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

The different origins of magnetic fields and activity in the Hertzsprung gap stars, OU Andromedae and 31 Comae

Context: When crossing the Hertzsprung gap, intermediate-mass stars develop a convective envelope. Fast rotators on the main sequence, or Ap star descendants, are expected to become magnetic active subgiants during this evolutionary phase. Aims: We compare the surface magnetic fields and activity indicators of two active, fast rotating red giants with similar masses and spectral class but diferent rotation rates - OU And (Prot=24.2 d) and 31 Com (Prot=6.8 d) - to address the question of the origin of their magnetism and high activity. Methods: Observations were carried out with the Narval spectropolarimeter in 2008 and 2013.We used the least squares deconvolution technique to extract Stokes V and I profiles to detect Zeeman signatures of the magnetic field of the stars. We provide Zeeman-Doppler imaging, activity indicator monitoring, and a precise estimation of stellar parameters. We use stellar evolutionary models to infer the evolutionary status and the initial rotation velocity on the main sequence. Results: The detected magnetic field of OU And is a strong one. Its longitudinal component Bl reaches 40 G and presents an about sinusoidal variation with reversal of the polarity. The magnetic topology of OU And is dominated by large scale elements and is mainly poloidal with an important dipole component, and a significant toroidal component. The detected magnetic field of 31 Com is weaker, with a magnetic map showing a more complex field geometry, and poloidal and toroidal components of equal contributions. The evolutionary models show that the progenitors of OU And and 31 Com must have been rotat Conclusions: OU And appears to be the probable descendant of a magnetic Ap star, and 31 Com the descendant of a relatively fast rotator on the main sequence.Comment: 16 pages, 12 figure

Search for surface magnetic fields in Mira stars. First detection in chi Cyg

In order to complete the knowledge of the magnetic field and of its influence during the transition from Asymptotic Giant Branch to Planetary Nebulae stages, we have undertaken a search for magnetic fields at the surface of Mira stars. We used spectropolarimetric observations, collected with the Narval instrument at TBL, in order to detect - with Least Squares Deconvolution method - a Zeeman signature in the visible part of the spectrum. We present the first spectropolarimetric observations of the S-type Mira star chi Cyg, performed around its maximum light. We have detected a polarimetric signal in the Stokes V spectra and we have established its Zeeman origin. We claim that it is likely to be related to a weak magnetic field present at the photospheric level and in the lower part of the stellar atmosphere. We have estimated the strength of its longitudinal component to about 2-3 Gauss. This result favors a 1/r law for the variation of the magnetic field strength across the circumstellar envelope of chi Cyg. This is the first detection of a weak magnetic field at the stellar surface of a Mira star and we discuss its origin in the framework of shock waves periodically propagating throughout the atmosphere of these radially pulsating stars. At the date of our observations of chi Cyg, the shock wave reaches its maximum intensity, and it is likely that the shock amplifies a weak stellar magnetic field during its passage through the atmosphere. Without such an amplification by the shock, the magnetic field strength would have been too low to be detected. For the first time, we also report strong Stokes Q and U signatures (linear polarization) centered onto the zero velocity (i.e., at the shock front position). They seem to indicate that the radial direction would be favored by the shock during its propagation throughout the atmosphere.Comment: 9 pages, 4 figures accepted by Astronomy and Astrophysics (21 November 2013

Specificity of Authorial Strategy in 19th Century Women’s Travelogues: A Study of E.A. Sverbeeva’s Travel Diary

The article is dedicated to the interpretation of the phenomenon of women’s writing and its representation in the genre of travelogue. For the first time, the ‘Diary of E.A. Sverbeeva for 1833’ is studied in the context of the evolution of women’s documentary travelogue in the 19th century, focusing on the issue of authorship. It is established that E.A. Sverbeeva’s travel diary expresses the main tendencies of the evolution of ‘women’s writing’ in the 1830s. It is revealed that Ekaterina Alexandrovna’s diary demonstrates a focus on the self, on modes of self-expression, self-analysis, and self-discovery. At the same time, the self is clearly expressed as a feminine self, which is manifested in the selection of objects from real life for describing the journey and in the ways they are characterized. As an individual authorial strategy, a combination of elements of a personal diary and a travelogue can be identified, while more often female travelers differentiated these types of entries, even designating the fundamental difference between them in the text of the travel diary. The analysis of the biographical basis of the diary and the ways in which the self is expressed in the narrative structure allows for the identification of a combination of different perspectives — that of a society lady, a ‘sensitive heroine,’ a mother, a married woman — reflecting the main tendencies in the development of ‘women’s writing’ in the historical-literary process of the 19th century

“Frigate Pallada” by I. A. Goncharov in Context of Travelogue Genre: Narrative Strategies of Official Traveller

