Backward Inducing and Exponential Decay of Correlations for Partially Hyperbolic Attractors

We study partially hyperbolic attractors of C 2 dieomorphisms on a compact manifold. For a robust (non-empty interior) class of such diffeomorphisms, we construct Sinai-Ruelle-Bowen measures, for which we prove exponential decay of correlations and the central limit theorem, in the space of H\u7folder continuous functions. The techniques we develop (backward inducing, redundancy elimination algorithm) should be useful in the study of the stochastic properties of much more general non-uniformly hyperbolic systems. 1 Introduction In this work, M will always be a compact manifold and H will be the space of H\u7folder continuous functions on M . Moreover, 0 is a physical or SRB (Sinai- Ruelle-Bowen) probability measure for f . That is, 0 gives the time averages 0 = lim n!+1 1 n n 1 X j=0 f j (z) ; p = Dirac measure at p of a set B( 0 ) of points z 2 M with positive Lebesgue measure. This set B( 0 ) will be called the basin of 0 . We say that (f; 0 ) has exponential dec..

Backward Inducing and Exponential Decay of Correlations for Partially Hyperbolic Attractors

We study partially hyperbolic attractors of class C 2 diffeomorphisms in a finite dimensional compact manifold. For a robust (open) class of such diffeomorphisms, we construct Sinai-Ruelle-Bowen measures, for which we prove exponential decay of correlations and the central limit theorem, in the space of Holder continuous functions. For the proof of such results we develop new techniques (backward inducing, redundance elimination algorithm) which should be useful in the study of the stochastic properties of more general systems. 1 Introduction In this work, M will always be a compact manifold, and H will be the space of Holder continuous functions on M . Moreover, in all the cases we treat, ¯ 0 is a physical or SRB (Sinai-Ruelle-Bowen) probability measure for f . That is, ¯ 0 gives the time averages ¯ 0 = lim n!+1 1 n n\Gamma1 X j=0 ffi f j (z) ; ffi p = Dirac measure at p of a set B(¯ 0 ) of points z 2 M with positive Lebesgue measure. This set B(¯ 0 ) will be called the..

Evaluation of in vitro toxicity of N,N-dimethyl-2-propen-1-amines isomers

The trypanocidal activities of cis-3-(4'-bromo[1,1'-biphenyl]-4-yl)-3-(phenyl)-N,N-dimethyl-2-propen-1-amine (Vb) and cis-3-(4'-bromo[1,1'-biphenyl]-4-yl)-3-(4-bromophenyl)-N,N-dimethyl-2-propen-1-anine (Vg) appeared 6.3 and 3.5 fold more active than the trans-isomers, respectively Multi-endpoints for toxicity were also applied. Neutral red uptake (NRU), tetrazolium salt reduction (MTT), DNA content on V79 fibroblast cell culture and acute toxicity von E. coli were measured. The IC50 through DNA contents was lower for the cis-isomers in both series of compounds 5b: 7.8 mu M and 5g: 5.2 mu M). NRU values for derivative 5b in isomeric mixture shows the same value as the isolated isomers however, in the case of 5g a more significant toxicity of the cis-isomer was found. MTT values show that 5g is more toxic than 5b. In both cases, the acute toxicity of the trans-isomers was higher than that of the cis-isomers.541184785

Application of a multi-endpoint cytotoxicity assay to the trypanocidal compounds 2-propen-1-amine derivatives and determination of their acute toxicity

A multi-endpoint cytotoxicity method using the V79 fibroblast cell line was applied to 2-propen-1-amine derivatives and Nifurtimox that presented trypanocidal activity. The acute toxicity of the compounds was also studied using E. coli. The 2-propen-1-amine derivatives (X = p-H; p-Br; p-CH3SO2; p-NO2) exhibited higher trypanocidal activity (ID50) (trypomastigotes) 12.1-35.0 mu M) than Nifurtimox (157.0 mu M). For the cytotoxicity assessment, three independent endpoints, namely DNA content, neutral red uptake, and MTT, were used. Nifurtimox exhibited a lower toxicity (250-500 mu M) than the 2-propen-1-amine derivatives (4.9-48.0 mu M) and the 2-propen-1-amine derivatives exhibited lower EC50 values (5.7-24.0 mu M) than Nifurtimox (35.0 mu M), except for the p-CH3SO2 group whose IC50 was 110.0 mu M. Although Nifurtimox is a recognized toxic compound that needs metabolization to express its toxicity, its toxicity was lower than that of 2-propen-1-amines in all tests, Thus, we conclude that the multi-endpoint method for cytotoxicity evaluation using the V-79 fibroblast cell line is not adequate for compounds that need metabolization. This study led us to select the p-bromo 2-propen-1-amine derivative as one of the less toxic and more active trypanocide derivatives for further in vivo studies.11215316