Volume 106, Issue 1
February 1996, pages 1-103
pp 1-11 February 1996
We give necessary and sufficient conditions for sequences in the space AP(R) of continuous almost periodic functions on the real line to converge in the weak topology. The abstract results are illustrated by a number of examples which show that weak convergence seems to be a rare phenomenon. We also characterize the weakly compact subsets in AP(R). In particular, earlier statements made in the monograph by Dunford and Schwartz are refined and completed. We close with some open problems.
pp 13-38 February 1996
We study the absolute Euler summability problem of some series associated with Fourier series and its conjugate series generalizing some known results in the literature. Also, it is shown that absolute Euler summability of rth derived Fourier series and rth derived conjugate series can be ensured under local conditions.
pp 39-51 February 1996
In this paper an attempt has been made to give a very simple method of extending certain results of Ramanujan, Evans and Stanton on obtaining the asymptotic behaviour of a class of zero-balanced hypergeometric series. A more recent result of Saigo and Srivastava has also been used to obtain a Ramanujan type of result for a partial sum of a zero-balanced4F3 (1) and similar other partial series of higher order.
pp 53-64 February 1996
The present paper is in continuation to our recent paper  in these proceedings. Therein, three composition formulae for a general class of fractional integral operators had been established. In this paper, we develop the Mellin transforms and their inversions, the Mellin convolutions, the associated Parseval-Goldstein theorem and the images of the multivariableH-function together with applications for these operators. In all, seven theorems and two corollaries (involving the Konhauser biorthogonal polynomials and the Jacobi polynomials) have been established in this paper. On account of the most general nature of the polynomials Snm[x] and the multivariableH-function whose product form the kernels of our operators, a large number of (new and known) interesting results involving simpler polynomials and special functions (involving one or more variables) obtained by several authors and hitherto lying scattered in the literature follow as special cases of our findings. We give here exact references to the results (in essence) of seven research papers which follow as simple special cases of our theorems.
pp 65-68 February 1996
In this paper we have shown that one can obtain a curve, with prescribed maximaminima, as a graph of a polynomial function. The proof involves elementary topology.
pp 69-77 February 1996
Understanding Karmarkar’s algorithm is both desirable and necessary for its efficient implementation, for further improvement and for carrying out complexity analysis. In this report an algorithm based on the concept of angular projection matrix, to solve linear programming problems is derived. Surprisingly, this algorithm coincides with the affine version of Karmarkar’s algorithm.
pp 79-90 February 1996
We show that the separating subspaces for the component operators of a densely valued homomorphism pair into anH*-triple system are contained in the annihilator ideal. Accordingly, the continuity of densely valued homomorphisms into H*-algebras and H*-triple systems with zero annihilator follows.
pp 91-103 February 1996
This paper concerns with the problem of determining the anti-plane dynamic stress distributions around four coplanar finite length Griffith cracks moving steadily with constant velocity in an infinitely long finite width strip. The two-dimensional Fourier transforms have been used to reduce the mixed boundary value problem to the solution of five integral equations. These integral equations have been solved using the finite Hilbert transform technique to obtain the analytic form of crack opening displacement and stress intensity factors. Numerical results have also been depicted graphically.