On the computation of the term w21z2zˉw_{21}z^2\bar{z} of the series defining the center manifold for a scalar delay differential equation

In computing the third order terms of the series of powers of the center manifold at an equilibrium point of a scalar delay differential equation, with a single constant delay $r>0,$ some problems occur at the term $w_{21}z^2\bar{z}.$ More precisely, in order to determine the values at 0, respectively $-r$ of the function $w_{21}(\,.\,),$ an algebraic system of equations must be solved. We show that the two equations are dependent, hence the system has an infinity of solutions. Then we show how we can overcome this lack of uniqueness and provide a formula for $w_{21}(0).$Comment: Presented at the Conference on Applied and Industrial Mathematics- CAIM 2011, Iasi, Romania, 22-25 September, 2011. Preprin

Characterization of Trametes versicolor: Medicinal Mushroom with Important Health Benefits

Trametes species represents a rich source of nutritive compounds with important pharmacological properties like antioxidant, antiinflammatory and anti-cancer properties. However, factors like genetic background, harvesting period, geographic location, climatic conditions and others are influencing the biosynthesis of bioactive compounds, their fingerprint and their concentration. The aim of this study was to determine the antioxidant capacity, total phenolic compounds and total flavonoids content of two mushroom species, namely Tramestes versicolor (TV) and Trametes gibbosa (TG), mushrooms with potential health benefits, harvested from north-west part of Romania. In order to determine the phenolic compounds profile, water, methanol, and acetone mushroom extracts were analyzed using UV-Vis spectroscopy, FTIR spectroscopy and LC-MS analysis. In total 28 compounds were tentatively identified as phenolic acids (11 compounds), flavonols (6 compounds), flavones (6 compounds), coumarins (2 compounds), flavanols, isoflavonoids and biflavonoids (1 compound). The highest antioxidant activity was determined for the methanolic extract while the highest total polyphenols content and total flavonoids content were determined for the water extract. The results obtained suggested that Trametes species can be considered important sources of bioactive compounds, their phenolics composition and content being influenced by a series of factors like geographic area origin and genetic background

Study of the behaviour of proliferating cells in leukemia modelled by a system of delay differential equations

Abstract For the model of periodic chronic myelogenous leukemia considered by Pujo-Menjouet, Mackey et al., model consisting of two delay differential equations, the equation for the density of so-called “resting cells” was studied from numerical and qualitative point of view in several works. In this paper we focus on the equation for the density of proliferating cells and study it from a qualitative point of view.</jats:p