iosr-Jm   Volume-7 ~ Issue-2

Abstract: The self Help Group (SHG) is group of rural poor who have organized themselves into a group for eradicationof poverty. The members of the group belong to families below the poverty line. This will help the families of occupational groups like agricultural labourers, marginal farmers, designers and artisans marginally above the poverty line, or who may have been excluded from the Below Poverty Line (BPL) list to become members of the Self Help Group. A self help group consists of two categories. One named as magalier thittam and another is non- magalier thittam. The factors of Self help group categories are random in nature. These factors can be handled using stochastic linear programming problem (SLPP). Here the data is collected from Tuticorin district. The optimization technique such as two stage programming and chance constrained programming can be adopted for SLPP. In this paper chance constrained programming (CPP) is used to obtain optimal solution.

Keywords: SLPP, CCP, LP, SHG.

[1] Li P., Arellano-Garcia H., Wozny G., "Chance Constrained Programming Approach to Process Optimization under Uncertainty",
Computers and Chemical Engineering 32,25-45,2008.
[2] CHARNESA, and W.W. COOPER", Chance Constrained Programming,"Management Science, Vol. 5, 1959, pp. 73-79.
[3] Cigdem Z. Gurgur a; James T. Luxhoj," Application of Chance-Constrained Programming to Capital Rationing Problems With
Asymmetrically Distributed Cash. Flows and Available Budget,"The Engineering Economist, Vol. 48, 2003.
[4] Harvey ARELLANO-GARCIA," Chance ConstrainedOptimization of Process Systems under Uncertainty".
[5] R. Jagannathan , Chance-Constrained Programming with Joint Constraints, http://www.jstor.org/action 1974.
[6] Kantiswarup, P. K. Gupta and Man Mohan,"Operations research", Sultan Chand &Sons, New Delhi, 1993.
[7] S. S. RAO, Optimization theory and applications, Wiley, New York, 1992
[8] RENE HENRION,"Introduction to Chance –Constrained Programming"www.stoprog.org.
[9] Suvrajeet Sen and Julia L. Higle, "An Introductory Tutorial on Stochastic LinearProgramming Models", Programming Stochastic
Tutorial.
[10] H. A. Taha, Operations research: an introduction, Macmillan, New York, 1971.

Abstract:In this paper, we investigated the effects of magnetic field and thermal in Stokes' second problem for unsteady second grade fluid flow through a porous medium. The expressions for the velocity field and the temperature field are obtained analytically. The effects of various pertinent parameters on the velocity field and temperature field are studied through graphs in detail.

Keywords: Thermal Effects, Fluid Flow, Porous Medium, Magnetic field.r

[1] L. Ai and K. Vafai, An investigation of stokes' second problem for non-Newtonian fluids, Numerical Heat Transfer, Part A, 47(2005), 955-980.

[2] C. Argento and D. Bouvard, A Ray, Tracing Method for Evaluating the Radiative Heat Transfer in Porous Medium", Int. J. Heat Mass Transfer, 39(1996), 3175-3180.

[3] S. Asghar, T. Hayat and A.M. Siddiqui, Moving boundary in a non-Newtonian fluid, Int. J. Nonlinear Mech., 37(2002), 75 - 80.

[4] A. J. Chamkha, Hydromagnetic three-dimensional free convection on a vertical stretching surface with heat generation or absorption, Int. J. Heat Fluid Flow, 20(1999), 84 - 92.

[5] H. Chen and C. Chen, Free convection flow of non-newtonian fluids along a vertical plate embedded in a porous medium, Journal of Heat Transfer, 110(1988), 257 - 260.

[6] C.I. Chen, C.K. Chen and Y.T. Yang, Unsteady unidirectional flow of an Oldroyd-B fluid in a circular duct with different given volume flow rate conditions. Heat and Mass Transfer, 40(2004), 203 - 209.

[7] R.V. Dharmadhikari and D.D. Kale, Flow of non-newtonian fluids through porous media, Chem. Eng. Sci., 40(1985), 527-529.

