iosr-Jm   Volume-1 ~ Issue-2

ABSTRACT: In this paper, we propose numerical method to solve singularly perturbed delay differential
equations which works smoothly in both the cases, i.e., whether the delay is of O( ) or of o( ) . The numerical
method uses the modified upwind finite difference scheme on a special type of mesh to tackle the delay
argument. The stability and error analysis is given for in both the cases, when the sign of the coefficient of the
reaction term is negative or positive. To demonstrate the efficiency of the method and how to discuss the size of
the delay argument affects the layer behaviour we have implemented it on several test examples.
Keywords: Boundary Layer modified upwind finite difference scheme, Singular perturbation delay differential
equation.

[1] R. Bellman, K. L. Cooke, Differential-Difference Equations, Academic Press, New York, USA, 1963.
[2] R. D. Driver, Ordinary and Delay Differential Equations, Belin-Heidelberg, New York, Springer, 1977.
[3] V. Y. Glizer, Asymptotic solution of a boundary-value problem for linear singularly-perturbed functional differential equations
arising in optical control theory, J. Optim. Theory Appl. 106 (2000) 309-335.
[4] M. K. Kadalbajoo, K. K. Sharma, Numerical analysis of singularly perturbed delay differential equations with layer behavior,
Applied Mathematics and Computation, 157 (2004) 11–28.
[5] M. K. Kadalbajoo, K. K. Sharma, Numerical treatment of boundary value problems for second order singularly perturbed delay
differential equations, Computational & Applied Mathematics, 24 (2005) 151–172.
[6] M. K. Kadalbajoo, K. K. Sharma, A Numerical method based on finite differences for boundary value problems for singularly
perturbed delay differential equations, Applied Mathematics & Computation, 197 (2008) 692–707.
[7] C. G. Lange, R. M. Miura, Singular perturbation analysis of boundary-value problems for differential-difference equations. v. small
shifts with layer behavior, SIAM J. Appl. Math. 54 (1994) 249–272.
[8] C. G. Lange, & R. M. Miura, Singular perturbation analysis of boundary-value problems for differential-difference equations. vi.
Small shifts with rapid oscillations, SIAM J. Appl. Math. 54 (1994) 273–283.
[9] M. K. Kadalbazoo, Y. N. Reddy, A non asymptotic method for general linear singular perturbation problems, J. Optim. Theory
Appl. 55 (1986) 439-452.
[10] H. Tian, Numerical treatment of singularly perturbed delay differential equations, Ph.D. thesis, University of Manchester, 2000.

[1] Chlodovsky, I (1937). Sur le development des fonctions definies dans un interval infini en series de polynomes de M S Bernstein composition math, 4,380-93 .
[2] Kantorovic, L A (1930). Sur certains developpements suivaint les polynomes de la forme de S Bernstein I , II, C R Acad. Sci. USSR , 20,563-68,595- 600 .
[3] Anwar Habib and S Umar (1980) "On Generalized Bernstein Polynomials" Indian J. pure appl. Math. , 11(2) , 177-189.

Abstract: Calendar is the key of our life. In every aspect of our life we need to follow it. It is not possible to keep calendar of the range ZERO to INFINITE. Generally we can have calendar up-to 300 years from the current one. There is some formula to calculate the year/month etc. but they have some limitation, they cannot be applicable for ZERO to INFINITE calendar. In this paper, we proposed a novel methodology to extract the day, month, year from ZERO to INFINITE range of calendar with a few seconds.
Keywords: Mid-point of the Operator, leap – year.

[1] www.scribd.com/.../11707676-An-Exploratory-Study-of-Personal-Calendar-Use.
[2] iris.usc.edu/information/Iris-Conferences.html.
[3] www.cs.utep.edu/novick/courses/CS5317/Schedule.pdf.

