Maximum curves and isolated points of entire functions

Given M(r; f) =maxjzj=r (jf(z)j) , curves belonging to the set of points M = fz : jf(z)j = M(jzj; f)g were de�ned by Hardy to be maximum curves. Clunie asked the question as to whether the set M could also contain isolated points. This paper shows that maximum curves consist of analytic arcs and determines a necessary condition for such curves to intersect. Given two entire functions f1(z) and f2(z), if the maximum curve of f1(z) is the real axis, conditions are found so that the real axis is also a maximum curve for the product function f1(z)f2(z). By means of these results an entire function of in�nite order is constructed for which the set M has an in�nite number of isolated points. A polynomial is also constructed with an isolated point.

Antioxidant principles of Tanacetum vulgare L. aerial parts

The methanolic extract of aerial parts of Tanacetum vulgare L. (Asteraceae) and its fractions were investigated for antioxidant activity. The crude extract displayed DPPH radical scavenging effects with an EC50 value of 37 +/- 1.2 microg/mL (n=3). Activity-guided fractionations of the crude extract resulted in the isolation of three antioxidant compounds; 3,5-O-dicaffeoylquinic acid (3,5-DCQA), axillarin and luteolin. 3,5-DCQA was the major constituent with antioxidant activity (IC50 = 9.7 microM) comparable with that of the standard quercetin (IC50 = 8.8 microM). Though the isolated compounds were previously known for their antioxidant effects, this is the first report on the identification of 3,5-DCQA from Tanacetum vulgare. The displayed potent antioxidant activity of the crude extract and isolated active principles is in support of the traditional medicinal uses of the plant for disease conditions such as wound healing, rheumatic arthritis and other inflammatory conditions.