The point of maximum curvature as a marker for physiological time series

We present a geometric analysis of the model of Stirling. In particular we analyze the curvature of a heart rate time series in response to a step like increment in the exercise intensity. We present solutions for the point of maximum curvature which can be used as a marker of physiological interest. This marker defines the point after which the heart rate no longer continues to rapidly rise and instead follows either a steady state or slow rise. These methods are then applied to find analytic solutions for a mono exponential model which is commonly used in the literature to model the response to a moderate exercise intensity. Numerical solutions are then found for the full model and parameter values presented in Stirling

In the House but out of the Household? Why Congress Needs to Codify a Substantial Support Test for Courts to Use When Calculating a Debtor’s Household Size

Article published in the Michigan State University School of Law Student Scholarship Collection

Capacity of elements of Banach algebras

As its name suggests, this thesis is an account of the recent theory of the capacity of elements of Banach algebras. The first chapter contains a summary of the background theory, other than fundamentals, used, and consists mainly of perturbation theory of linear operators and certain properties (Jf strictly singular operators. This chapter relies heavily on the work of T„ Kato, both in his own papers and the book by S. Goldberg "Unbounded Linear Operators". Chapter 2 introduces the notion of capacity, following Halmos in his paper "Capacity in Banach algebras", and several small new results are proved, and counterexamples given, to tidy up "loose ends". The question of the capacity of the sum of two quasialgebraic elements (i.e. ones with capacity zero) is raised, and a partial solution given. The perturbation theory of Chapter 1 is applied to show the equality of the capacity of the spectrum and the Fredholn spectrum of an operator on a Banach space, whence it is shown that if J is a closed two-sided ideal of B(x) containing only Riesz operators, then perturbation by an element of J leaves the capacity invariant; this is true, in particular, for compact operators. A converse theorem is proved for Hilbert space, Chapter 3 introduces the new concept of the joint capacity of an r-tuple of elements cf a commutative Banach algebra, and develops the theory of this notion, Much of the theory parallels, xn a weaker form, that of the original concept, but there are significant differences. Finally, a perturbation theorem, similar to the original one is proved for the joint capacity

Effect of copper fungicide on Colletotrichum gloeosporioides and other microorganisms on avocado leaves and fruit

An investigation into the effect of copper fungicide on non-target microorganisms on avocado (cvv. Hass and Nabal) showed that populations of filamentous fungi, yeasts, and bacteria on leaves were at least 10-fold less after a single application of copper than on unsprayed leaves. This detrimental effect of copper on microorganisms on the phylloplane was confirmed in random samples collected from 5 commercial avocado orchards with regular pesticide spray programs but where isolated unsprayed trees were also available. An intensive 16-month study was carried out on 2 adjacent orchards, 1 that was sprayed with copper fungicide at monthly intervals from October to April each year, and the other that had not been sprayed for at least 6 years. Populations of filamentous fungi, yeasts, and bacteria on leaves and fruit were 10–100-fold lower in the sprayed orchard than in the unsprayed orchard. However, populations in the sprayed orchard recovered during the winter non-spray periods to levels comparable to the unsprayed orchard. In 1993 and 1994, fruit were harvested from both orchards, ripened, and assessed for anthracnose caused by Colletotrichum gloeosporioides. In both years, there was significantly less disease in unsprayed fruit (mean disease rating 1.13 and 0.32, respectively) than in sprayed fruit (mean disease rating 1.83 and 2.18, respectively). These results show that copper fungicide is detrimental to phylloplane microorganisms and suggest that those organisms are providing some natural suppression of C. gloeosporioides on avocado