[8] J.E. Dunn and K.R. Rajagopal, Fluids of differential type: critical review and thermodynamic analysis, Int. J. Engng. Sci., 33(1995), 689 - 729.

[9] M. E. Erdogan, Plane surface suddenly set in motion in a non-Newtonian fluid, Acta Mech., 108(1995), 179 - 187.

[10] M. E. Erdogan, A note on an unsteady flow of a viscous fluid due to an oscillating plane wall, Int. J. Non-Linear Mech., 35(2000), 1 - 6.

Abstract:Experts in the mathematical modeling for two interacting technologies have observed the different contributions between the intraspecific and the interspecific coefficients in conjunction with the starting population sizes and the trading period. In this complex multi-parameter system of competing technologies which evolve over time, we have used the numerical method of mathematical norms to measure the sensitivity values of the intraspecific coefficients b and e, the starting population sizes of the two interacting technologies and the duration of trading. We have observed that the two intraspecific coefficients can be considered as most sensitive parameter while the starting populations are called least sensitive. We will expect these contributions to provide useful insights in the determination of the important parameters which drive the dynamics of the technological substitution model in the context of one-at-a-timesensitivity analysis.

Keywords: Sensitivity Analysis, Mathematical Model, Interacting Technologies.

[1] Bazykin A., Nonlinear Dynamics of Interacting Populations, World Scientific Series on Nonlinear Science, Series A, Vol 11, Leon Chua, ed., World Scientific, New Jersey, 1998

[2] Kumar U. and Kumar V., Technological Innovation Diffusion: The Proliferation of Substitution Models and Easing the User's Dilemma, IEEE Transactions on Engineering Management 39(2), 158-168 (1992).

[3] Young P., Technological Growth Curves, A Competition of Forecasting Models, Technological Forecasting and Social Change 44, 375-389 (1993)

[4] Bhargava S. C., Generalized Lotka-Volterra Equations and the Mechanism of Technological Substitution, Technological Forecasting and Social Change 35, 319-326 (1989)

[5] S. A. Morris, David Pratt, Analysis of the Lotka-Volterra Competition Equations as a Technological Substitution Model. Technological Forecasting and Social change 70(2003) 103-133.

[6] E. N. Ekaka-a, Computational and Mathematical Modelling of Plant Species Interactionsin a Harsh Climate, PhD Thesis, Department of Mathematics, The University of Liverpool and The University of Chester, United Kingdom, 2009.

Abstract: The complex dynamics of facultative mutualism is best described by a system of continuous non-linear first order ordinary differential equations. The methods of 1-norm, 2-norm, and infinity-norm will be used to quantify and differentiate the different forms of the sensitivity of model parameters. These contributions will be presented and discussed.

[1]. Ekaka-a E. N. (2009): Computational and Mathematical Modelling of Plant Species interactions in a Harsh Climate. PhD Thesis, Dept. of Mathematics, The university of Liverpool and The University of Chester, United Kingdom.
[2]. Ford Neville J, Lumb Patricia M, Ekaka-a Enu (2010): Mathematical modelling of plant species interactions in a harsh climate, Journal of Computational and Applied Mathematics, Vol. 234, pp. 2732-2744.

[3]. Hernandez MJ (1998): Dynamics of transitions between population interactions: a nonlinear interaction alpha-function defined, Proceedings of the Royal Society B Biological Sciences London 1998 265, 1433-1440..
[4]. Nwachukwu E. C. and E. N. Ekaka-a (2013): Sensitivity Analysis using a partially coupled system of differential equations without delay, Journal of Mathematics and System Science (ISSN 2159-5291, USA).
[5]. Morin P.J (2002), Community Ecology, Blackwell Publishing Company, United Kingdom.

Abstract: A six-step Continuous Block method of order (5, 5, 5, 5, 5, 5) T is proposed for direct solution of the second (2nd) order initial value problems. The main method and additional ones are obtained from the same continuous interpolant derived through interpolation and collocation procedures. The methods are derived by interpolating the continuous interpolant at 𝑥=𝑥𝑛+𝑗 ,𝑗=6 and collocating the first and second derivative of the continuous interpolant at 𝑥𝑛+𝑗 ,𝑗=0 and 𝑗=2,3,…5 respectively. The stability properties of the methods are discussed and the stability region shown. The methods are then applied in block form as simultaneous numerical integrators. Two numerical experiments are given to illustrate the efficiency of the new methods.

