The recently introduced concept of the dimension of an algebraic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> port [1] is shown to be an invariant of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> port. This property led to a unique classification of all linear algebraic n ports in terms of their dimensions. Contrary to common belief, it is shown that the representation port-current vectors. and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</tex> is an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> vector, (Unless specified otherwise, all vectors are column vectors. A vector <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x \in R^{n}</tex> is written as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x- = [x_{1},x_{2},\cdots,X_{n},]</tex> . When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</tex> is the composite of two vectors <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y \in R^{k}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">z \in R^{n-k}</tex> , we write <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x = [y,z]</tex> . In addition, we let 0 denote zero matrices of appropriate dimensions and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1_{k}</tex> , denote the identity matrix of order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> .) is not the most general form for characterizing a linear <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> port. A generalization of (1) which covers all linear algebraic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> ports is presented.
beta-Aryl eliminations from a series of iminyl complexes to form rhodium aryl complexes and free nitriles are reported. Iminyl complexes [Rh(PEt3)3(N=CArAr')] were prepared from [Rh(COE)Cl]2, PEt3, LiN(SiMe3)2, and the imines HN=CArAr'. One example of these complexes was characterized by X-ray diffraction. Heating of these complexes in cyclohexane generated the rhodium aryl complexes and free nitriles in high yields; heating in benzene formed the same products in slightly lower yields. Complexes with varied aryl groups on the imine were studied to assess the migratory aptitudes of the aryl groups. Migration of the o-anisyl group occurred much faster than migration of a phenyl group; migration of a phenyl group occurred slightly faster than migration of the more electron-rich p-anisyl group; and migration of a phenyl group occurred slightly faster than migration of the more hindered o-tolyl group. Kinetic studies showed that the reaction was inverse first-order in the concentration of added phosphine and zero-order in added nitrile. These results show that the beta-aryl elimination most likely occurs by dissociation of phosphine from the starting complex and carbon-carbon bond cleavage of the resulting 14-electron intermediate.
Eichengreen Barry. L’euro et la Banque centrale europeenne en 2019 . In: Revue d'economie financiere, n°96, 2010. L'euro en 2019. pp. 39-44.
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Abstract Bacterivory by ciliates in various water ecosystems, both natural and artificial, plays a significant role on the microbial population composition and consequently affects water quality. A convenient, rapid and inexpensive methodology to evaluate the capacity of the ciliate protozoan Tetrahymena thermophila for bacterivory was developed utilizing fluorescent protein expressing bacteria (FPEB) in a microtitre plate fluorimeter. Bacterivory was correlated with a loss in fluorescence measured in the fluorimeter and confirmed by fluorescence microscopy showing that the FPEB were engulfed during the assay and subsequently lost their fluorescence, whereas Cytochalasin B, a known inhibitor of phagocytosis, prevented a decrease in relative fluorescence units (RFUs). The ciliate bacterivory (CB) assay has a great dynamic range allowing the assay to be performed with a variety of predator:prey concentrations. A model toxicant, CuCl2, known to have a toxicological impact on protozoa and often present in different types of wastewater, resulted in measurable decreases in bacterivory. As well, starvation of Tetrahymena for 24 h resulted in reduced bacterivory. In the future, the CB assay could be developed for water monitoring purposes to rapidly assess water samples for the capacity to support bacterivory as an indicator of ecosystem health.
This tutorial presents an in-depth introduction to chaos in dynamical systems, and presents several practical techniques for recognizing and classifying chaotic behavior. These techniques include the poincaré map, Lyapunov exponents, capacity, information dimension, correlation dimension, Lyapunov dimension, and the reconstruction of attractors from a single time series.