Review on computational methods for Lyapunov functions

Lyapunov functions are an essential tool in the stability analysis of dynamical systems, both in theory and applications. They provide sufficient conditions for the stability of equilibria or more general invariant sets, as well as for their basin of attraction. The necessity, i.e. the existence of Lyapunov functions, has been studied in converse theorems, however, they do not provide a general method to compute them. Because of their importance in stability analysis, numerous computational construction methods have been developed within the Engineering, Informatics, and Mathematics community. They cover different types of systems such as ordinary differential equations, switched systems, non-smooth systems, discrete-time systems etc., and employ di_erent methods such as series expansion, linear programming, linear matrix inequalities, collocation methods, algebraic methods, set-theoretic methods, and many others. This review brings these different methods together. First, the different types of systems, where Lyapunov functions are used, are briefly discussed. In the main part, the computational methods are presented, ordered by the type of method used to construct a Lyapunov function

Direct measurement of the total antioxidant capacity of foods: the ‘QUENCHER’ approach

Extraction-dependent methods were used to evaluate the antioxidant capacity up to now. The extraction conditions applied before the measurement represent a source of variations among laboratories and in some cases are not reliable. The direct procedure described in this paper skips all time-consuming solvent extraction and hydrolysis steps. A review of the solubility and localization of food antioxidant compounds was provided as base to understand the advantage of the direct procedure with respect to the extraction protocols present in the literature. The application of the procedure to some case-studies was also illustrated

Direct measurement of total antioxidant capacity of cereal products.

A simple and rapid procedure was developed for the direct measurement of the antioxidant capacity of cereals. It entails grinding of cereals, mixing with 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) reagent, centrifugation and measure of the absorbance. The ABTS reagent was dissolved in a mixture of ethanol:water (50:50, v/v), instead of 100% ethanol, in order to overcome low solubility of water-soluble antioxidant compounds of some cereals. A reaction time of 30 min allowed plateau values to be reached during the antioxidant capacity measurement of cereal samples. The accuracy of the direct procedure was confirmed by measuring, in solid state, the antioxidant activity of pure phenolic compounds. The direct procedure gave results of total antioxidant capacities significantly higher than those determined by the traditional procedure (multiple extraction followed by alkaline hydrolysis) for most whole meal cereals, suggesting that such a procedure was not always sufficient to properly assess the antioxidant capacity of bound phenolic compounds in cereals. The proposed extraction-independent procedure for measuring antioxidant capacity of cereals will facilitate the inter-laboratory data comparison, the construction of reliable antioxidant capacity database and the screening of large sampling of cereals for their nutraceutical characteristics

Determination of furosine in thermally processed foods by hydrophilic interaction liquid chromatography

Furosine, a marker of the impairment of lysine residues in protein, is formed during acid hydrolysis of the Amadori compound generated at the early stage of the Maillard reaction in thermally treated foods. An analytical method is described for the determination of furosine in thermally processed foods. The method entails acid hydrolysis of food, SPE cleanup with a hydrophilic- lipophilic sorbent, and hydrophilic interaction LC separation. The main advantage of the method is the separation of furosine by means of hydrophilic interaction LC analysis, which simply avoids ion-pairing agents during the chromatography for a complete baseline separation, or avoids the use of a metal-free chromatographic device. In addition, by combining microwave hydrolysis with hydrophilic interaction LC, the complete determination of furosine in a food sample takes approximately 25-30 min. The LOD and the LOQ were 0.7 and 2.3 mg/kg, respectively, for furosine, based on S/Ns of 3 and 10, respectively. The recoveries ranged from 94.6 ± 3.1 to 98.6 ± 1.7% for spiking levels of 100-1000 mg/kg sample. The method is easy to use and cost-effective, and gave reproducible results for both within-day and day-to-day tests.Peer Reviewe