Small cycles, generalized prisms and Hamiltonian cycles in the Bubble-sort graph

The Bubble-sort graph $BS_n,\,n\geqslant 2$, is a Cayley graph over the symmetric group $Sym_n$ generated by transpositions from the set $\{(1 2), (2 3),\ldots, (n-1 n)\}$. It is a bipartite graph containing all even cycles of length $\ell$, where $4\leqslant \ell\leqslant n!$. We give an explicit combinatorial characterization of all its $4$- and $6$-cycles. Based on this characterization, we define generalized prisms in $BS_n,\,n\geqslant 5$, and present a new approach to construct a Hamiltonian cycle based on these generalized prisms.Comment: 13 pages, 7 figure

Structural and entropic insights into the nature of the random-close-packing limit

Disordered packings of equal sized spheres cannot be generated above the limiting density (fraction of volume occupied by the spheres) of ??0.64 without introducing some partial crystallization. The nature of this “random-close-packing” limit (RCP) is investigated by using both geometrical and statistical mechanics tools applied to a large set of experiments and numerical simulations of equal-sized sphere packings. The study of the Delaunay simplexes decomposition reveals that the fraction of “quasiperfect tetrahedra” grows with the density up to a saturation fraction of ?30% reached at the RCP limit. At this limit the fraction of aggregate “polytetrahedral” structures (made of quasiperfect tetrahedra which share a common triangular face) reaches it maximal extension involving all the spheres. Above the RCP limit the polytetrahedral structure gets rapidly disassembled. The entropy of the disordered packings, calculated from the study of the local volume fluctuations, decreases uniformly and vanishes at the (extrapolated) limit ?K?0.66. Before such limit, and precisely in the range of densities between 0.646 and 0.66, a phase separated mixture of disordered and crystalline phases is observed

Superbroad Component in Emission Lines of SS 433

We have detected new components in stationary emission lines of SS 433; these are the superbroad components that are low-contrast substrates with a width of 2000--2500 km s-1 in He I $\lambda4922$ and H$\beta$ and 4000--5000 km s-1 in He II $\lambda4686$. Based on 44 spectra taken during four years of observations from 2003 to 2007, we have found that these components in the He II and He I lines are eclipsed by the donor star; their behavior with precessional and orbital phases is regular and similar to the behavior of the optical brightness of SS 433. The same component in H$\beta$ shows neither eclipses nor precessional variability. We conclude that the superbroad components in the helium and hydrogen lines are different in origin. Electron scattering is shown to reproduce well the superbroad component of H$\beta$ at a gas temperature of 20--35 kK and an optical depth for Thomson scattering $\tau \approx$ 0.25--0.35. The superbroad components of the helium lines are probably formed in the wind from the supercritical accretion disk. We have computed a wind model based on the concept of Shakura-Sunyaev supercritical disk accretion. The main patterns of the He II line profiles are well reproduced in this model: not only the appearance of the superbroad component but also the evolution of the central two-component part of the profile of this line during its eclipse by the donor star can be explained.Comment: 17 pages, 13 figures, 2 tables, published in Astronomy Letters, 2013, vol. 39, N 12, pp. 826 - 84

Physiological Characteristics of Platelet Activity in Calves of the Dairy and Plant Nutrition of the Holstein Breed

The hemostatic properties of platelets to a large degree determine the activity of metabolic processes that have great biological significance especially in early ontogeny. This study was conducted on 43 calves of the Holstein breed during the phase of milk-vegetable diet. It was found during the observation period that the indicators were stable in the calves between 31 and 60 days of life, and the platelet aggregation weakened. In the blood of the calves of the Holstein breed there was a slight increase in the number of discocytes. The total number of active thrombocytes in calves observed after stability between 31-60 days of life decreased during the follow-up observation. The levels of circulating platelet aggregates of small and large sizes decreased between 60 and 90 days by 66.7% and 2.5 times, respectively. This contributed to a weakening of the calves’ platelet synthesis of thromboxane, a decrease in the content of adenosinfosfatom, and to inhibition of their secretion. During the observation period, the number of actin and myosin in the platelets of the animals also decreased, which reduced the overall platelet activity. In the second part of the phase of lacto-vegetarian nutrition, the synthesis of actin and myosin in the exposed aggregate platelets weakened in the calves. The stability of the hemostatic platelet counts of the Holstein calves at the age of 31-60 days was typical, which changed their physiologically acceptable weakening by the end of observation. Keywords: calves, dairy plant phase, Holstein breed, platelets, aggregation, secretio

Fermi-liquid and Fermi surface geometry effects in propagation of low frequency electromagnetic waves through thin metal films

In the present work we theoretically analyze the contribution from a transverse Fermi-liquid collective mode to the transmission of electromagnetic waves through a thin film of a clean metal in the presence of a strong external magnetic field. We show that at the appropriate Fermi surface geometry the transverse Fermi-liquid wave may appear in conduction electrons liquid at frequencies $\omega$ significantly smaller than the cyclotron frequency of charge carriers $\Omega$ provided that the mean collision frequency $\tau^{-1}$ is smaller than $\omega.$ Also, we show that in realistic metals size oscillations in the transmission coefficient associated with the Firmi-liquid mode may be observable in experiments. Under certain conditions these oscillations may predominate over the remaining size effects in the transmission coefficient.Comment: 9 pages, 5 figures, text adde