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[1]. M.K. AOUF and H.M. SRIVASTAVA, A new criterion for meromorphically p–valent convex functions of order , Math.Sci.Res.
Hot. Line 1(8)(1997), 7–12.
[2]. S.B. JOSHI and H.M. SRIVASTAVA, A certain family of meromorphically multivalent functions, Computers Math. App. 38(3/4)
(1999), 201–211.
[3]. J.L. LIU and H.M. SRIVASTAVA, A linear operator and associated families of meromorphically multivalent functions. J. Math.
Anal. Appl. 259(2001), 566–581.
[4]. J.L. LIU and S. OWA, On a class of meromorphic p–valent functions involving certain linear operators. Intermat. J. Math. Math. Sci.
32(2002), 271–280.
[5]. J.L. LIU and H.M. SRIVASTAVA, Some convolution conditions for starlikeness and convexity of meromorphically multivalent
functions, Applied Math. Letters, 16(2003), 13–16.
[6]. S. OWA, H.E. DARWISH and M.K. AOUF, Meromorphic multivalent functions with positive and fixed second coefficients, Math.
Japan, 46(1997), 231–236.
[7]. H.M. SRIVASTAVA, H.M. HOSSEN and M.K. AOUF, A unified presentation of some classes of meromorphically multivalent
functions, Computers Math. Appl. 38(11/12)(1999), 63–70.

Abstract: Tachibana (1967) have studied on the Bochner curvature tensor. Singh (1971-72) studied on Kaehlerian recurrent and Ricci-recurrent spaces of second order. Further, Negi and Rawat (1994) have been studied some bi-recurrent and bi-sym metric properties in a Kaehlerian space. In the present paper, we have been studied Hyperbolically Kaehlerian bi-recurrent and bi-symmetric spaces also several theorems have been established and proved therein.
Keywords: Bi-recurrent, bi-symmetric, Hyperbolically Kaehlerian Space, Kaehlerian space, Sasakian space.

[1] Okumura, M.: Some remarks on space with a certain contact structures , Tohoku Math. Jour., 14, (1962) 135 – 145 .
[2] Tachibana, S.: On the Bochner curvature tensor, Nat. Sci. Report Ochanomizu Univ., 18(1), (1967)15-19.
[3] Singh, S.S.: On Kaehlerian spaces with recurrent Bochner curvature tensor, Acc. Naz. Dei. Lincei, Rend , Series VIII, 51, 3-4, (1971) 213-220.
[4] Singh, S.S.: On Kaehlerian recurrent and Ricci-recurrent spaces of second order, Atti della Acad-emia delle Scienze di Torino, 106, 11, (1971-72) 509-518.
[5] Yano, K.: Differential Geometry of Complex and almost complex spaces, Pergamon press (1965).
[6] Negi, D.S. & Rawat, K.S. : Some bi-recurrence and bi-symmetric properties in a Kaehlerian space, Acta Ciencia Indica, Vol. XX M, No. 1 (1994) 95-100.
[7] Rawat, K.S. & Silswal, G.P. : Some theorems on subspaces of subspaces of a Tachibana spaces,
[8] Acta Ciencia Indica , Vol. XXXI M, No. 4, (2005) 1009-1016.
[9] Rawat,K.S.&Silswal,G.P.:TheoryofLie-derivativesandmotionsinTachibanaspaces,News Bull. Cal. Math. Soc. , 32 (1-3), (2009) 15-20.
[10] Rawat,K.S.&PrasadVirendra:SometheoremsonKaehlerianConharmonicbi-recurrent spaces,Acta Ciencia indica , Vol. XXXV M, No. 2, (2009) 417-421 MR 2666522.
[11] RawatK.S.&PrasadVirendra:OnLie-derivativesofscalars,VectorsandTensors,Purea Applied Mathematica Sciences, Vol. LXX, No. 1-2, (2009) 135-140.
[12] Rawat, K.S. & Dobhal Girish : On Einstein-Kaehlerian s-recurrent space, International Trans. in
[13] Mathematical Sciences and Computer , Vol. 2, No. 2, (2009) 339-343.
[14] Rawat,K.S.&MukeshKumar:OncurvaturecollineationsinaTachibanarecurrentspace, Aligarh Bull. Math. , 28 , No. 1-2 , (2009) 63-69 MR 2769016.
[15] Rawat,K.S.&UniyalNitin:StudyonKaehlerianrecurrentandsymmetricspacesofsecond order, Jour. of the Tensor Society, Vol. 4 , (2010) 69-76.
[16] Rawat , K.S. & Prasad Virendra : On Holomorphically Projectively flat parabolically Kaehlerian
[17] spaces, Rev. Bull. Cal. Math. Society, 18 (1), (2010) 21-26.
[18] Rawat,K.S.&DobhalGirish:ThestudyofTachibanabi-recurrentspaces,AntarcticaJour. Math. ,7(4) , (2010) 413-420.
[19] Rawat, K. S. & Kumar Mukesh : On hyper surfaces of a Conformally flat Kaehlerian recurrent
[20] space , Pure and Applied Mathematika Sciences , Vol. LXXIII , No. 1-2, (2011) 7-13 .
[21] Rawat,K.S.&UniyalNitin:OnConformaltransformationsinanalmostKaehlerian and Kaehlerian spaces, Jour. of Progressive Science , Vol. 2 , No. 2 , (2011) 138-141.

