On weak spreadability of distributed-parameter systems and its achievement via linear--quadratic control techniques

In this paper, the concept of weak spreadability is introduced.It constitutes an extension of the idea developed by El Jai& Kassara. In the case of linear distributed systems weconsider quadratic control techniques with a conveniently penalizedcriterion which makes the system weakly spreadable. The approachis outlined for a convection—diffusion system, and theresults of a numerical study are also included to illustratethe main features of the considered problem.     

Effect of Bauhinia monandra Kurz Leaf Preparations on Embryonic Stages and Adult Snails of Biomphalaria glabrata (Say, 1818), Schistosoma mansoni Cercariae and Toxicity in Artemia salina

Biomphalaria glabrata snails constitute the main vector of schistosomiasis in Brazil, and Bauhinia monandra Kurz, the leaves of which contain BmoLL lectin with biocidal action, is a plant widely found on continents in which the disease is endemic. This work describes the composition of B. monandra preparations and the effect on embryos and adult snails, their reproduction parameters and hemocytes. We also describe the results of a comet assay after B. glabrata exposure to sublethal concentrations of the preparations. Additionally, the effects of the preparations on S. mansoni cercariae and environmental monitoring with Artemia salina are described. In the chemical evaluation, cinnamic, flavonoid and saponin derivatives were detected in the two preparations assessed, namely the saline extract and the fraction. Both preparations were toxic to embryos in the blastula, gastrula, trochophore, veliger and hippo stages (LC₅₀ of 0.042 and 0.0478; 0.0417 and 0.0419; 0.0897 and 0.1582; 0.3734 and 0.0974; 0.397 and 0.0970 mg/mL, respectively) and to adult snails (LC₅₀ of 6.6 and 0.87 mg/mL, respectively), which were reproductively affected with decreased egg deposition. In blood cell analysis, characteristic cells for apoptosis, micronucleus and binucleation were detected, while for comet analysis, different degrees of nuclear damage were detected. The fraction was able to cause total mortality of the cercariae and did not present environmental toxicity. Therefore, B. monandra preparations are promising in combating schistosomiasis since they can control both the intermediate host and eliminate the infectious agent, besides being safe to the environment.     

Essential Conditions for the Full Synergy of Probability of Occurrence Distributions

In this contribution, we specify the conditions for assuring the validity of the synergy of the distribution of probabilities of occurrence. We also study the subsequent restriction on the maximal extension of the strict concavity region on the parameter space of Sharma–Mittal entropy measures, which has been derived in a previous paper in this journal. The present paper is then a necessary complement to that publication. Some applications of the techniques introduced here are applied to protein domain families (Pfam databases, versions 27.0 and 35.0). The results will show evidence of their usefulness for testing the classification work performed with methods of alignment that are used by expert biologists.     

Lyapunov exponent diagrams of a 4-dimensional Chua system

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.     

Phase diagram of the Ising Model on a Cayley tree in the presence of competing interactions and magnetic field

We study the phase diagram for the Ising Model on a Cayley tree with competing nearest-neighbor interactionsJ ₁ and next-nearest-neighbor interactionsJ ₂ andJ ₃ in the presence of an external magnetic field. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular cases, previous works by Vannimenus and by Inawashiroet al. At vanishing temperature, the phase diagram is fully determined, for all values and signs ofJ ₂/J ₁ andJ ₃/J ₂; in particular, we verify that values ofJ ₃/J ₂ high enough favor the paramagnetic phase. At finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into two disconnected pieces, etc.) are exhibited for typical values ofJ ₂/J ₁ andJ ₃/J ₂.Partially supported by the Brazilian Agencies CNPq and FINEP.     

Alternative Entropy Measures and Generalized Khinchin–Shannon Inequalities

The Khinchin–Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems to be essential for deriving these inequalities for the two-parameter Sharma–Mittal set of entropy measures. We also emphasize the derivation of these inequalities for the special cases of one-parameter Havrda–Charvat’s, Rényi’s and Landsberg–Vedral’s entropy measures.     

Periodic solutions for a nonautonomous ordinary differential equation

We consider the nonautonomous differential equation of second order x^″+a(t)x−b(t)x²+c(t)x³=0, where a(t),b(t),c(t) are T-periodic functions. This is a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of at least two positive T-periodic solutions for this equation, using coincidence degree theories.     

DC electrical resistivity for CoxNi5/3−xSb1/3Fe1O4 ferrites

The DC electrical resistivity (p) was studied for Co substituted SbNi ferrites as a function of temperature and composition. The experimental results showed that DC resistivity, Curie temperature and activation energies for electrical conduction increase as Co-ion substitution decreases. The DC electrical conductivity increases as temperature increases. The real part of dielectric constant (e') was found to be inversely proportional to the root mean square value of the electrical resistivity.