]. Chang,C.T.,2004.An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. International Journal of Production Economics 88,307-316.
[3]. Chung, K. J. (2000)The inventory replenishment policy for deteriorating items under permissible delay in payments.Opsearch, 37 (4) : 267-281.
[4]. Chand,S.,WARD,j., 1987 .A note on economic order quantity under conditions of permissible delay in payments. Journalof operational research socity ,38,832-84.
[5]. Dye, C. Y. (2002)A deteriorating inventory mode! with stock dependent demand andpartial backlogging under conditions of permissible delay in payments.Opsearch, 39 : (3&4) : 189-201.

Abstract: In this paper an inventory model is formulated and analyzed for random deteriorating items with the assumption of life period of time. Demand rate is taken to be a linear function of the on hand inventory. Replenishment is assumed to be instantaneous. The model is developed for infinite time horizon. Shortages are allowed and they are partially backlogged. The backlogging rate is taken to be inversely proportional to the waiting time for the next replenishment. Two special cases also have been discussed. d and they are partially backlogged. The backlogging rate is taken to be inversely proportional to the waiting time for the next replenishment. Two special cases also have been discussed.

[1] Baker, R. C. and Urban, T. L. (1988)A deterministic inventory system with an inventory level dependent demand rate.Jour of Opl.
Res. Soc., 39 (9): 823-831.
[2] Datta, T. K. and Pal, A. K. (1990 )Deterministic inventory systems for deteriorating items with inventory level dependent demand
rate and shortages.Opsearch, 27 (4) : 214-22
[3] Goyal, S.K.and Giri, B.C.(2001)A comment on Chang andDye (1999) :An EOQ model for deteriorating items with time varying
demand and partial backlogging.Jour, of Opl. Res. Soc., 52: 238-239.
[4] Mandal, B. N. and Phaujdar, S. (1989)An inventory model for deteriorating items and stock dependent consumption rate.Jour, of
Opl. Res. Soc., 40: 483-488.
[5] Mandal B. N. and Phaujdar, S. (1989)A note on an inventory model with stock dependent consumption rate.Opsearch, 26 (1) : 43-
46.

Abstract: The purpose of this study was to determine whether or not computer-aided learning using a software program called Math Lab (Pearson, 2010) has a significant difference in students' achievement on mathematics, their comprehension of mathematics, and their prospects for course completion. The study was based on a partial replication of similar recent studies with similar research goals. Based on principles of educational constructivism, the use of software programs must improve learning and acquisition of knowledge. Appropriate implementation of this software into curricular............

Keywords: Students achievement, Math Lab software, course compl

[1] Almeqdadi, F.(2000). The Effect of Using Math Lab (ML) on Jordanian Student's Understanding of Mathematics Concept. Jordan: Yarmouk University.
[2] Bennett S., Maton K. & Kervin L. (2008). The 'digital natives' debate: a critical review of the evidence. British Journal of Educational Technology 39: 775-786
[3] Berge, O. & Slotta, J. (2007). "Learning technology standards and inquiry-based learning". In Koohang, A. and Harman, K. (Eds.), Learning Objects and Instructional Design (pp. 327 - 358). Santa Rosa, CA: Informing Science Press
[4] Biesinger, K. D., Crippen, K. J., & Muis, K. R. (2008). The impact of block scheduling on student motivation and classroom practice in mathematics. Nassp Bulletin 92(3): 191-208.
[5] Bodner, G. M. (1986). Constructivism: A Theory of Knowledge. Journal of Chemical Education,63,873-878.Retrieved from http://chemed.chem.purdue.edu/chemed/bodnergroup/pdf/24_Construct.pdf.

Abstract: Pool-testing prevalence estimators are poor estimators of the actual prevalence of a trait that is they have large bias and Mean Square Error (MSE) and this is a drawback tostatistical inference. This paper proposes a method of minimizing bias and MSE when weallow errors in inspection. The probability of declaring a group as defective is derived byassumption of law of total probability. Using Maximum Likelihood Estimators (MLE) method we constructed a prevalence estimator of the ordered probabilities. Theseprobabilities are used to order the groups via the method of Pool.............

Keywords: Best Linear Unbiased Estimator (BLUE), Lagrange Multiplier, Maximum Likelihood Estimators (MLE), Pool AdjacentViolators Algorithm (PAVA), Weights

[1] Dorfman R. (1943). The detection of defective members of large populations. Annals of mathematical statistics 14, 436-440.
[2] Sobel M., Ellashoff R.M. (1975).Group testing with a new goal, Estimation.Biometrika 62, 181-193.
[3] Nyongesa, L. K., (2011). Dual Estimation of Prevalence and Disease Incidence in Pool-Testing Strategy. Communication in Statistics Theory and Method. 40, 3218-3229.
[4] Brookmeyer, R. (1999). Analysis of Multistage Pooling Studies of Biological Specimensfor Estimating Disease Incidence and Prevalence. Biometrics 55,608-612.
[5] Hwang, F.K., (1976). Group testing with a dilution effect. Biometrika 63,611-613..

Abstract: In this article, the inverse problem for the singular Sturm-Liouville operator is studied. A set of values of eigenfunctions in some internal point and spectrum are given as a data. Uniqueness theorems are also obtained.

Keywords: Best Linear Unbiased Estimator (BLUE), Lagrange Multiplier, Maximum Likelihood Estimators (MLE), Pool AdjacentViolators Algorithm (PAVA), Weights

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[2] V.A. Ambarzumyan, Über eine frage der eigenwerttheorie, Z. physics. 53 (1929) 690-695.
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[4] F. Gesztesy and B. Simon, Inverse spectral analysis with partial information on the potential II, The case of discrete spectrum, Trans. Amer. Math. Soc. 352(6) (2000), 2765-2787.
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