We propose a definition for geometric mean of k positive (semi) definite matrices. We show that our definition is the only one in the literature that has the properties that one would expect from a geometric mean, and that our geometric mean generalizes many inequalities satisfied by the geometric mean of two positive semidefinite matrices. We prove some new properties of the geometric mean of ...

A study was completed of more than 170,000 records of pediatric venous blood levels and supporting demographic information collected in New York City during 1970-1976. The geometric mean (GM) blood lead level shows a consistent cyclical variation superimposed on an overall decreasing trend with time for all ages and ethnic groups studied. The GM blood lead levels for blacks are significantly gr...

This paper, in considering aspects of the geometric mean sequence, offers new results connecting Jacobsthal and Horadam numbers which are established and then proved independently.

This report presents the geometric mean blood lead levels of an 80% cross-sectional sample of children aged 1-72 months in New Haven, Connecticut. Blood lead levels were related to age, sex and race. It was found that age and race were independently important sources of variation in blood lead levels. Sex of children in this age group was not related to differences in blood lead levels. The hig...

the rehabilitation of sandy desertified land in various dryland ecosystems by different management practices has a great potential to increase aggregate stability and improve soil quality. however, plants in general may have a different ability to sustain soil. the objective was to determine the effects of reclamation practices including haloxylon ammodendron and atriplex canescens plantation o...

Parallel subtraction is an operation defined on pairs of positive operators. In terms of electrical networks, one may pose the following problem: Given an electrical network, represented by a specified positive operator, determine the set of positive operators which when connected in parallel with the specified operator yield another prescribed operator. The set of solutions of this electrical ...

We introduce a model for the dynamics of a patchy population in a stochastic environment and derive a criterion for its persistence. This criterion is based on the geometric mean (GM) through time of the spatial-arithmetic mean of growth rates. For the population to persist, the GM has to be >/=1. The GM increases with the number of patches (because the sampling error is reduced) and decreases ...

In this paper, we obtain two refinements of the ordering relations among Heinz means with different parameters via the Taylor series of some hyperbolic functions and by the way, we derive new generalizations of Heinz operator inequalities. Moreover, we establish a matrix version of Heinz inequality for the Hilbert-Schmidt norm. Finally, we introduce a weighted multivariate geometric mean and sh...

In this note, we present sharp inequalities relating hypergeometric analogues of the arithmetic-geometric mean discussed in [5] and the power mean. The main result generalizes the corresponding sharp inequality for the arithmetic-geometric mean established in [10].