Volume 96, Issue 2
November 1987, pages 71-139
pp 71-73 November 1987
In a recent paper, Srinivasan and Prasad criticize certain approximations that were made in early work on shock dynamics. The criticism however is based on certain misinterpretations. This short note offers the correct interpretations and explains the issues.
pp 75-85 November 1987
We introduce the concept of completely closed operators in Banach spaces and then obtain the existence of random solutions of operator equations involving such operators. As simple corollaries we obtain the existence theorems for random operator equations involving monotone operators as well as operators of type (M).
pp 87-102 November 1987
By employing a new embedding technique, a short-time analytical solution for the melting of a long cylinder due to an axisymmetric hot spot is presented in this paper. The melt is removed as soon as it is formed. The initial propagation of the melt along the interior of the cylinder exhibits a well-known behaviour. However, the melt propagation along the surface of the cylinder is of a new type and depending on the applied flux whether it is the continuation of the pre-melting flux or diferent, the initial propagation of the melt along the surface is proportional tot1/2 ort1/4, wheret is the dimensionless time. The melt propagation is much faster along the surface of the cylinder than towards the interior.
pp 103-118 November 1987
Following the work of Carter on nonlinear perfectly elastic solid and perfect nonlinearly polarizable nonconducting solid, we have constructed models whose free gravitational field is of Petrov typeD: (i) in inertial reference frame (IRF), (ii) with pure expansion and (iii) with pure rotation with the assumption that the flow field is expressible in terms of two real null vectors of the Newman-Penrose (N-P) tetrad. By using the strain variation equation, the necessary and sufficient conditions on the dynamical variables are obtained in Newman-Penrose version. We observe that the initial pressure tensor depends on the polarizable and electromagnetic properties of the material. Further, we conclude that there does not exist such a material with pure expansion but there exists such a material moving rigidly with or without rotation. We obtain the Hawking energy conditions and invariants for this material in IRF.
pp 119-124 November 1987
L Weisner's group theoretic method has been introduced in the study of special function. In this paper we obtain two differential operators, one of which simultaneously raises the index and lowers the parameter of modified Gegenbauer polynomialsCnv+n (x) by unity and the other acts onCnv+n(x) in the reversed way by suitable interpretation to the indexn and the parameterv ofCnv+n(x). We have also found out the extended form of the groups generated by the operatorsAij(i,j=1,2). We have also derived some novel generating functions ofCnv+n(x) from which several special generating functions can be easily derived.
pp 125-130 November 1987
A theorem which reveals an interesting relationship between originals of related functions inH-function transform and Meijer Bessel function transforms is established. Another theorem interconnecting the two Meijer Bessel function transforms is also obtained. These theorems seem to be capable of unifying and extending a large number of results obtained by earlier workers. Finally, we evaluate an integral by way of illustration.
pp 131-139 November 1987
The purpose of this paper is to discuss focal points of submanifolds of naturally reductive compact Riemannian homogeneous spaces. Focal points have been studied by other workers [1, 4, 7]. In this paper we have estimated location of focal points along geodesic and obtained a condition under which a point is a focal point along geodesic.