Rolling in the Higgs Model and Elliptic Functions

Asymptotic methods in nonlinear dynamics are used to improve perturbation theory results in the oscillations regime. However, for some problems of nonlinear dynamics, particularly in the case of Higgs (Duffing) equation and the Friedmann cosmological equations, not only small oscillations regime is of interest but also the regime of rolling (climbing), more precisely the rolling from a top (climbing to a top). In the Friedman cosmology, where the slow rolling regime is often used, the rolling from a top (not necessary slow) is of interest too. In the present work a method for approximate solution to the Higgs equation in the rolling regime is presented. It is shown that in order to improve perturbation theory in the rolling regime turns out to be effective not to use an expansion in trigonometric functions as it is done in case of small oscillations but use expansions in hyperbolic functions instead. This regime is investigated using the representation of the solution in terms of elliptic functions. An accuracy of the corresponding approximation is estimated.Comment: Latex, 36 Pages, 8 figures, typos correcte

Effect of Physical Training on the Morphology of Parasympathetic Atrial Ganglia after Unilateral Vagotomy in Rats

Cardiac denervation is a serious problem in a number of patients, including patients after heart transplantation. The status of the parasympathetic ganglia after crossing the preganglionic fibers of the vagus nerve has not been enough studied. The aim of our study was to assess the effect of physical training on the morphological parameters of the parasympathetic atrial ganglia and autonomic regulation of heart rate after right- and left-sided vagotomy in rats. Morphometric characteristics of the right atrial ganglia were evaluated using an immunohistochemical method after a study that included a three-time assessment of heart rate variability. It was found that right-sided vagotomy leads to both an increase in the volume of ganglion and autonomic dysfunction. No significant change in the number of nerve cells was found in animals with false and left-sided vagotomy while maintaining preganglionic innervation after the physical training, whereas exercises led to a decrease in the volume of nerve tissue of rats with right-sided denervation. It was also found that in animals with preserved vagal innervation, the volume of atrial ganglion tissue correlates with overall heart rate variability and a normalized parasympathetic component. Therefore, a positive effect from regular physical activity on parasympathetic regulation can be expected only if preganglionic vagal influence is preserved

Biological Evaluation of 3-Azaspiro[Bicyclo[3.1.0]Hexane-2,5′-Pyrimidines] as Potential Antitumor Agents

A series of heterocyclic compounds containing spirofused barbiturate and 3-azabicyclo[3.1.0]hexane frameworks have been studied as potential antitumor agents. Antiproliferative activity of products was screened in human erythroleukemia (K562), T lymphocyte (Jurkat), and cervical carcinoma (HeLa) as well as mouse colon carcinoma (CT26) and African green monkey kidney epithelial (Vero) cell lines. The most effective among the screened compounds show IC50 in the range from 4.2 to 24.1 μM for all tested cell lines. The screened compounds have demonstrated a significant effect of the distribution of HeLa and CT26 cells across the cell cycle stage, with accumulation of cells in SubG1 phase and induced apoptosis. It was found, using a confocal microscopy, that actin filaments disappeared and granular actin was distributed diffusely in the cytoplasm of up to 90% of HeLa cells and up to 64% of CT26 cells after treatment with tested 3-azaspiro[bicyclo [3.1.0]hexane-2,5′-pyrimidines]. We discovered that the number of HeLa cells with filopodium-like membrane protrusions was reduced significantly (from 91% in control cells to 35%) after treatment with the most active compounds. A decrease in cell motility was also noticed. Preliminary in vivo experiments on the impact of the studied compounds on the dynamics of CT26 tumor growth in Balb/C mice were also performed