Self-assembly of programmed building blocks into structurally uniform dendrimers

Selective and independent dimerization of tri- and tetraurea derivatives was used to build up dendritic assemblies which are uniform in size and structure. Dendrimers with the total molecular masses of about 25 000 g/mol were obtained. The existence of uniform assemblies was proved by 1H and 1H DOSY NMR experiments and also by dynamic light scattering.     

Not every -set is perfectly meager in the transitive sense

We prove the following theorems:

1.

It is consistent with ZFC that there exists a - set which is not perfectly meager in the transitive sense.

2.

Every set which is perfectly meager in the transitive sense has the property.

3.

The product of two sets perfectly meager in the transitive sense has also that property.

     

Critical changes in vibrational modes in a magnetic debye crystal with a magnon-phonon coupling

Using the Green function technique we calculate the mean square of the vibrational amplitude of an ion (or equivalently the Debye Waller factor W, or the Mössbauer recoil free fraction ?) in a magnetic Debye crystal near the magnetic phase transition temperature T_c. We find that the magnon-phonon coupling which leads to the phonon spectrum broadening and frequency shift leads to sharp changes in W near T_c. The frequency shift leads to an increase in W, the broadening leads to a decrease in W. These results can explain the anisotropic critical changes in W near T_c observed recently in the magnetostrictive materials RFe₂ and RCo₂ (R = rare earth). In addition we calculate the expected changes in the second order Doppler shift near T_c. We find that when T approaches T_c from above a positive discontinuity and decrease in absolute value of slope of the thermal shift should occur.     

Mössbauer studies of valence fluctuations

In the last ten years the Mössbauer technique has made a considerable contribution to the research of the phenomena of mixed valencies, valence instabilities, valence fluctuations and intermediate valencies of transition elements. The sensitivity of the hyperfine interaction parameters and in particular the isomer shift, to the valency of the Mössbauer ion, enabled the research of dynamics of valence fluctuations and the temperature, pressure and composition dependence of the ionic intermediate valence state. Studies of¹⁴⁹Sm,¹⁵²Sm and¹⁵³Eu in Sm_1?xR_xS contributed to the understanding of the outstanding insulator-metal phase transition that occurs in these systems. Studies of⁵⁷Fe and¹⁵¹Eu in mixed valent systems yield the charge fluctuation rates of the “hopping” mechanism, contributing to the conductivity in these systems. Studies of¹⁵¹Eu in EuRh₂, EuCu₂Si₂, EuPd₂Si₂, EuFe₄Al₈, and EuPd₆B₄ as a function of temperature and pressure reveal many aspects of the thermodynamics of intermediate valencies. Studies of systems like Eu_1?xLa_xRh₂, EuA_2?xB_x, EuA_5?xB_x reveal strong local environment dependence of the intermediate valency. Mössbauer spectra of¹⁶⁹Tm in TmSe,¹⁷⁰Yb in YbAl₃ and²³⁷Np in NpOs₂ also display phenomena associated with fluctuating valencies.     

Selective and efficient electrocatalytic way to spirobarbituric dihydrofurans

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Approximation of Fractional Brownian Motion by Martingales

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exists a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.