Keywords: Collocation and Interpolation, Second Order Equations, Block Method, Initial Value Problem.

[1] Aiken,R.C, Stiff Computation.New York, (Oxford:Oxford University Press ,1985).

[2] Atkinson,K.E, An introduction to Numerical Analysis,2nd Edition, (John Wiley and sons,New York ,1987).

[3] Awoyemi,D.O , On some continuous Linear Multistep Methods for Initial Value Problems,PhD.Thesis (Unpublished), University of Ilorin,Nigeria, (1992).

[4] Butcher,J.C , Numerical Methods for Ordinary differential systems, (John Wiley & sons,west Sussex,England, 2003).

[5] Fatunla,S.O , Block methods for second order IVP's. Inter.J.Comp.Maths.72,No.1 ,(1991).

[6] Fatunla,S.O , Parallel methods for second order ODE's Computational ordinary differential equations, (1992).

[7] Fatunla,S.O , Higher order parallel methods for second order ODE's.Scientific Computing.Proceeding of fifth International Conference on Scientific Computing, (1994).

[8] Henrici,P., Discrete variable methods for ODE's.John Wiley, New York ,(1962).

Abstract: The study sheds light on the two-fuzzy normed space concentrating on some of their properties like convergence, continuity and the in order to study the relationship between these spaces
Keywords: fuzzy set, Two-fuzzy normed space, α-norm, 2010 MSC: 46S40

[1]. J. Zhang, The continuity and boundedness of fuzzy linear operators in fuzzy normed space, J.Fuzzy Math. 13(3) (2005) 519-536.
[2]. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.
[3]. RM. Somasundaram and ThangarajBeaula, Some Aspects of 2-fuzzy 2-normed linear spaces, Bull. Malays. Math. Sci. Soc. 32(2) (2009) 211-222.
[4]. S. Gahler, Lineare 2-normierte Raume, Math. Nachr. 28 (1964) 1- 43.
[5]. THANGARAJBEAULA, R. ANGELINE SARGUNAGIFTA. Some aspects of 2-fuzzy inner product space. Annals of Fuzzy Mathematics and Informatics Volume 4, No. 2, (October 2012), pp. 335-342
[6]. T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11(3) (2003) 687-705.

[1]. Mason J.C. and Handscomb, D.C., Chebyshev Polynomials, Chapman & Hall – CRC, Roca Raton, London, New York, Washington D.C , 2003
[2]. Olagunju A. S., Chebyshev Series Representation For Product of Chebyshev Polynomials and some notable functions, IOSR Journal of Maths., vol. 2(2), pp 09-13, 2012
[3]. Richard Bronson, Differential Equations, Schaum's Outline series, McGRAW-HILL (2003).
[4]. Taiwo O. A, Olagunju A. S, Olotu O. T, Aro O. T, Chebyshev Coefficient Comparison Method for the numerical solution of nonlinear BVPs. Pioneer JAAM. 3(2), pp 101-110, 2011
[5]. David, S.B. Finite Element Analysis, from concepts to applications, AT&T Bell Laboratory, Whippany, New Jersey, (1987)
[6]. Taiwo O. A, Olagunju A. S, Chebyshev methods for the numerical solution of fourth-order differential equations, International Journal of Physical Sciences Vol. 7(13), pp. 2032 - 2037, 2012
[7]. Grewal, B.S. (2005): Numerical Methods in Engineering and Science, 7th ed. Kanna Publishers, Delhi.
[8]. Olagunju, A.S, Olaniregun D. G, Legendre-coefficients Comparison methods for the Numerical solution of a class of Ordinary differential equation, IOSR Journal of Maths. vol. 2(2), pp 14-19, 2012
[9]. Hermann, B. Collocation Methods for Volterra integral and related functional Differential Equations, Cambridge University press, New York, (2004)
[10]. Lanczos, C. Legendre Versus Chebyshev polynomials. Miller topics in Numerial analysis, Academic press, London, 1973.

