Strong linear polarization of V4332 Sgr: a dusty disc geometry

The eruption of V4332 Sgr was observed in 1994. During the outburst, the object became extremely red, so it is considered as belonging to luminous red transients of the V838 Mon type. It has recently been suggested that the central object in V4332 Sgr is now hidden in a dusty disc and that the photospheric spectrum of this object observed in the optical results from scattering the central star radiation on dust grains in the disc. One expects significant polarization of the spectrum in this case. We investigate this prediction. We present and analyse polarimetric observations of V4332 Sgr in the V and R photometric bands done with the NOT telescope. The optical light of V4332 Sgr is linearly polarized with a degree of ~26% in the V band and ~11% in R. Discussion of the observed polarization leads us to conclude that the photospheric spectrum observed in V4332 Sgr is probably produced by dust scattering not only in the disc but also in the outflow from the object seen in the emission features.Comment: accepted in Astronomy & Astrophysics as a research not

A revision of the Lower Cretaceous foraminiferal genus Falsogaudryinella from northwest Europe and Romania, and its relationship to Uvigerinammina

We emend the definition of the foraminiferal genus Falsogaudryinella Bartenstein, 1977 based on observations of the type species, F. tealbyensis from the Barremian Lower Tealby Clay of Lincolnshire, U.K. The genus was described by Loeblich & Tappan (1987) as having initial triserial coiling which reduces to biserial and finally uniserial. However, topotype specimens display high trochospiral coiling in the microsphaeric generation, with at least four chambers in the initial whorl. The genus, therefore, does not belong in the family Verneuilinidae, but must be transferred to the Prolixoplectidae. The wall is solid, non-canaliculate. The connections between chambers are in the form of tubes that extend from the basal part of the chamber lumina toward a terminal aperture. This tubular connection is partially separated from the main part of the chamber lumina by a septum. The presence of this tubular connection in F. tealbyensis is closely analogous to that observed in the type species of Uvigerinammina Majzon, 1943. The two genera, therefore, are separated mainly on the basis of cement type, with Falsogaudryinella possessing calcareous cement and Uvigerinammina organic cement. We illustrate five species of Falsogaudryinella from the Barremian of Lincolnshire, the U.K. sector of the Central North Sea, and from the Barremian and the Albian of Romania (F. neagui Bartenstein, 1981, F. praemoesiana n.sp. F. tealbyensis (Bartenstein, 1956), F. xenogena n.sp. and F. moesiana (Neagu, 1966)). Our investigations reveal that upper Hauterivian to Barremian specimens from the North Sea that have been previously regarded as F. moesiana (e.g. King et al., 1989) in fact belong in a new species, Falsogaudryinella praemoesiana n.sp. A second new species, Falsogaudryinella xenogena n.sp. is described from the Barremian of the Central North Sea. Evolution within the mid- Cretaceous Falsogaudryinella group appears to progress by reduction of the terminal uniserial part, since the coiling in the stratigraphically youngest form (F. moesiana) is predominantly triserial. Our interpretations of the phylogeny of the Cretaceous Falsogaudryinella and Uvigerinammina lineages are presented

Exploring the diffeomorphism invariant Hilbert space of a scalar field

As a toy model for the implementation of the diffeomorphism constraint, the interpretation of the resulting states, and the treatment of ordering ambiguities in loop quantum gravity, we consider the Hilbert space of spatially diffeomorphism invariant states for a scalar field. We give a very explicit formula for the scalar product on this space, and discuss its structure. Then we turn to the quantization of a certain class of diffeomorphism invariant quantities on that space, and discuss in detail the ordering issues involved. On a technical level these issues bear some similarity to those encountered in full loop quantum gravity.Comment: 20 pages, no figures; v3: corrected typos, added reference, some clarifications added; version as published in CQ

Combustion Process in a Spark Ignition Engine: Dynamics and Noise Level Estimation

