Volume 87, Issue 9
September 1978, pages 161-263
pp 161-168 September 1978
An algorithm that uses integer arithmetic is suggested. It transforms anm ×n matrix to a diagonal form (of the structure of Smith Normal Form). Then it computes a reflexive generalized inverse of the matrix exactly and hence solves a system of linear equations error-free.
pp 169-175 September 1978
On a class of nonlinear integral equations
In this paper we consider abstract equations of the typeK_{ν}ν +ν =w_{0}, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K_{v} :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations of the typeν(s)+ν(s)∫_{0}^{1}k(s,t)ν(t)dt =W_{0}(s) in the spaceL^{2} [0,1].
pp 177-179 September 1978
It is proved that a high subgroup of a large subgroup is closed in a high subgroup of the group itself. Also a necessary and sufficient condition for a subgroup to be a pureabsolute summand is obtained.
pp 181-188 September 1978
A cylindrically symmetric universe in general relativity
A cylindrically symmetric universe with two degrees of freedom which is of Petrov Type I degenerate, has been derived. Various physical and geometrical properties of the model have also been discussed.
pp 189-200 September 1978
In this paper stability and asymptotic behaviour of solutions of the integrodifferential system$$x'\left( t \right) = A\left( t \right)x\left( t \right) + f\left( {t,x\left( t \right),\int_{t_0 }^t {k\left( {t,s,x\left( s \right)} \right)ds} } \right) + g\left( {t,x\left( t \right)} \right)$$ in a Banach space is related to that of the integrodifferential system$$y'\left( t \right) = A\left( t \right)y\left( t \right) + f\left( {t,y\left( t \right),\int_{t_0 }^t {k\left( {t,s,y\left( s \right)} \right)ds} } \right)$$ in a Banach space. The results obtained constitute a generalization of similar results for ordinary differential equations in a Banach space, which motivate the approach and proofs.
pp 201-207 September 1978
On some fundamental integrodifferential inequalities and their discrete analogues
Some fundamental integrodifferential inequalities and their discrete analogues which can be used in the analysis of a class of integrodifferential and summary difference equations as handy tools are discussed.
pp 209-217 September 1978
Heat transfer for laminar flow through parallel porous disks of different permeability
The problem of temperature distribution and heat transfer for laminar flow through two parallel porous disks of different permeability, has been investigated when the flow is entirely due to injection and/or suction at the two disks. Viscous dissipation terms have been included in the energy equation and the injection and/or suction velocities at the two disks are assumed to be small. The boundaries are kept at constant temperatures. The variation of temperature and Nusselt numbers at the two disks has been graphically depicted for various values of the injection and suction velocities.
pp 219-225 September 1978
Magnetohydrodynamic flow of a rarefied gas near an accelerated porous plate
An investigation is made of the flow of an electrically conducting rarefied gas due to the time-varying motion of an infinite porous plate, the gas being permeated by a transverse magnetic field. The suction is taken to be a constant and the magnetic lines of force are taken to be fixed relative to the fluid. The effects of magnetic field, rarefaction parameter, suction parameter are shown by means of some tables. The expressions of the skin friction for the two particular cases have also been obtained.
pp 227-236 September 1978
Steady flow and heat transfer in a visco-elastic fluid between two coaxial rotating disks
Rama Sankar Rath Surendra Nath Bastia
Flow and heat transfer of an elastico-viscous liquid between two parallel uniformly porous disks rotating about a common axis, are studied by perturbation technique. It is seen that for such a fluid, drag increases with suction and decreases with injection, while the rate of heat transfer increases in the presence of either suction or injection.
pp 237-245 September 1978
The analysis of convective flow and heat transfer of a viscous heat generating fluid past a uniformly moving, infinite, vertical, porous plate has been made systematically with a view to throw adequate light on the effects of the plate-motion and the presence of heat generation/absorption on the flow and heat transfer characteristics. The equations of conservation of momentum and energy which govern the flow and heat transfer of the said problem have been solved numerically by the method of Runge-Kutta-Gill. The numerical results thus obtained for the flow and heat transfer characteristics have revealed many an interesting behaviour, of the skin friction and the rate of heat transfer coefficient at the plate.
pp 247-252 September 1978
Point force in a stratified fluid in a cylinder under a magnetic field
K N Venkatasiva Murthy R Seetharamaswamy
The flow induced by a body moving in an inviscid incompressible density stratified fluid in an infinite circular cylinder under the influence of a uniform axial magnetic field is studied using the method of replacing the body by an isolated point force. This method was adopted by Childress and others in discussing the body effects in a viscous fluid. The solution is obtained using the Fourier transformation and the Lighthill’s radiation condition. The cases of weak and strong magnetic fields are discussed.
pp 253-263 September 1978
Aerodynamic noise from wave-turbulence interaction
In order to estimate the acoustic energy scattered when a unit volume of free turbulence, such as in free jets, interacts with a plane steady sound wave, theoretical expressions are derived for two simple models of turbulence: eddy model and isotropic model. The effect of convection by mean motion of the energy-bearing eddies on the incident sound wave and on the sound generated from wave-turbulence interaction is taken into account. Finally, by means of a representative calculation, the directionality pattern and Mach number dependence of the noise so generated is discussed.
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