Antioxidant behaviour of 2′‐hydroxy‐chalcones: a study of their electrochemical properties

The electrochemical behaviour of 13 chalcone analogues was systematically studied by means of cyclic voltammetry and chronoamperometry at a glassy carbon (GC), gold and platinum working electrodes using two different supporting electrolyte/solvent combinations. It was found that chalcone analogues can be easily oxidized at both GC and gold working electrodes, but not at a platinum electrode. Principal component analysis was further employed to reveal similarities/dissimilarities between oxidation potentials, chronoamperometric signals and ability of the compounds to scavenge the reactive oxygen species H₂O₂. The study reveals the inverse proportional relationship between the scavenging ability of H₂O₂, expressed as IC₅₀, and chronoamperometric signal at 800 mV using gold as working electrode. Copyright © 2012 John Wiley & Sons, Ltd.     

Linear systems, singularity and not too ramified morphisms

Given a smooth k-variety Y (where k is a field of arbitrary characteristic) and a linear systemL on Y we study the dimension of the singular locus of the general element ofL, both inside and outside the base locus B ofL. We interpret these results from the point of view of the transversality theory, and we improve a result by Speiser about the not too ramified morphisms. Moreover, we show that our results can be applied in some cases where a criterion by Zhang, for the smoothness of the general element ofL, fails. Entrata in Redazione il 15 settembre 1997, e in versione definitiva il 28 ottobre 1999.     

Cycles in dense digraphs

Let G be a digraph (without parallel edges) such that every directed cycle has length at least four; let β(G) denote the size of the smallest subset X ? E(G) such that G?X has no directed cycles, and let γ(G) be the number of unordered pairs {u, v} of vertices such that u, v are nonadjacent in G. It is easy to see that if γ(G) = 0 then β(G) = 0; what can we say about β(G) if γ(G) is bounded?

We prove that in general β(G) ≤ γ(G). We conjecture that in fact β(G) ≤ ½γ(G) (this would be best possible if true), and prove this conjecture in two special cases:

• when V(G) is the union of two cliques
• when the vertices of G can be arranged in a circle such that if distinct u, v, w are in clockwise order and uw is a (directed) edge, then so are both uv, vw.

     

Asymptotic stability and stabilizability of special classes of discrete-time positive switched systems

In this paper we consider discrete-time positive switched systems, switching among autonomous subsystems, characterized either by monomial matrices or by circulant matrices. Necessary and sufficient conditions are provided guaranteeing either (global uniform) asymptotic stability or stabilizability (i.e. the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence). Such conditions lead to simple algorithms that allow to easily detect, under suitable conditions, whether a given positive switched system is not stabilizable.     

A genetic algorithm with neural network fitness function evaluation for IMRT beam angle optimization

Intensity Modulated Radiotherapy Treatment (IMRT) is a technique used in the treatment of cancer, where the radiation beams are modulated by a multileaf collimator allowing the irradiation of the patient using non-uniform radiation fields from selected angles. Beam angle optimization consists in trying to find the best set of angles that should be used in IMRT planning. The choice of this set of angles is patient and pathology dependent and, in clinical practice, most of the times it is made using a trial and error procedure or simply using equidistantly distributed angles. In this paper we propose a genetic algorithm that aims at calculating good sets of angles in an automated way, given a predetermined number of angles. We consider the discretization of all possible angles in the interval [0 \(^{\circ }\) , 360 \(^{\circ }\) ], and each individual is represented by a chromosome with 360 binary genes. As the calculation of a given individual’s fitness is very expensive in terms of computational time, the genetic algorithm uses a neural network as a surrogate model to calculate the fitness of most of the individuals in the population. To explicitly consider the estimation error that can result from the use of this surrogate model, the fitness of each individual is represented by an interval of values and not by a single crisp value. The genetic algorithm is capable of finding improved solutions, when compared to the usual equidistant solution applied in clinical practice. The genetic algorithm will be described and computational results will be shown.     

On the blowing up of solutions to quantum hydrodynamic models on bounded domains

The blow-up in finite time for the solutions to the initial-boundary value problem associated to the multi-dimensional quantum hydrodynamic model in a bounded domain is proved. The model consists on conservation of mass equation and a momentum balance equation equivalent to a compressible Euler equations corrected by a dispersion term of the third order in the momentum balance. The proof is based on a priori estimates for the energy functional for a new observable constructed with an auxiliary function, and it is shown that, under suitable boundary conditions and assumptions on the initial data, the solution blows up after a finite time. I.M. Gamba is supported by NSF-DMS0507038. M.P. Gualdani acknowledges partial support from the Deutsche Forschungsgemeinschaft, grants JU359/5 and was partially supported under the Feodor Lynen Research fellowship. P. Zhang is partially supported by the NSF of China under Grant 10525101 and 10421101, and the innovation grant from the Chinese Academy of Sciences. Part of the work was done when P. Zhang visited the Department of Mathematics of Texas University at Austin, the author would like to thank the hospitality of the department. Support from the Institute for Computational Engineering and Sciences at the University of Texas at Austin is also gratefully acknowledged.     

On forced fast oscillations for delay differential equations on compact manifolds

We prove an existence result for forced oscillations of delay differential equations on compact manifolds with nonzero Euler-Poincaré characteristic. When the period is smaller than the delay we need the asymptotic fixed point index theory for C¹ maps due to Eells and Fournier, and Nussbaum.