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

Разработка бизнес-плана открытия кафе-кондитерской "SweetCake" в г. Юрга

В работе были проанализированы теоретические основы бизнес-планирования; выявлены преимущества малого бизнеса и рассмотрены новые льготы для его поддержки; разработан бизнес-проект предприятия общественного питания "Кафе-кондитерская "SweetCake" в г. Юрга, а так же были просчитаны мероприятия, направленные на развитие кафе-кондитерской "SweetCake".In work theoretical bases of business planning have been analyzed; the advantages of small business are revealed and new benefits for its support are considered; the business project of the public catering enterprise "Cafe-confectionery" SweetCake "in Yurga was developed, as well as the activities aimed at the development of the cafe-confectionery" SweetCake "

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added, references added, accepted for publication in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:0903.517

Testing of solderability by Coancoat MUST SYSTEM II

Předkládaná bakalářská práce se zabývá problematikou pájitelnosti a jejího měření. V úvodních kapitolách jsou vysvětleny základní pojmy a popsány metody testování pájitelnosti. Dále pak popisuje metodiku návrhu experimentu a realizovaný experiment pro testování pájitelnosti na drátových vývodech za použití různých tavidel a materiálů. Test byl proveden metodou smáčecích vah, pomocí testeru pájitelnosti Concoat MUST SYSTEM II. V závěrečné kapitole jsou vyhodnoceny výsledky experimentu.Katedra technologií a měřeníObhájenoThis bachelor thesis deals with solderability and its measurement. The basic concepts and solderability testing methods are explained in the opening chapters. The following chapters describe the methodology and implementation an experiment to test the solderability of wired outlets. The test was performed by using the wetting balance method with tester Concoat MUST SYSTEM II using different materials and fluxes. Experiment results are evaluated in the final chapters

Modelling railway delay propagation as diffusion-like spreading

Railway systems form an important means of transport across the world. However, congestions or disruptions may significantly decrease these systems' efficiencies, making predicting and understanding the resulting train delays a priority for railway organisations. Delays are studied in a wide variety of models, which usually simulate trains as discrete agents carrying delays. In contrast, in this paper, we define a novel model for studying delays, where they spread across the railway network via a diffusion-like process. This type of modelling has various advantages such as quick computation and ease of applying various statistical tools like spectral methods, but it also comes with limitations related to the directional and discrete nature of delays and the trains carrying them. We apply the model to the Belgian railways and study its performance in simulating the delay propagation in severely disrupted railway situations. In particular, we discuss the role of spatial aggregation by proposing to cluster the Belgian railway system into sets of stations and adapt the model accordingly. We find that such aggregation significantly increases the model's performance. For some particular situations, a non-trivial optimal level of spatial resolution is found on which the model performs best. Our results show the potential of this type of delay modelling to understand large-scale properties of railway systems

Dichlorido[(1,2,3,3a,8b-η)-2,4-dimethylcyclopenta[b]indolyl)(η5-pentamethylcyclopentadienyl)zirconium(IV)

In the structure of the title compound, [Zn(C13H12N)(C10H15)Cl2], the dihedral angle between the planes of rings coordinating to Zr is 51.6 (2)°. The Cl—Zr—Cl angle is 97.52 (4)°. The crystal structure is stabilized by H...Cl and C—H...π interactions