The article is devoted to the analysis of the phenomenon of “travel prose” by I. A. Goncharov in the context of the tradition of Russian travelogue of the 19th century. Traditionally, in the process of analysis of text material (travel notes) the principles and forms of combining the two main narrative strategies are distinguished: the author-documentarian, ethnographer, historian and author-writer, artist. The subject of this study was the individual narrative strategies of the official traveller. “Frigate Pallada” by I. A. Goncharov is defined as a “landmark” in the evolution of travelogue genre. Different narrative strategies of the author-traveller, perceiving the world from the point of view of two minds - “modest official” and “new Argonauts” - are revealed and compared. The phenomenon of narrative in travel essays by I. A. Goncharov is characterized, on the one hand, as a syncretic text, combining elements of scientific and literary travel, on the other hand, as an individual author’s text, demonstrating the destruction of various patterns and stereotypes of the genre form of travelogue, developed by the 1850-ies. The author comes to the conclusion that in the travel prose by I. A. Goncharov there is an increase in the subjective and personal principle, which in the narrative is expressed by the constant change of narrative strategies and demonstrates the constant search for a point of view on the world

Communicating solidarity? Public responses to UK government communication of COVID-19

This article explores public responses to UK government communication of COVID-19, focusing on public solidarity as a crucial part of an effective pandemic response. Drawing on focus group research with members of the public, we identify three limitations in the way solidarity was communicated by government. What solidarity meant and entailed was not always (1) clear and understandable, (2) adequately justified to all, or (3) demonstrated by the actions of political leaders themselves. In conclusion, we consider the implications of our analysis for how the communication of solidarity could have been improved. Beyond any specific communicative shortcomings, communicating solidarity was always bound to be difficult. What solidarity meant and entailed in the context of the pandemic was never normatively self-evident, especially given the different values and interests at stake. Given this, we suggest that a more deliberative-democratic approach to solidarity would have been both normatively desirable and more likely to be effective in sustaining solidarity. But the need for this approach reveals an underlying systemic weakness in the political-communication environment: the lack of adequate opportunities for those called upon to show solidarity to reflect on, contest, and shape its meaning

Magnetic fields in single late-type giants in the Solar vicinity: How common is magnetic activity on the giant branches?

We present our first results on a new sample containing all single G,K and M giants down to V = 4 mag in the Solar vicinity, suitable for spectropolarimetric (Stokes V) observations with Narval at TBL, France. For detection and measurement of the magnetic field (MF), the Least Squares Deconvolution (LSD) method was applied (Donati et al. 1997) that in the present case enables detection of large-scale MFs even weaker than the solar one (the typical precision of our longitudinal MF measurements is 0.1-0.2 G). The evolutionary status of the stars is determined on the basis of the evolutionary models with rotation (Lagarde et al. 2012; Charbonnel et al., in prep.) and fundamental parameters given by Massarotti et al. (1998). The stars appear to be in the mass range 1-4 M_sun, situated at different evolutionary stages after the Main Sequence (MS), up to the Asymptotic Giant Branch (AGB). The sample contains 45 stars. Up to now, 29 stars are observed (that is about 64 % of the sample), each observed at least twice. For 2 stars in the Hertzsprung gap, one is definitely Zeeman detected. Only 5 G and K giants, situated mainly at the base of the Red Giant Branch (RGB) and in the He-burning phase are detected. Surprisingly, a lot of stars ascending towards the RGB tip and in early AGB phase are detected (8 of 13 observed stars). For all Zeeman detected stars v sin i is redetermined and appears in the interval 2-3 km/s, but few giants with MF possess larger v sin i.Comment: 4 pages, 3 figures, Proceedings IAU Symposium No. 302, 201

Direct detection of a magnetic field in the photosphere of the single M giant EK Boo: How common is magnetic activity among M giants?

We study the fast rotating M5 giant EK Boo by means of spectropolarimetry to obtain direct and simultaneous measurements of both the magnetic field and activity indicators, in order to infer the origin of the activity in this fairly evolved giant. We used the new spectropolarimeter NARVAL at the Bernard Lyot Telescope (Observatoire du Pic du Midi, France) to obtain a series of Stokes I and Stokes V profiles for EK Boo. Using the Least Square Deconvolution technique we were able to detect the Zeeman signature of the magnetic field. We measured its longitudinal component by means of the averaged Stokes V and Stokes I profiles. The spectra also permitted us to monitor the CaII K&H chromospheric emission lines, which are well known as indicators of stellar magnetic activity. From ten observations obtained between April 2008 and March 2009, we deduce that EK Boo has a magnetic field, which varied in the range of -0.1 to -8 G. We also determined the initial mass and evolutionary stage of EK Boo, based on up-to-date stellar evolution tracks. The initial mass is in the range of 2.0-3.6 M_sun, and EK Boo is either on the asymptotic giant branch (AGB), at the onset of the thermal pulse phase, or at the tip of the first (or red) giant branch (RGB). The fast rotation and activity of EK Boo might be explained by angular momentum dredge-up from the interior, or by the merging of a binary. In addition, we observed eight other M giants, which are known as X-ray emitters, or to be rotating fast for their class. For one of these, beta And, presumably also an AGB star, we have a marginal detection of magnetic field, and a longitudinal component Bl of about 1G was measured. More observations like this will answer the question whether EK Boo is a special case, or whether magnetic activity is, rather, more common among M giants than expected.Comment: Accepted for publication in Astronomy & Astrophysics, 10 pages, 8 figure