RP-Department of Mathematics
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Item The method of the false transient for the solution of coupled elliptic equations(Elsevier, 1973-08-04) Gatheri, F. K.A method for the numerical solution of a system of coupled, nonlinear elliptic partial differential equations is described, and the application of the method to the equations governing steady, laminar natural convection is presented. The essential feature of the method is the conversion of the equations to a parabolic form by the addition of false time derivatives, thus, enabling a marching solution, equivalent to a single iterative procedure, to be used. The method is evaluated by applying it to a well known two-dimensional problem and some examples of its use in three dimensions are given.Item The applicability of mathematics(Taylor & Francis, 1984) Uppal, S. M.Item Hall Effects on the Oscillatory MHD Flow through Porous Medium in a Rotating Fluid(Springer-Verlag, 1988) Ram, P. C.Taking Hall currents into account the unsteady magnetohydrodynamical flow through a porous medium bounded by an infinite vertical limiting surface in a rotating frame of reference is theoretically investigated when a strong magnetic field is imposed in a plane which makes an angle a with the normal to the plate. The influence of Hall currents on the velocity and temperature distribution are shown graphically for various values of α.Item Unsteady MHD Free-convective Flow through a Porous Medium with Hall Currents(Kluwer Academic Publishers, 1988) Ram, P. C.The two-dimensional unsteady free-convective flow through a porous medium bounded by an infinite vertical plate for an incompressible viscous and electrically conducting fluid is considered, when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle α to the vertical direction. The effects of Hall currents on the flows are studied for various values of α.Item Hall Effects on Hydromagnetic Convection Flow in a Rotating Fluid(Kluwer Academic Publishers, 1989) Ram, P. C.An analysis of Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically-conducting liquid passed an infinite vertical porous plate in a rotating frame of reference is carried out when a strong magnetic field is imposed in a plane which makes an angle α with the normal to the plate. The expressions for the mean velocity, mean temperature in the boundary layer, and the mean skin-friction, the mean rate of heat transfer on the plate are derived. The influence of Hall currents on the flow is studied for various values of α.Item Unsteady MHD Free-convective flow of a Viscous Rotating Fluid through a Porous Medium with Constant Heat Flux and Heat Generation(Kluwer Academic Publishers, 1989) Ram, P. C.A theoretical analysis of unsteady MHD convective flow in a rotating frame of reference is presented when a viscous, incompressible, heat generating, and electrically-conducting fluid flows through a porous medium occupying a semi-infinite region of space bounded by an infinite vertical porous plate. A strong magnetic field is imposed in a plane which makes an angle α with the normal to the plate and the fluid is subjected to a normal suction velocity while the heat flux at the plate is constant. An analytical solution of the problem is obtained and the effects of Hall current on the flows are studied for various values of α.Item The spectrum of the Cesàro operator on c0(c0)(Cambridge University Press, 1989-01) Okutoyi, J. I.; Thorpe, B.In a recent paper [6], the spectrum of the Cesàro operator C on c0 (the space of null sequences of complex numbers with the sup norm) was obtained by finding the eigenvalues of the adjoinoperator on and showing that the operator (C–λI)−1 lies in B(c0) for all λ outside the closure of this set of eigenvalues. In this paper we apply a similar method to find the spectrum of the two-dimensional Cesàro operator on a space of double sequences c0(c0) (defined in §2). We shall introduce a simplification to the proof in [6] by observing that (C – λI)−1, when it exists, is a Hausdorff summability method (see page 288 of [11] for the single variable case on the space of convergent sequences c), and the crux of our proof is to show that the moment constant associated with the method (C – λI)−1 is regular for the space c0(c0) and the set of λ under consideration. It turns out that c0(c0) c0 c0 (see page 237 of [7]) and that the two-dimensional Cesàro operator on c0(c0) is the tensor product C C of the Cesàro operator C on c0. Thus our result gives a direct proof that the spectrum σ(C C) equals σ(C)σ(C), which is a special case of the result of Schechter in [8].Item A Unified Presentation of the Voigt Functions(Kluwer Academic Publishers, 1990) Siddiqui, A.In the present paper, we have given a generalization of a unified study of the Voigt functionsK(x, y) andL(x, y) obtained by Srivastava and Miller (1987; Vol. 135, pp. 111–118) which play an important role in several diverse fields of physics-such as astrophysical spectroscopy and the theory of neutron reactions. Explicit expressions for these functions are given in terms of relatively more familiar special functions of one and two variables; indeed, each of these representations will naturally lead to various other needed properties of the Voigt functions.Item On the spectrum(Cambridge University Press, 1990) Okutoyi, J. I.Item Heat and Mass Transfer on MHD Heat Generating Flow through a Porous Medium in a Rotating Fluid(Kluwer Academic Publishers, 1990) Ram, P. C.The problem of the free-convection flow of a viscous heat generating fluid through porous media in a rotating frame of reference is considered for the case when a strong magnetic field is imposed in a direction which is perpendicular