This paper makes a contribution to differential elimination and more precisely to the problem of computing a representation of the radical differential ideal generated by a system of differential equations (ordinary or partial). The approach we use here involves characteristic set techniques;‡ these were introduced by J. F. Ritt, the founder of differential algebra. The basic idea is to write t...

Generalized Pareto distribution play an important role in reliability, extreme value theory, and other branches of applied probability and statistics. This family of distributions includes exponential distribution, Pareto distribution, and Power distribution. In this paper, we established exact expressions and recurrence relations satisfied by the quotient moments of generalized order statistic...

In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

‎Recently‎, ‎a new distribution‎, ‎named as extended generalized exponential distribution‎, ‎has been introduced by Kundu and Gupta (2011). ‎In this paper‎, ‎we consider the extended generalized exponential distribution with known shape parameters α and β. ‎At first‎, ‎the exact expressions for marginal and product moments of o...

We shall prove the following analogue of a theorem of Kronecker's : Let J be a difference field containing an element t which is distinct from its transforms of any order. Every perfect ideal in the ring 7\yu ' ' ' y y<n\ has a basis consisting of n + 1 difference polynomials. The corresponding theorem for differential polynomials was proved by J. F. Ritt. We shall follow in all but details a b...

In this paper we specify the conditions on the parameters of pairs of gOS’s under which the corresponding generalized order statistics are ordered according to usual stochastic ordering, hazard rate ordering, likelihood ratio ordering and dispersive ordering. We consider this problem in one-sample as well as two-sample problems. We show that some of the results obtained by Franco et al. ...