We analyse the experimental time series of internal pressure in a four cylinder spark ignition engine. In our experiment, performed for different spark advance angles, apart from usual cyclic changes of engine pressure we observed oscillations. These oscillations are with longer time scales ranging from one to several hundred engine cycles depending on engine working conditions. Basing on the pressure time dependence we have calculated the heat released per cycle. Using the time series of heat release to calculate the correlation coarse-grained entropy we estimated the noise level for internal combustion process. Our results show that for a smaller spark advance angle the system is more deterministic.Comment: 15 pages, 7 figures, submitted to CHAO

Aluminium oxide in the optical spectrum of VY Canis Majoris

We report the first identification of the optical bands of the B-X system of AlO in the red supergiant VY CMa. In addition to TiO, VO, ScO, and YO, which were recognized in the optical spectrum of the star long time ago, AlO is another refractory molecule which displays strong emission bands in this peculiar star. Simulating the bands of AlO, we derive a rotational temperature of the circumstellar gas of Trot=700K. By resolving individual rotational components of the bands, we derive the kinematical characteristics of the gas, finding that the emission is centered at the stellar radial velocity and its intrinsic width is 13.5 km/s (full width at half maximum). It is the narrowest emission among all (thermal) features observed in VY CMa so far. The temperature and line widths suggest that the emission arises in gas located within ~20 stellar radii, where the outflow is still being accelerated. This result contradicts equilibrium-chemistry models which predict substantial AlO abundances only to within a few stellar radii. We argue that non-equilibrium models involving propagation of shocks are needed to explain the observations.Comment: to appear in A&

Forbidden induced subgraphs and the price of connectivity for feedback vertex set.

Let fvs(G) and cfvs(G) denote the cardinalities of a minimum feedback vertex set and a minimum connected feedback vertex set of a graph G, respectively. For a graph class G, the price of connectivity for feedback vertex set (poc-fvs) for G is defined as the maximum ratio cfvs(G)/fvs(G) over all connected graphs G in G. It is known that the poc-fvs for general graphs is unbounded. We study the poc-fvs for graph classes defined by a finite family H of forbidden induced subgraphs. We characterize exactly those finite families H for which the poc-fvs for H-free graphs is bounded by a constant. Prior to our work, such a result was only known for the case where |H|=1

A reconfigurations analogue of Brooks’ theorem.

Let G be a simple undirected graph on n vertices with maximum degree Δ. Brooks’ Theorem states that G has a Δ-colouring unless G is a complete graph, or a cycle with an odd number of vertices. To recolour G is to obtain a new proper colouring by changing the colour of one vertex. We show that from a k-colouring, k > Δ, a Δ-colouring of G can be obtained by a sequence of O(n 2) recolourings using only the original k colours unless G is a complete graph or a cycle with an odd number of vertices, or k = Δ + 1, G is Δ-regular and, for each vertex v in G, no two neighbours of v are coloured alike. We use this result to study the reconfiguration graph R k (G) of the k-colourings of G. The vertex set of R k (G) is the set of all possible k-colourings of G and two colourings are adjacent if they differ on exactly one vertex. It is known that if k ≤ Δ(G), then R k (G) might not be connected and it is possible that its connected components have superpolynomial diameter, if k ≥ Δ(G) + 2, then R k (G) is connected and has diameter O(n 2). We complete this structural classification by settling the missing case: if k = Δ(G) + 1, then R k (G) consists of isolated vertices and at most one further component which has diameter O(n 2). We also describe completely the computational complexity classification of the problem of deciding whether two k-colourings of a graph G of maximum degree Δ belong to the same component of R k (G) by settling the case k = Δ(G) + 1. The problem is O(n 2) time solvable for k = 3, PSPACE-complete for 4 ≤ k ≤ Δ(G), O(n) time solvable for k = Δ(G) + 1, O(1) time solvable for k ≥ Δ(G) + 2 (the answer is always yes)