The L(r, t) Summability Transform

Abstract

In a recent article Cheney and Sharma (1) studied the linear operator Pn defined bywherehere Lj(n)(t) denotes the Laguerre polynomial of degree j. Cheney and Sharma proved that if f is continuous on [0, 1], then Pn(f, x) converges uniformly to f(x) on [0, a] where 0 < a < 1.

Changes in cattle tick control practices in south eastern Queensland from 1977 to 1982

“…A much higher percentage (22.9%) of owners of crossbred Zebu cattle dipped in spring-summer only than in autumn only (2.5%). Both times are appropriate for crossbred Zebu cattle but it seems that the widely held opinion, that autumn is a more convenient time for dipping than spring (Powell and Reid 1982), may not be correct in practice.…”

Effect of imidocarb dipropionate prophylaxis on the infectivity and immunogenicity of a Babesia bovis vaccine in cattle

“…This prophylactic effect of imidocarb, which allowed immunising B. bovb infections to become established in cattle without causing adverse clinical signs, encouraged its use in conjunction with vaccination. One procedure adopted was treatment with imidocarb followed 3 to 4 weeks later by vaccination with B. bovb vaccine (De Vos 1979;Timms et a1 1981;Powell and Reid 1982).…”

The Gibbs Phenomenon for [S, αn] Means and [T, αn] Means

“…In this note, we study the same for the [S, a n ] method of summability introduced by Meir and Sharma [3]. The corresponding result for the [T, a n ] method of summability due to Powell [5] can be worked out in exactly the same way.…”