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  • 1
    Publication Date: 2015-02-11
    Description: A 1 H and 19 F nuclear magnetic resonance study of [Mg(H 2 O) 6 ](BF 4 ) 2 has confirmed the existence of two phase transitions at T c1 ≈ 257 K and T c2 ≈ 142 K, detected earlier by the DSC method. These transitions were reflected by changes in the temperature dependences of both proton and fluorine of second moments M 2 H and M 2 F and of spin-lattice relaxation times T 1 H and T 1 F . The study revealed anisotropic reorientations of whole [Mg(H 2 O) 6 ] 2+ cations, reorientations by 180° jumps of H 2 O ligands, and aniso- and isotropic reorientations of BF 4 − anions. The activation parameters for these motions were obtained. It was found that the phase transition at T c1 is associated with the reorientation of the cation as a whole unit around the C 3 axis and that at T c2 with isotropic reorientation of the BF 4 − anions. The temperature dependence of the full width at half maximum value of the infrared band of ρ t (H 2 O) mode (at ∼596 cm −1 ) indicated that in phases I and II, all H 2 O ligands in [Mg(H 2 O) 6 ] 2+ perform fast reorientational motions (180° jumps) with a mean value of activation energy equal to ca 10 kJ mole −1 , what is fully consistent with NMR results. The phase transition at T c1 is associated with a sudden change of speed of fast ( τ R ≈ 10 −12 s) reorientational motions of H 2 O ligands. Below T c2 (in phase III), the reorientations of certain part of the H 2 O ligands significantly slow down, while others continue their fast reorientation with an activation energy of ca 2 kJ mole −1 . This fast reorientation cannot be evidenced in NMR relaxation experiments. Splitting of certain IR bands connected with H 2 O ligands at the observed phase transitions suggests a reduction of the symmetry of the octahedral [Mg(H 2 O) 6 ] 2+ complex cation.
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
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  • 2
    Publication Date: 2020-03-13
    Description: Financial markets give a large number of trading opportunities. However, over-complicated systems make it very difficult to be effectively used by decision-makers. Volatility and noise present in the markets evoke a need to simplify the market picture derived for the decision-makers. Symbolic representation fits in this concept and greatly reduces data complexity. However, at the same time, some information from the market is lost. Our motivation is to answer the question: What is the impact of introducing different data representation on the overall amount of information derived for the decision-maker? We concentrate on the possibility of using entropy as a measure of the information gain/loss for the financial data, and as a basic form, we assume permutation entropy with later modifications. We investigate different symbolic representations and compare them with classical data representation in terms of entropy. The real-world data covering the time span of 10 years are used in the experiments. The results and the statistical verification show that extending the symbolic description of the time series does not affect the permutation entropy values.
    Electronic ISSN: 1099-4300
    Topics: Chemistry and Pharmacology , Physics
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