Inability of Lyapunov exponents to predict epileptic seizures

It has been claimed that Lyapunov exponents computed from electroencephalogram or electrocorticogram (ECoG) time series are useful for early prediction of epileptic seizures. We show, by utilizing a paradigmatic chaotic system, that there are two major obstacles that can fundamentally hinder the predictive power of Lyapunov exponents computed from time series: finite-time statistical fluctuations and noise. A case study with an ECoG signal recorded from a patient with epilepsy is presented.     

The ion-pair association constant of oxalate with fac-tris(2-aminomethylpyridine)cobalt(III)

The equilibrium constant K for the ion-pair formation fac-[Co(pic)₃]³⁺ + C₂O₂₂₋ fac-[Co(pic)₃]³⁺/C₂O₄²⁻¹ where pic = 2-aminomethylpyridine, has been determined spectrophotometrically at 0.35 M (KCl) ionic strength and 25.0°C, using four different calculation approaches. The best results were obtained when the concentration of the minor component (the cobalt complex ion) was not neglected in comparison with the oxalate ion concentration. The value of K (5.3 M⁻¹) increases when the supporting electrolyte is LiCl (K = 8.2 M⁻¹). The effect of the ionic strength variation from 0.35 to 2.0 M (LiCl) was also investigated.     

Peroxycarbenium-mediated C-C bond formation: applications to the synthesis of hydroperoxides and peroxides

The Lewis acid-mediated reaction of alkene nucleophiles with peroxyacetals provides an effective route for the synthesis of homologated peroxides and hydroperoxides. In the presence of Lewis acids such as TiCl(4), SnCl(4), and trimethylsilyl triflate, peroxyacetals and peroxyketals undergo reaction with allyltrimethylsilane, silyl enol ethers, and silyl ketene acetals to afford homoallyl peroxides, 3-peroxyketones, and 3-peroxyalkanoates, respectively. Reactions of peroxyacetals are Lewis acid dependent; TiCl(4) promotes formation of ethers while SnCl(4) and trimethylsilyl triflate promote formation of peroxides. Lewis acid-promoted reactions of silylated hydroperoxyacetals furnish silylated hydroperoxides, which can be deprotected to homologated hydroperoxides. Hydroperoxyketals undergo Lewis acid-mediated allylation to furnish 1,2-dioxolanes via attack of hydroperoxide on the intermediate carbocation. Lewis acid-mediated cyclization of unsaturated peroxyacetals furnishes 1,2-dioxanes, 1,2-dioxepanes, and 1,2-dioxacanes through 6-endo/exo, 7-endo/endo, and 8-endo/endo pathways. The corresponding reactions involving 6-endo/endo and 5-endo/exo pathways were unsuccessful.     

Influence of organic matter removal on competitive and noncompetitive adsorption of copper and zinc in acid soils

We studied competitive and noncompetitive adsorption of copper and zinc in four acid soils, and compared the behavior of the two metals in untreated samples and samples treated with hydrogen peroxide to remove organic matter in the soil. Copper exhibited stronger competitive adsorption than zinc in the untreated samples. However, removal of organic matter reduced copper adsorption to a greater extent than zinc adsorption, the two metals exhibiting a more similar adsorption pattern than the untreated samples. The presence of copper dramatically reduced zinc competitive adsorption in untreated samples; on the other hand, that of zinc only resulted in slightly reduced competitive adsorption of copper. The hydrogen peroxide treatment decreased competitive adsorption in both metals; however, copper continued to be more efficient than zinc in competing for binding sites on adsorbing surfaces. Desorption of Cu occurred much less readily than desorption of Zn and hysteresis is apparent especially for Cu.