Abstract: Flow of water at its maximum density past a porous vertical plate is considered. Effects of a transversely applied magnetic field, first order chemical reaction and suction of the plate on the flow field are studied by a similarity transformation of the governing equations. For various values of the magnetic, chemical reaction and suction parameters numerical values proportionate to Skin friction, Nusselt number and Sherwood number are tabulated and graphical results for the velocity, temperature and concentration profiles are presented. Computed values and graphical results for flow of water at a normal temperature are compared with that of flow at 4⁰C.
Key words: Maximum density of water, porous plate, Chemical reaction, suction, Prandtl number

[1] H. Schlichting and K. Gersten : Boundary Layer Theory (8th ed.), Springer , 1999
[2] V.M. Soundalgekar, H.S.Takhar and N.V.Vighnesam (1988): Combined free and forced convection flow past a semi-infinite vertical plate with variable surface temperature: Nuclear Engineering anddesign:110, pp 95-98
[3] Graham Wilks (1973): Combined forced and free convection flow on vertical surfaces: Int. J. of Heat and Mass Transfer: 16, pp1958-1964
[4] M.S.Raju, X.Q.Liu and C.K. Law (1984): A formulation of combined forced and free convection past horizontal and vertical surfaces: Int. J. of Heat and Mass Transfer: 27(12), pp2215-2224
[5] U.N. Das, R.K. Deka and V.M. Soundalgekar (1998): Effect of mass transfer on flow past an impulsively started infinite vertical plate with chemical reaction: The Bulletin, GUMA,5, pp13-20
[6] A. Jyothi Bala and Vijaya Kumar Varma (2011): Unsteady MHD heat and mass transfer flow past asemi-infinite vertical porous moving plate with variable suction in the presence of heat generation and homogeneous chemical reaction: Int. J. of Appl. Math. And Mech., 7(7), pp20-24
[7] Mostafa AA Mahmoud (2007): A note on variable viscosity and chemical reaction effects on mixed convection heat and mass transfer along a semi-infinite vertical plate: Mathematical Problems in Engineering, 2007, pp1-7
[8] S. L. Goren (1966): On free convection in water at : Chemical Engineering Science, 21, pp515-518
[9] H. Herwig (1985): An asymptotic approach to free-convection flow at maximum density: Chemical Engineering Science, 40(9), pp1709-1715
[10] V.M. Soundalgekar, T.V. Ramana Murty and N.V. Vighnesam (1984): Combined forced and freeconvective flow of water at past a semi-infinite vertical plate: Int.J. of Heat & Fluid Flow, 5(1), pp54-56

Abstract : A new hybrid algorithm by integrating a nested partitions (NP) method with successive quadratic programming (SQP) is presented for global optimization of general optimal control problems involving lumped parameter system. The control parameterization technique first employed to reduce the control problem into a parameter selection problem. Then, in the global phase a vicinity of global optimizer is approximated by an appropriate NP method. Subsequently, the SQP algorithm in the local phase promotes the accuracy of final solution. The effectiveness of the hybrid NP–SQP algorithm is also illustrated by means of numerical simulations.
Keywords - Constraints, Nested partitions, Optimal control problem, Successive quadratic programming