Abstract: This paper proposed the use of third-kind Chebyshev polynomials as trial functions in solving boundary value problems via collocation method. In applying this method, two different collocation points are considered, which are points at zeros of third-kind Chebyshev polynomials and equally-spaced points. These points yielded different results on each considered problem, thus possessing different level of accuracy. The method is computational very simple and attractive. Applications are equally demonstrated through numerical examples to illustrate the efficiency and simplicity of the approach.

Keywords - Collocation method, equally-spaced point, third-kind Chebyshev polynomial, trial function, zeros of Chebyshev polynomial

[1]. Richard Bronson, Differential Equations, Schaum‟s Outline series, McGRAW-HILL (2003).
[2]. Mason J.C. and Handscomb, D.C., Chebyshev Polynomials, Rhapman & Hall – CRC, Roca Raton, London, New York, Washington D.C , 2003
[3]. Taiwo O. A, Olagunju A. S, Chebyshev methods for the numerical solution of fourth-order differential equations, International Journal of Physical Sciences Vol. 7(13), pp. 2032 - 2037, 2012
[4]. Hermann, B. Collocation Methods for Volterra integral and related functional Differential Equations, Cambridge University press, New York, (2004)
[5]. David, S.B. Finite Element Analysis, from concepts to applications, AT&T Bell Laboratory, Whippany, New Jersey, (1987)
[6]. Lanczos, C. Legendre Versus Chebyshev polynomials. Miller topics in Numerial analysis, Academic press, London, 1973.
[7]. Lanczos, C. Applied Analysis, Prentice Hall, Endlewood Cliffs, New Jersey, 1957.
[8]. Erwin Kreyszig, Advance engineering mathematics, 8th ed. John Wiley & sons. Inc. New York.
[9]. Taiwo O. A, Olagunju A. S, Perturbed segmented Domain collocation Tau- method for the numerical solution of second order BVP, Journal of the Nigerian Assoc. of mathematical physics. Vol. 10 pp293-298, 2006
[10]. Olagunju A. S., Chebyshev Series Representation For Product of Chebyshev Polynomials and some notable functions, IOSR Journal of Maths., vol. 2(2), pp 09-13, 2012

Abstract: In this article, we used the automata theory to highlight the syntactic property representing the formal knowledge, and also we can use other contexts to represent the semantic property.

Keywords - truth table, formalism, formal symbolic system, Artificial Intelligence, black box, automaton.

[1] Gilles-Gaston Granger, " Philosophie, Langage, Science" les Ulis Cedex A, France, EDP Sciences. 2003 [2] Desanti, Jean-Toussaint, La Philosophie silencieuse ou Critique des philosophies de science, Paris, Éditions du Seuil,. 1975 [3] Ludwig,, Les principes de la caractérologie, Paris, Delachaux et Niestlé, 1950 [4] Jean-Luis Dessailles, Aux origines du langage : une histoire naturelle de la parole, Paris, HEMES Science Publicatio2000
[5] http://agora.qc.ca/mot.nsf/Dossiers/Formalisme
[6] http://fr.wikipedia.org/wiki/Grammaire_formelle#Langages
[7] http://fr.wikipedia.org/wiki/Connaissance
[8] http://fr.wikipedia.org/wiki/Gestion_des_connaissances#Connaissances_tacites_vs_connaissa nces_explicites
[9] http://www.universalis.fr/encyclopedie/formalisme/1-l-idee-de-connaissance-formelle/ Authors Article: Etienne Balibar (master-assistant at the University of Paris-I), Pierre MACHEREY (maitre-assistant at the University of Paris-I)

Abstract: This research is a part of the work devoted on the application of analytical Discrete Ordinate (ADO) method to the polarized monochromatic radiative transfer equation undergoing anisotropic scattering with source function matrix in a finite coupled Atmosphere –Ocean media having flat interface boundary conditions involving specular reflection and transmission matrix. Discontinuities in the derivatives of the Stokes vector with respect to the cosine of the polar angle at smooth interface between the two media with different refractive indices (air and water) is tackled by using a suitable quadrature scheme devised earlier. Atmosphere and ocean are assumed to be homogeneous. No stratification is adopted in the two media. Exact expression for the emergent radiation intensity vector from the top of the atmosphere is derived. Exact expressions for the emergent polarized radiation intensity vector from the air-water interface as well as from any point of the two medium in any direction can also be derived in terms of eigenvectors and eigenvalues.

