Ergodic Transport Theory and Piecewise Analytic Subactions for Analytic Dynamics

We consider a piecewise analytic real expanding map $f: [0,1]\to [0,1]$ of degree $d$ which preserves orientation, and a real analytic positive potential $g: [0,1] \to \mathbb{R}$. We assume the map and the potential have a complex analytic extension to a neighborhood of the interval in the complex plane. We also assume $\log g$ is well defined for this extension. It is known in Complex Dynamics that under the above hypothesis, for the given potential $\beta \,\log g$, where $\beta$ is a real constant, there exists a real analytic eigenfunction $\phi_\beta$ defined on $[0,1]$ (with a complex analytic extension) for the Ruelle operator of $\beta \,\log g$. Under some assumptions we show that $\frac{1}{\beta}\, \log \phi_\beta$ converges and is a piecewise analytic calibrated subaction. Our theory can be applied when $\log g(x)=-\log f'(x)$. In that case we relate the involution kernel to the so called scaling function.Comment: 6 figure

Derivatization Does Not Influence Antimicrobial and Antifungal Activities of Applanoxidic Acids and Sterols from Ganoderma spp.

Abstract Applanoxidic acids and sterols, isolated from Ganoderma spp., were acetylated and/or methylated. The antibacterial activity against Escherichia coli and Staphylococcus aureus and the antifungal activity against Candida albicans and Trichophyton mentagrophytes of the derivatives were investigated by a microdilution method, and compared with those of the natural products. Both natural and modified compounds exhibited comparable antibacterial and antifungal activities in a range of 1.0 to > 2.0 mg/ml minimal inhibitory concentratio

Atividade antimicrobiana do australato de metila de Ganoderma australe

In addition to nine known steroidal compounds, australic acid and the new methyl australate have been isolated from the Brazilian fungus Ganoderma australe. Both methyl australate and its corresponding acid were shown to be active against fungi and Gram-positive bacteria, the methyl ester being also active against Gram-negative bacteria. Do fungo brasileiro Ganoderma australe foram isolados o ácido austrálico e o novo composto australado de metila, além de outros 9 compostos já conhecidos. Tanto o australado de metila quanto o ácido correpondente foram ativos contra fungos e bactérias Gram-positivas, sendo o éster metílico ainda ativo contra bactérias Gram-negativas