[1] N. U., Ahmed, Dynamic systems and control with application. World Scientific, Singapore, (2006).
[2] A., Antoniou, W. S., Lu, Practical Optimization: Algorithms and Engineering Applications. Springer, New York, (2007).
[3] E., Polak, An historical survey of computational methods in optimal control, Siam Rev. 15 (1973), no. 2, 553-584.
[4] F., Glover, G. A., Kochenberger, Handbook of metaheuristics, Kluwer academic publishers. Dordrecht, Netherlands, (2003).
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[6] C. P., Neuman, A., Sen, A suboptimal control algorithm for constrained problems using cubic splines. Automatica 9 (1973), 601-613.
[7] J., Nocedal, S. J., Wright, Numerical Optimization. 2nd Ed, Springer, New York, USA, (2006).
[8] L. S., Pontryagin, V. G., Boltyanskii, R. V., Gamkrelidze, and E. F., Mischenko, The Mathematical Theory of Optimal Processes (Translation by L. W., Neustadt), Macmillan, New York, USA, (1962).
[9] M. J. D., Powell, Y., Yuan, A recursive quadratic programming algorithm that uses differentiable exact penalty functions, Math. Program. 35 (1986) 265–278.
[10] L., Shi, S., Ólafsson, Nested partitions method for global optimization. Oper. Res. 48 (2000), no. 3, 390- 407. [11] K. L., Teo, C. J. Goh, and K. H., Wong, A unified computational approach to optimal control problems. Longman Scientific and Technical, (1991).
[12] K. L., Teo, V., Rehbock, and L. S., Jennings, A new computational algorithm for functional inequality constrained optimization problems. Automatica 29 (1993), no. 3, 789-792.
[13] J., Vlassenbroeck, A Chebyshev polynomial method for optimal control with state constraints. Automatica 24 (1988), no. 4, 499- 506.
[14] B. Yang, K. Zhang, Z. You, A successive quadratic programming method that uses new corrections for search directions, J. Comput. Appl. Math. 71 (1996) 15-31.

Abstract: This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distributions. More specifically the authors visualize a new generalization of Sam-Solai's Multivariate symmetric arcsine distribution of Kind-1 from the univariate case. Further, we find its Cumulation, Marginal, Conditional distributions, Generating functions and also discussed its special case.The special cases include the transformation of Sam-solai's Multivariate symmetric arcsine distribution of kind-1 into Multivariate symmetric log arcsine distribution of kind-1 and Multivariate symmetric Inverse arcine distribution of Kind-1. It is found that the conditional variance of Sam-Solai's Multivariate conditional symmetric arcsine distribution is homoscedastic and the correlation co-efficient among the random variables are similar to Pearson's product moment correlation co-efficient. Finally area values are obtained for Bi-variate symmetric arcsine distribution of kind-1 and Bivariate probability surfaces and contours are visualized.
Keywords: Sam-Solai's Multivariate symmetric arcsine distribution of kind-1, homoscedastic, Multivariate symmetric log arcsine distribution of kind-1, Multivariate symmetric Inverse arcsine distribution of Kind-1.

[1] M. Abramowitz and I. A. Stegun (Handbook of Mathematical Functions. Dover Publications, 1964)
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Abstract:In colleges, students often study calculus with linear algebra, which is a fundamental abstract mathematical subject. It was first discovered via research on d eterminants. The earliest courses to make use of linear algebra as a textbook were those offered at graduate levels at American colleges. This lecture is a required component of the undergraduate studies of scientific departments at educational institution s located all over the globe. The study of linear systems of equations, which was initially developed by the Babylonians about the year around Cardan devised a straightforward method for solving systems of linear equations by developing a formula that......

Keywords: linear algebra, linear equation, Formulation

[1]. C. R. Smaill, G. B. Rowe, E. Godfrey and Rod O. Paton, "An Investigation Into the Understanding and Skills of First Year
Electrical Engineering Students." IEEE Trans. on Educ. v ol. 55, pp. 29 35, 2012.
[2]. R. S. Santos, "Avaliação do desempenho de ensino aprendizagem de Cálculo Diferencial e Integral I (O caso da UFC)," M.S. thesis,
Dept. of Education, Federal University of Ceará, Fortaleza, Brazil, 2012 .
[3]. S. S. Nieto, C. M. C. Lopes . "A importância da disciplina álgebra linear nos cursos de engenharia."World Congress on Computer
Science, Engineering and Technology Education. March 19 22, 2012 , São Paulo, Brazil.
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questions2.pdf, 2012 .
[5]. L. Dorier. "Recherches en Histoire et en Didactique des Mathématiques sur L'Algèbre Linéaire Perspectives Théoriques sur leurs
Interactions." In: Les Cahiers du Laboratoire Leibn iz. No. 12. Grenoble. 2012