Keywords: Polarized Radiative transfer, Eigenvectors, Eigenvalues, Green function, specular.

[1] S. Chandrasekhar, Radiative transfer, (Dover publications, New York, 1960)
[2] I. Kuscer, M. Riberic: Matrix formalism in the theory of diffusion of light, Optica Acta1959; 6, 42.
[3] C. E. Siewert, On the equation of transfer relevant to the transfer of polarized light, Astrophys. J. 1981; 245, 1080.
[4] R. S. Fraser, W. H. Walker, Effect of specular reflection at the ground on light scattered from a Raleigh atmosphere, JOSA 1968;
58, 636.
[5] J. V. Dave, Technical Report Contract No.Nasa-21680.NASA-Goddard Space Flight Centre, Greenbelt, MD, 1972.
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Ocean. 1973; 3, 353.
[7] E. Raschke, Multiple Scattering Calculations of the transfer of solar radiation in an atmosphere-ocean system. Beit. Phys. Atmos
1972; 45, 1.

Abstract: The present analysis is made to investigate the effects of heat source and thermal diffusion on an unsteady free convection flow along a porous vertical plate in a rotating system. The plate is subjected to constant heat and mass flux also. The problem is solved analytically and expressions for velocity. Energy and temperature profiles, skin friction and Nusselt number are obtained. The effects of different parameter entered in the problem are discussed on the primary and secondary velocities, temperature and concentration distributions, primary and secondary skin frictions and Nusselt number with the help of tables and graphs.

Key Words: Diffusion, Heat Source, Porous Medium, Slip Velocity, Unsteady Flow.

[1]. V. M. Soundalgekar, N. V.Vighnesam and I. Pop, Combined free and forced convection flow past a vertical porous plate, Int. J. Energy Research 5, 1981, 215-226.
[2]. A. Raptis and C. Predikis, Mass transfer and free convection flow through a porous medium, Int. J. Energy Research, 11 1987, 423-428.
[3]. A. S. Mohammad, Free and forced convection boundary layer flow through a porous medium with large suction", Int. J. Energy Research, 17 (1993), 1-7.
[4]. K. A. Helmy, MHD unsteady free convection flow past a vertical porous plate, ZAMM, J. applied mathematics and mechanics, 78 1998, 255-270.
[5]. N. C. Jain and P.Gupta, Hall effects on unsteady free convection slip flow in a rotating fluid along a porous vertical surface bounded by porous medium, Int. J. Applied Mechanics and Engineering, 12 2007, 609-627.
[6]. B. C. Chandrasekhara and P.M.S. Namboodiri, Influence of variable permeability on combined free and forced convection about inclined surface in porous, Int. J. Heat mass transfer, 28 1985, 199-206.
[7]. Y. Joshi and B. Gebhart, Mixed convection in porous medium adjacent to a vertical uniform heat flux surface, Int. J. Heat mass transfer, 28 1985, 1783-1786.
[8]. F. C.Lai and F.A. Kulacki, The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium, Int. J. Heat mass transfer, 33, 1990, 1028-1031.
[9]. A. Raptis and N.G. Kafousias, N.G., "Free convection and mass transfer flow through a porous medium under the action of magnetic field", Rev. Roun. Sci. Tech. Mec. Appl. 27 (1982), 37-43.
[10]. A. Bejan and K.R. Khair, Effect of thermal diffusion on an oscillatory MHD convective flow with mass transfer through a porous medium. Int. J. Heat mass transfer, 28 1985, 902-918.

