Volume 89, Issue 2
May 1980, pages 75-132
pp 75-93 May 1980
In this paper, we develop a cipher system based on finite field transforms. In this system, blocks of the input character-string are enciphered using congruence or modular transformations with respect to either primes or irreducible polynomials over a finite field. The polynomial system is shown to be clearly superior to the prime system for conventional cryptographic work.
pp 95-100 May 1980
Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation.
pp 101-102 May 1980
In this note, the fallacy in the method given by Sharma and Swarup, in their paper on time minimising transportation problem, to determine the setShkof all nonbasic cells which when introduced into the basis, either would eliminate a given basic cell (h, k) from the basis or reduce the amountxhkis pointed out.
pp 103-112 May 1980
The MHD Couette flow of a viscous stratified fluid of large electrical conductivity with suction and injection at the plane boundaries is studied when the plane boundaries are maintained at different temperatures. The Oseen type governing equations are formulated using the method suggested by Greenspan for stratified fluids. Introducing the similarity variables, the linearised equations are solved to obtain the velocity and temperature distributions. The results show that the behaviour of velocity and temperature in fluids of large conductivity is different from the behaviour of velocity and temperature for fluids of finite conductivity. The effect of the magnetic field on the load capacity is investigated for the case when the width of the channel is small.
pp 113-123 May 1980
The problem of forced convection heat transfer over a semi-infinite flat plate is treated by the method of series truncation, so as to yield results valid from leading edge to far downstream (0 < -R0< ∞). Results are presented for Prandtl number Pr = 0.1, 0.7, and 10. It is found that the effect of leading edge on heat transfer is smaller than on skin friction.
pp 125-132 May 1980
The generalising dispersion equations of flow through porous media have been investigated. The Laplace transform has been applied to obtain the solution to dispersion problem as a result of adsorption. The generalised closed form solution for dispersion has been presented and the different types of variations in concentration have been graphically discussed. When the steady state occurs, the concentration becomes constant but for small value of time (say 0.5) the concentration tends to zero as distance increases.