Pali Sen

Some characterizations of geometric tail distributions based on record values

Let Rj be the jth upper record value from an infinite sequence of independent identically distributed positive integer valued random variables. We show that their common distribution must have geometric tail if Rj+k−Rj and Rj are partially independent for some j≥1 and k≥1 or if E(Rj+2−Rj+1| Rj) is a constant. Three versions of partial independence, each of which provides a characterization of the geometric tail are presented.

A calcium model with random absorption: A stochastic approach

Absorption of calcium, or any mineral, by the body is subject to the random fluctuations typical of diffusion through membranes. In this paper we consider the absorption of calcium from the gut as a white noise process added to the deterministic model of Sen & Mohr (1990, J. theor. Biol. 142, 179-188). The first two moments for the amount of calcium in the extracellular fluid (ECF) have been derived using the Ito Calculus. A confidence interval for the total amount of calcium in the ECF is constructed. The equations for the first two moments of the fraction of dose calcium in the ECF are also given. Suggestions are made for the collection of experimental data in a form which should be helpful in investigating the magnitude of the stochastic effect.

A kinetic model for calcium distribution

Models for the distribution of minerals in the body are of interest as they allow researchers to trace the effect of a dose on mineral levels in plasma, storage and other compartments. Limited models are available in the literature for tracing the distribution of a calcium dose through a short time period. We propose a more general kinetic model which includes both limited absorption through the gut and loss of calcium via excretion. This new method has the advantages of giving reasonable results over moderate time periods, and allowing the extrapolation of calcium levels in extracellular fluid and storage. We fit the model to published data in order to obtain typical parameter values. These values are then used to analyze the implications of the model regarding the effect of calcium dose on calcium levels in various compartments.

A Tauberian theorem for a generalized power series method

Abstract The power series summability method is one of the most important and general methods in Summability Theory. In this work we will extend the power series method by considering the Burmann series method (i.e. f s ( z n ) = 1 f ( z n ) ∑ k = 0 ∞ s k b k [ h ( z n ) ] k , where f ( z n ) = ∑ k = 0 ∞ b k [ h ( z n ) ] k and | h ( z n ) | 1 ). Using the generalization we obtain a Tauberian theorem which contains, as special cases, some standard theorems for Abel, Borel, and Sonnenschein methods. We use the Abel and Borel matrix methods to illustrate this theorem.