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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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.
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[5] Popoviciu,T. (1935). Sur l'approximation des fonctions convex-es d' ordre supérierur. Mathematica (cluj) 10,49-54.
[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,

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[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.
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[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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Abstract: In this paper, we study the invariant set of dynamical systems in which attractor and non-attractor sets exist. We aim to carve out a small section of the theory of chaotic dynamical systems – that of attractors – and outline its fundamental concepts from a computational mathematics perspective. The motivation for this paper is primarily to define what an attractor is and to clarify what distinguishes its various types (non-strange, strange non-chaotic, and strange chaotic). We discuss the Hénon and Lorenz attractors as important examples of this type of chaotic system.
Keywords: Attractor, Basin of attractor, Chaos, Strange

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Abstract: Modeling of the stress accumulation process during quasi-static aseismic period in the presence of non planar strike-slip fault in seismically active regions has been considered. A viscoelastic half space was taken to represent the lithosphere-asthenosphere system and forces arising out some tectonic processes e.g. mantle convection and the resulting driving forces, were considered to be the main reason for the accumulation of stress in the lithosphere near the earthquake faults. When the accumulated stresses exceed the frictional and cohesive forces across the fault, a sudden and/or creeping movement across the fault occurs. In this paper the pattern of stress accumulation near the faults and the surface shear strain during the aseismic period have been considered using suitable mathematical techniques including integral transforms and Green's functions. A detail study may lead to an estimation of the time-span between two consecutive seismic events. It is expected that such studies may be useful in earthquake prediction.
Key Words- Aseismic, Earthquake prediction, Stress Accumulation, Strike-slip faults, Viscoelastic.

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Abstract: In this paper, we define and study the concepts of bounded closed complex complement normalized fuzzy numbers, and generalized rectangular valued bounded closed complex complement normalized fuzzy numbers, so that some basic properties and some characterizations are presented. Some important theorems of a fuzzy derivative for fuzzy complex functions which map a regular complex numbers into bounded closed complex complement normalized fuzzy numbers are proved. All this may be a foundation for researching fuzzy complex analysis.
Keywords− Fuzzy numbers, Fuzzy complex numbers, Fuzzy derivatives.

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Abstract: must have knowledge of the practical applications of a lgebra and how it is applied. Due to the fact that mathematics is used in day to day life, we may now examine the ideas of algebra and the applications of algebra in day to day life. At this point in time, we have developed a modest division of the objects that are carried about in a bag when shopping. When we eventually get to the algebra part of pre algebra, it's called Basic Algebra. The ideas that are presented here will be used in every subsequent math course that you enroll in after this one. We'll ge.....

Keywords Variables, Equation, Variable Exponent Algebra

[1]. Adhikari, M.R., Adhikari, A.: Groups, Rings and Modules with Applications, 2nd edn. Universities Press, Hyderabad ( 2012
[2]. Adhikari, M.R., Adhikari, A.: Text Book of Linear Algebra: An Introduction to Modern Algebra. Allied Publishers, New Delhi
2012
[3]. Bell, E.T.: Men of Mathematics. Simon and Schuster, New York 2012
[4]. Birkhoff, G., Mac Lane, S.: A Survey of Modern Algebra. Universities Press, Andhra Pradesh ( 2012
[5]. Hazewinkel, M., Gubareni, N., and Kirichenko, V.V.: Algebras, Rings and Modules, Vol. 1. Springer, New Delhi ( 2012

Abstract: The research article is "The application of  and μ- pentajection operators". In this chapter in the theorem I, we have proved that each - pentajection operator on a topological linear space can be summing operator. In the theorem II We have proved that each summing operator can be a - pentajection operator. In the theorem - III we have proved that each μ- pentajection operator on a locally convex space can be a paracompact operator and a precompactly summing operator. In the theorem IV we have proved that each precompactly summing operator on a locally convex space can be a μ - pentajection operator. In the theorem V we have proved that for each μ- pentajection operator on a locally convex space there can exist that locally convex space as the nuclear locally convex space.......

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