Products of Photo- and Thermochemical Rearrangement of 19-Membered di-tert-Butyl-Azoxybenzocrown

The preparation and characterization of products of the photochemical and thermochemical rearrangements of 19-membered azoxybenzocrowns with two, bulky, tert-butyl substituents in benzene rings in the para positions to oligooxyethylene fragments (meta positions to azoxy group, i.e., t-Bu-19-Azo-O have been presented. In photochemical rearrangement, two colored typical products were expected, i.e., 19-membered o-hydroxy-m,m′-di-tert-butyl-azobenzocrown (t-Bu-19-o-OH) and 19-membered p-hydroxy-m,m′-di-tert-butyl-azobenzocrown (t-Bu-19-p-OH). In experiments, two colored atypical macrocyclic derivatives, one 6-membered and one 5-membered ring, bearing an aldehyde group (t-Bu-19-al) or intramolecular ester group (t-Bu-20-ester), were obtained. Photochemical rearrangement led to one more macrocyclic product being isolated and identified: a 17-membered colorless compound, without an azo moiety, t-Bu-17-p-OH. The yield of the individual compounds was significantly influenced by the reaction conditions. Thermochemical rearrangement led to t-Bu-20-ester as the main product. The structures of the four crystalline products of the rearrangement—t-Bu-19-o-OH, t-Bu-19-p-OH, t-Bu-20-ester and t-Bu-17-p-OH—were determined by the X-ray method. Structures in solution of atypical derivatives (t-Bu-19-al and t-Bu-20-ester) and t-Bu-19-p-OH were defined using NMR spectroscopy. For the newly obtained hydroxyazobenzocrowns, the azo–phenol⇄quinone–hydrazone tautomeric equilibrium was investigated using spectroscopic methods. Complexation studies of alkali and alkaline earth metal cations were studied using UV-Vis absorption spectroscopy. ¹H NMR spectroscopy was additionally used to study the cation recognition of metal cations. Cation binding studies in acetonitrile have shown high selectivity towards calcium over magnesium for t-Bu-19-o-OH.     

Tight multipartite Bell's inequalities involving many measurement settings

We derive tight Bell's inequalities for N>2 observers involving more than two alternative measurement settings. We give a necessary and sufficient condition for a general quantum state to violate the new inequalities. The inequalities are violated by some classes of states, for which all standard Bell's inequalities with two measurement settings per observer are satisfied.     

Surface tension and density of liquid Sn-Ag alloys

The surface tension and density measurements for Sn-Ag alloys were carried out with the sessile drop method. Seven different compositions were investigated in the range from 0.011 to 0.5 mole fraction of Ag, in a broad range of temperature. With increasing concentrations of Ag, both density and the surface tension are increased. With increasing temperature the density decreases for all of the alloys. A decrease of the surface tension is observed for most of the composition except for the alloy of 0.5 mole fractions of Ag. The obtained results are compared with existing literature data and Butler model calculations and relatively good agreement is observed.     

The structure of Valdivia compact lines

We study linearly ordered spaces which are Valdivia compact in their order topology. We find an internal characterization of these spaces and we present a counter-example disproving a conjecture posed earlier by the first author. The conjecture asserted that a compact line is Valdivia compact if its weight does not exceed ℵ₁, every point of uncountable character is isolated from one side and every closed first countable subspace is metrizable. It turns out that the last condition is not sufficient. On the other hand, we show that the conjecture is valid if the closure of the set of points of uncountable character is scattered. This improves an earlier result of the first author.     

On the fourth-order difference equation for the associated Meixner polynomials

Three equivalent forms of the fourth-order difference equation obeyed by the associated Meixner polynomials (with a nonnegative real association parameter) are derived from a refinement of a recent result due to Letessier et al. (1996).     

The process of front-to-side collision of motor vehicles in terms of energy balance

Nonlinear Dynamics - The reconstruction of a road accident can be treated as the resolution of an “inverse problem” in mechanics using analytical or numerical models. In the road...     

Nonlinear dynamics and complexity in the generalized Lorenz system

Nonlinear Dynamics - Dynamics of magnetized fluids is much more complex than expected from the standard magnetohydrodynamics. Besides chaotic behavior that often appears in nonlinear dynamical...     

Pointwise consistency of the hermite series density estimate

The Hermite series estimate of a density f?L_p, p > 1, convergessin the mean square to f (x) for almost all x? |R, ifN (n) → ∞ and N (n) / n² → ) as n → ∞, where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is O(n^?(2m?1)/2m). Results for complete convergence are also given.