The number of non-solutions to an equation in a group and non-topologizable torsion-free groups

It is shown that, for any pair of cardinals with infinite sum, there exist a group and an equation over this group such that the first cardinal is the number of solutions to this equation and the second cardinal is the number of non-solutions to this equation. A countable torsion-free non-topologizable group is constructed.Comment: 5 pages; minor changes in the introduction and reference

Reflection principle characterizing groups in which unconditionally closed sets are algebraic

We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that this is always the case when G is a direct product of an Abelian group with a direct product (sometimes also called a direct sum) of a family of countable groups. This is the widest class of groups known to date where the answer to the 63 years old problem of Markov turns out to be positive. We also prove that whether every unconditionally closed subset of G is algebraic or not is completely determined by countable subgroups of G.Comment: 14 page

Methods of predicting relapsing hemorrhage.

In this article the authors presented their own original methods for predicting ulcerous gastroduodenal bleeding defended by Patent of Ukraine. The implementation of these procedures led to substantial lowing of recurrent hamorrhage rate – more than twice. All methods have pathogenetic foundation and are based on ulcerogenesis mechanisms revealed during the longlasting complex clinical and experimental research. In such a way surgeons obtain some possibilities of early diagnostics of bleeding relapses and adequate treatment and effective hemorrhage prevention accordingly.

Optimal control over geomorphological systems

The method presented can be used for the planning of shore protection measures without seawalls or other cliff-protecting structures; it is particularly appropriate in cases where the system is eventually to control itself by adjustment to a dynamic equilibrium regim

Quantitative modeling of \textit{in situ} x-ray reflectivity during organic molecule thin film growth

Synchrotron-based x-ray reflectivity is increasingly employed as an \textit{in situ} probe of surface morphology during thin film growth, but complete interpretation of the results requires modeling the growth process. Many models have been developed and employed for this purpose, yet no detailed, comparative studies of their scope and accuracy exists in the literature. Using experimental data obtained from hyperthermal deposition of pentane and diindenoperylene (DIP) on SiO$_2$, we compare and contrast three such models, both with each other and with detailed characterization of the surface morphology using ex-situ atomic force microscopy (AFM). These two systems each exhibit particular phenomena of broader interest: pentacene/SiO$_2$ exhibits a rapid transition from rough to smooth growth. DIP/SiO$_2$, under the conditions employed here, exhibits growth rate acceleration due to a different sticking probability between the substrate and film. In general, \textit{independent of which model is used}, we find good agreement between the surface morphology obtained from fits to the \insitu x-ray data with the actual morphology at early times. This agreement deteriorates at later time, once the root-mean squared (rms) film roughness exceeds about 1 ML. A second observation is that, because layer coverages are under-determined by the evolution of a single point on the reflectivity curve, we find that the best fits to reflectivity data --- corresponding to the lowest values of $\chi_\nu^2$ --- do not necessarily yield the best agreement between simulated and measured surface morphologies. Instead, it appears critical that the model reproduce all local extrema in the data. In addition to showing that layer morphologies can be extracted from a minimal set of data, the methodology established here provides a basis for improving models of multilayer growth by comparison to real systems.Comment: 34 pages (double-spaced, including figures and references), 10 figures, 3 appendice