iosr-Jm   Volume-2 ~ Issue-5

Abstract : Many activities and phenomena on earth which are of interest to man and require to be studied are not quantitative in nature, they are rather qualitative. Sometimes their contributions, as independent variables, in a multiple regression, to variations in a specified quantitative dependent variable and to characterize them are of interest. Usually dummy variables with equal spacing are used in generating the design matrix despite its uninterpretable coefficients. Here a cumulatively coded design matrix is proposed and the coefficients are interpreted. This method is applied to an illustrative example, alongside two other possible methods, to demonstrate its applicability, and the proposed method showed a comparatively good performance with an additional advantage of interpretable coefficients which is very useful for practical purposes.
Keywords:cumulative, dummy, independent, ordinal, qualitative

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[4] M. LYONS (1971), Techniques for using ordinal measures in regression and path analysis, in Herbert Costner (ed.)( Sociological Methods , Josey Bass Publishers, San Francisco).

Abstract:We have tested the convergence of the Generalized Stancu's Polynomial 𝑅𝛼𝑛 𝑓,𝑥 and have also tested the degree of approximation of Lebesgue integrable functions by 𝑅𝛼𝑛 𝑓,𝑥

[1] Anwar Habib (1981). On the degree of approximation of functions by certain new Bernstein type Polynomials. Indian J. pure Math. , 12(7):882-888.
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[3] Kantorovitch, L.A.(1930). Sur certains développments suivant lés pôlynômes dé la forme S.Bernstein I,II. C.R. Acad. Sci. URSS,20,563-68,595-600.
[4] Lorentz, G.G. (1955). Bernstein Polynomials. University of Toronto Press, Toronto
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[6] Stancu, D.D. : Approximation of function by a new class of linear Polynomial operator. Rev. Roum. Math. Pures at Appl. No. 8, pp.1173-1194. Bucharest 1968

Abstract: The problem of MHD flow and heat transfer in a Newtonian viscous incompressible fluid over a stretching sheet with temperature gradient dependent heat sink/source and radiation is investigated. The governing partial differential equations are converted into ordinary differential equations by similarity transformation technique . The effects of viscous dissipation, work due to deformation, thermal radiation are considered in the energy equation and the variations of dimensionless surface temperature as well as the heat transfer characteristics with various values of non-dimensional parameters like Prandtl number, suction parameter , radiation parameter, temperature gradient dependent heat sink parameter are graphed and tabulated. The heating process of the type i ) the sheet with prescribed surface temperature (PST case) is studied.
Key words; MHD, viscous fluid, stretching sheet, radiation parameter, temperature gradient dependent heat sink,

[1] A. Rapits, C. Perdikis, Viscoelastic Flow by the Presence of Radiation. ZAMM, 78 (1998), 277-279.
[2] A. Raptis, Technical note, Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation. Int. J. Heat Mass Transfer, 41 (1998.), 2865-2866.
[3] A. Raptis, Radiation and Viscoelastic Flow. Int. Comm. Heat Mass. Transfer, 26, (1999), 889-895.
[4] A. Raptis, C. Perdikis, H. S. Takhar, Effect of Thermal Radiation on MHD Flow. Appl. Math. Comput. 153 (2004), 645-649.
[5] Ajay Kumar Singh., Heat transfer and boundary layer flow past a stretching porous wall with temperature gradient dependent heat sink. J.E.H.M.T., 28 (2006), 109-125.
[6] Angirasa, D., Peterson, G.P., and Pop, I., Combined Heat Mass Transfer by Convection in a Saturated Thermally Stratified Porous Medium. Numerical Heat Transfer, A31 (1997), 255-271.
[7] Anjalidevi, S.P., and Thiyagarajan, M., Nonlinear Hydromagnetic Flow and Heat Transfer Over a Surface Stretching with a Power Law Velocity, Heat and Mass Transfer, 38 (2002), 723-726.
[8] B.S.Dandapat, A.S. Gupta, Flow and Heat Transfer in a Visco-elastic Fluid over a Stretching Sheet.Int. J. Non-Linear Mech, 24 (1989), 215-219.
[9] Hong, J. T., and Tien, C.L., Analysis of Thermal Dispersion, Effect on Vertical Plate Natural Convection in Porous Media. International Journal of Heat Mass Transfer, 30 (1987), 143-150.
[10] Khan, S.K., Abel, M.S., and Sonth, R.M., Visco-elastic MHD Flow Heat and Mass Transfer Over a Stretching Sheet with Dissipation of Energy and Stress Work. Heat and Mass Transfer, 40 (2004), 47-57.

../papers/vol2-issue5/D0252024.pdf

Paper Type	:	Research Paper
Title	:	Fractional Integral Operators Involving the Generalized Riemann Zeta Function with a Product of Certain Special Functions
Country	:	India
Authors	:	V.B.L. Chaurasia, Vinod Gill
	:	10.9790/5728-0252024

Abstract:In this paper, we study two most general integral operators whose kernels are the product of the generalized Riemann Zeta function, a general class of polynomials and two multivariable H-function. First, we established the Mellin-transform of these operators. Then, due to general nature of the kernel, we can obtain a large number of Mellin-transforms involving product of several useful special functions.
Key Words: Fractional Integral Operators, Generalized Riemann Zeta function, General class of polynomials, Multivariable H-function, Mellin transform.
AMS Subject Classification: primary 26A33, 44A10, secondary 33C60

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