Abstract: In this paper, the concepts of sequences and series of complement normalized fuzzy numbers are introduced in terms of 𝛾-level, so that some properties and characterizations are presented, and some convergence theorems are proved.

Keywords: Fuzzy Numbers, Fuzzy Convergences, Fuzzy Series.

[1] Altin, Y., Et, M. and Basarir, M., On some generalized difference sequences of fuzzy numbers, Kuwait J. Sci. Eng. 34 (2007) 1–14.
[2] Aytar, S., Statistical limit points of sequences of fuzzy numbers, Inf. Sciences 165 (2004) 129-138.
[3] Basarir, M., and Mursaleen, M., Some differemce sequence spaces of fuzzy numbers, J. of Fuzzy Math., 12 (2004) 1-6.
[4] Chang, S. S. L., Zadeh, L. A., Fuzzy mappings and control, IEEE Trans. Syst., Man and Cyber., SMC-2, (1972) 30-34.
[5] Cheng, C. H., A new approach for ranking fuzzy numbers by distance method, Fuzzy Sets and Systems 95 (1998) 307-317.
[6] Diamond, P., Fuzzy least squares, Information Sciences 46 (1988) 141-157.
[7] Dubois, D. and Prade, H., Operations on fuzzy numbers, Int. J. Systems Sci. 9 (1978) 613–626.
[8] Fang, J. X. and Huang, H., On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets and Systems 147 (2004) 417–435.
[9] Kaufmann, A., and Gupta, M. M., Introduction to Fuzzy Arithmetic: Theory and Applications, Van Nostand Reinhold, NY, 1991.
[10] Kavikumar, J., Khamis, A. B., and Kandasamy, R., Fuzzy entire sequence spaces, Int. J. of Math. and Math. Sci. (2007), doi: 10.1155/2007/58368.

Abstract: The world is fast becoming a global village where national boundaries which had hitherto limited human interactions are fast disappearing. There is now integration among the countries and trade is moving from transactions in goods and commodities to include the commercialization of education, especially post-secondary school or higher education.
Key Words: Globalization, Cross-border, WTO, GATS, Open and Distance Education

[1]. Akinyele, R.T. (2004). Crossborder Provision of Higher Education in Africa: Opportunities, Challenges and Potential Impact. Paper presented at the African University Day Celebration, University of Lagos. 12 Nov., 2004.
[2]. Daniel, J.S. Mugridge, I., Snowden, B.L. and Smith, W.A.S. (1986). Cooperation in Distance Education and Open Learning. http://www.uni-oldenburg.de/zef/cde/policy/DANIEL.DOC.
[3]. Daniel, J.S., Kanwar, A. and Uvalic-Trumbic, S. (2005). Who‟s afraid of Crossborder Higher Education? A developing World Perspective. Higher Education Digest, Issue 52 Supplement, Cheri, London, pp. 1-8.
[4]. Daniel, J., Kanwar, A., Uvalic-Trumbic, S. and Varoglu, Z. (2006). Collaboration in the Time of Competition. Open and Distance Education in Global Environment (Opportunities for Collaboration), pp. 1-13.
[5]. E.I. (Education International Conference) (2002). 3rd. The Impact of Commercialization on Post-Secondary Education: Document prepared for Education International Higher Education and Research Conference. Montreal: March 14-16, 2002.
[6]. Fagbamiye, E.O. (2004). Strategies for Addressing the Challenges of Crossborder Provision of Higher Education, With or Without WTO/GATS Regime. A lead paper delivered at the African University Day Celebration at the University of Lagos on November 12, 2004.
[7]. Jegede, O. (2000). Evolving a National Policy on Distance Education: An Agenda for Implementation. Education Today, Vol.8 (3) 14-29, December, 2000.
[8]. Knight, Jane (2003). Elements and Rules of TATS. Crossborder Education in a Trade Environment, pp. 12-15.
[9]. Knight, Jane (2003). "Updating the Definition of Internationalization‟. International Higher Education. No. 33 Fall 2003 cited in www.bc.educ/bc_org/avp/soe/cihe/rewos/atters31/text002.htm.17k.
[10]. OECD, (2000). Education at a Glance, Paris.