to the free-stream and makes an angle α to the vertical direction. Analytical expressions for the velocity field and temperature are given, and the influences of the various parameters on the velocity field are discussed.Item Finite-difference Analysis of the MHD Stokes Problem for a Vertical Plate with Hall and Ion-slip Currents(Kluwer Academic Publishers, 1991) Ram, P. C.An explicit finite-difference method is employed to study the MHD free convection heat generating fluid past an impulsively started vertical infinite plate when a strong magnetic field is applied perpendicular to the plate. The velocity and temperature profiles are shown on graphs and the results are discussed in terms of the non-dimensional parameters β e (Hall parameter), β i (ionslip parameter), δ (heat source parameter), and Gr (Grashof number).Item MHD Convective Flow in a Rotating Fluid with Hall and Ion-slip Currents(Springer-Verlag, 1991) Ram, P. C.Taking Hall and Ion-slip currents into account the steady magnetohydrodynamic convective flow of a partially ionized gas past an infinite vertical porous plate in a rotating frame of reference is investigated theoretically. A strong magnetic field of uniform strength is applied perpendicular to the plate and the fluid is subjected to a normal suction velocity while the heat flux at the plate is constant. An analytic solution of the problem is obtained and the effect of Hall and ion-slip currents, as well as the other parameter entering into the problem, are discussed and shown graphically.Item Wall Temperature Oscillation on Convection Flow in a Rotating Fluid with Hall and Ion-slip Currents(Kluwer Academic Publishers, 1991) Ram, P. C.An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of β e (the Hall parameter), β i (the ion-slip parameter),E r (rotation parameter), and Ω have been discussed and shown graphically.Item Effects of hall current on the oscillatory MHD free-convection flow(Kluwer Academic Publishers, 1992) Ram, P. C.; Singh, S. S.; Bitok, J. K.An analysis of Hall currents and heat generation on the free-convection flow resulting from the combined effects of thermal and mass diffusion is considered. Analytical expressions for the transient velocity and transient temperature field are derived. The influence of the different parameters entering into the problem are discussed by graphs.Item A Note on Generalized Köthe-toeplitz Duals(Kluwer Academic Publishers, 1992) Okutoyi, J. I.Item Some Representations of Unified Voigt Functions Ω η, ν, λ μ (x,y)(Kluwer Academic Publishers, 1992) Siddiqui, A.; Uppal, S. M.This paper aims at some representation of unified Voigt functions which play a rather important role in several diverse fields of physics such as astrophysical spectroscopy and the theory of neutron reactions. We derive several representations of Ω η, ν, λ μ (x,y) in terms of series and integrals which are especially useful in situations when the parameters μ, η, ν, and λ take on particular values. Since it provides an interesting and useful unification of numerous families of special functions in one and more variables; indeed, each of these representations will naturally lead to various other needed properties of these functions.Item On the convexity of stampfli's numerical range(Cambridge University Press, 1996) Agure, J.O .This paper investigates a certain type of numerical range introduced by Stampfli. In particular, we investigate the convexity of this set of elements of operators on Hilbert spaces and its relationship to the algebra numerical range implemented by elements of a W*-algebraItem Nonparametric regression method for estimating the error variance in unistage sampling(Faculty of Science Kenyatta University, 2000) Otieno, Romanus Odhiambo; Mwalili, Tobias MbithiNonparametric regression provides computationally intensive estimation of unknown finite population quantities. Such estimation can be more robust than inference tied to model based inference. A nonparametric procedure for estimating error variance is suggested. An empirical example is given to illustrate the performance of the derived estimator vis-a-vis the currently popular variance estimator in model based surveys.Item A Bayesian Test for Equality of Scale Parameters of Several Exponential Distributions(2002) Odongo, L. O.; Samanta, M.This article develops a Bayesian test for equality of scale parameters of several exponential distributions. The null distribution of the test statistic is approximated by the chi-square distribution using heuristic reasoning in conjunction with the Wilson-Hilferty transfomation for the chi-square random variable. The accuracy of the chi-square approximation of the test statistic and the modified likelihood ratio statistic is examined and their powers compared using Monte Carlo simulation. The proposed test is found to be comparable to Bartlett's modified likelihood ratio test in terms of accuracy and power. A numerical example is included to illustrate the applications of these testsItem Normal Forms for Coupled Takens-Bogdanov Systems(Taylor & Francis, 2004) Malonza, D. M.The set of systems of differential equations that are in normal form with respect to a particular linear part has the structure of a module of equivariants, and is best described by giving a Stanley decomposition of that module. In this paper Groebner basis methods are used to determine a Groebner basis for the ideal of relations and a Stanley decomposition for the ring of invariants that arise in normal forms for Takens-Bogdanov systems. An algorithm developed by Murdock, is then used to produce a Stanley decomposition for the (normal form module) module of the equivariants from the Stanley decomposition for the ring of invariants.