Plants produce secondary plant metabolites via biosynthetic pathways to defend themselves from pathogens, herbivores and environmental stressors. These secondary plant metabolites are very useful in the chemical industry as they are unique sources for various pharmaceutical products, such as food additives and medicinals, the latter due to antiviral, antibiotic, antioxidant, and antifungal properties that they show.This investigation deals with Helichrysum melitense, an endangered endemic flowering species unique to the Maltese islands, and the effect of seasonal, defatting process and part of plant variation on its extracts phenolic content and antioxidant activity. Information regarding this plant is scarce, and this study will aim to give more insight regarding its phytochemicals and their properties, as well as helping profile Maltas biodiversity. Samples of this plant were taken from four different locations in Gozo (ekka, Qawra, Wardija and Ta en) during the winter and summer seasons. The samples were extracted from three different plant parts (leaves, root/stems and flowers) through one of two extraction methods. The extracts were then subjected to several assays for the quantification of phenolic content (TPC, TFC and ToPC) and antioxidant activity (DPPH, ABTS, CUPRAC, FRAP and OH). Results showed that phenolics are higher in winter, while antioxidant activity showed mixed results. DPPH, ABTS and CUPRAC indicated that antioxidant activity is higher in winter, while FRAP and OH exhibited opposing results. Polar fractions showed higher phenolic content as well as antioxidant activity than defatted fractions. The highest phenolic content and antioxidant activity were found in leaves followed by root/stems and then flowers. Correlation analysis was performed and, overall, a positive relationship between phenolic content and antioxidant activity was established implying that antioxidant activity increases upon increased values of phenolic content, and decreased upon decreased values.

We prove a number of results relating exit times of planar Brownian motion with the geometric properties of the domains in question. Included are proofs of the conformal invariance of moduli of rectangles and annuli using Brownian motion; similarly probabilistic proofs of some recent results of Karafyllia on harmonic measure on starlike domains; examples of domains and their complements which are simultaneously large when measured by the moments of exit time of Brownian motion, and examples of domains and their complements which are simultaneously small; and proofs of several identities involving the Cauchy distribution using the optional stopping theorem.

We prove a number of results relating exit times of planar Brownian with the geometric properties of the domains in question. Included are proofs of the conformal invariance of moduli of rectangles and annuli using Brownian motion; similarly probabilistic proofs of some recent results of Karafyllia on harmonic measure on starlike domains; examples of domains and their complements which are simultaneously large when measured by the moments of exit time of Brownian motion, and examples of domains and their complements which are simultaneously small; and proofs of several identities involving the Cauchy distribution using the optional stopping theorem.