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

Chrysomelidae of Arkansas

A list of Chrysomelidae of Arkansas is brought up to date by inclusion of species in the reference collection in the University of Arkansas, the collection in the Zoological Institute of Leningrad, and the private collection of L. Medvedev, as well as those reported in the literature. The list consists of 232 species, subspecies, and varieties and the ecological data where known. One new species and one new variety are included

Electronic and atomic kinetics in solids irradiated with free-electron lasers or swift-heavy ions

In this brief review we discuss the transient processes in solids under irradiation with femtosecond X-ray free-electron-laser (FEL) pulses and swift-heavy ions (SHI). Both kinds of irradiation produce highly excited electrons in a target on extremely short timescales. Transfer of the excess electronic energy into the lattice may lead to observable target modifications such as phase transitions and damage formation. Transient kinetics of material excitation and relaxation under FEL or SHI irradiation are comparatively discussed. The same origin for the electronic and atomic relaxation in both cases is demonstrated. Differences in these kinetics introduced by the geometrical effects ({\mu}m-size of a laser spot vs nm-size of an ion track) and initial irradiation (photoabsorption vs an ion impact) are analyzed. The basic mechanisms of electron transport and electron-lattice coupling are addressed. Appropriate models and their limitations are presented. Possibilities of thermal and nonthermal melting of materials under FEL and SHI irradiation are discussed

New species of African Clytrinae (Coleoptera: Chrysomelidae).

Im Ergebnis der Überarbeitung von Material aus dem Deutschen Entomologischen Institut wurden zwei Clytrinen aus Afrika ermittelt und in dieser Arbeit beschrieben. Die Holotypen befinden sich in der Sammlung des DEI. Nomenklatorische Handlungengallomima Medvedev, 1970 (Melitonoma), spec. n.oranjeensis Medvedev, 1970 (Tituboea), spec. n.As a result of a revision of material from Deutsches Entomologisches Institut two Clytrines from Africa were identified and are described in this paper. The holotypes are in the collection of DEI.Nomenclatural Actsgallomima Medvedev, 1970 (Melitonoma), spec. n.oranjeensis Medvedev, 1970 (Tituboea), spec. n

On the application of cluster analysis for vegetation pollution assessment in the area of mining enterprise

The assessment of vegetation contamination in the influence area of mining enterprises is an important part of the research during the environment monitoring. There are different statistical methods that can be used for the analysis of data obtained in environmental monitoring. The article presents the results of cluster analysis of the chemical composition of agricultural vegetation samples collected in the area of copper-pyrite ore deposit location. During the analysis, all samples were divided into three clusters. One can suggest that this separation may be due to different mechanisms of pollutants entry into the particular sampling sites, as well as to the location of these sampling sites relatively to the enterprise industrial area. According to the results of the study, it can be concluded that cluster analysis is an effective tool for distinguishing the zones being characterized by different pollution mechanisms of grassy vegetation, when there are a small number of measurements and relatively low levels of the samples pollution. © 2019 Author(s)