Time-dependent spectral-feature variations of stars displaying the B[e] phenomenon III. HD 50138

We analyse spectroscopic observations of the B[e] star HD 50138 (MWC 158, V743 Mon, or IRAS 06491-0654), a member of the FS CMa group, obtained over the last twenty years. Four different epochs are identified in the observational data, where the variability of the spectral features is substantially different. Additionally, two long periods of (3 000 +/- 500) and (5 000 +/- 1000) days are found in the variations of the equivalent widths of the H alpha and [OI] 6300 A lines and radial velocities of the H alpha line violet peak. Modest signatures of a regular period of ~34 days in the radial velocities of the H alpha red peak and H beta central depression are found in the season 2013/2014. The H alpha V/R changes indicate a periodicity of ~50 days. The correlations between individual spectral features significantly restricts the model of the object and suggest that it is most likely a binary system with a highly distorted disc with spiral arms around the primary component. At the same time, no obvious signs of the secondary component has been found in the object's spectrum

Pre-torsors and Galois comodules over mixed distributive laws

We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street's bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions $(N_A,R_A)$ and $(N_B,R_B)$ on one hand, and the category of regular comonad arrows $(R_A,\xi)$ from some equalizer preserving comonad ${\mathbb C}$ to $N_BR_B$ on the other. This generalizes a known relationship between pre-torsors over equal commutative rings and Galois objects of coalgebras.Developing a bi-Galois theory of comonads, we show that a pre-torsor over regular adjunctions determines also a second (equalizer preserving) comonad ${\mathbb D}$ and a co-regular comonad arrow from ${\mathbb D}$ to $N_A R_A$, such that the comodule categories of ${\mathbb C}$ and ${\mathbb D}$ are equivalent.Comment: 34 pages LaTeX file. v2: a few typos correcte

Coherent states for Hopf algebras

Families of Perelomov coherent states are defined axiomatically in the context of unitary representations of Hopf algebras possessing a Haar integral. A global geometric picture involving locally trivial noncommutative fibre bundles is involved in the construction. A noncommutative resolution of identity formula is proved in that setup. Examples come from quantum groups.Comment: 19 pages, uses kluwer.cls; the exposition much improved; an example of deriving the resolution of identity via coherent states for SUq(2) added; the result differs from the proposals in literatur

Zr alloy protection against high-temperature oxidation: Coating by a double-layered structure with active and passive functional properties

In this work, a new concept of metal surface protection against degradation caused by high-temperature oxidation in water environment is presented. We were the first to create a double-layered coating consisting of an active and passive part to protect Zr alloy surface against high-temperature oxidation in a hot water environment. We investigated the hot steam corrosion of ZIRLO fuel cladding coated with a double layer consisting of 500 nm nanocrystalline diamond (NCD) as the bottom layer and 2 m chromium-aluminum-silicon nitride (CrAlSiN) as the upper layer. Coated and noncoated ZIRLO samples were exposed for 4 days at 400 °C in an autoclave (working water-cooled nuclear reactor temperature) and for 60 minutes at 1000 °C (nuclear reactor accident temperature) in a hot steam furnace. We have shown that the NCD coating protects the Zr alloy surface against oxidation in an active way: carbon from NCD layer enters the Zr alloy surface and, by changing the physical and chemical properties of the Zr cladding tube surface, limits the Zr oxidation process. In contrast, the passive CrAlSiN coating prevents the Zr cladding tube surface from coming into physical contact with the hot steam. The advantages of the double layer were demonstrated, particularly in terms of hot (accident-temperature) oxidation kinetics: in the initial stage, CrAlSiN layer with low number of defects acts as an impermeable barrier. But after a longer time (more than 20 minutes) the protection by more cracked CrAlSiN decreases. At the same time, the carbon from NCD strongly penetrates the Zr cladding surface and worsen conditions for Zr oxidation. For the double-layer coating, the underlying NCD layer mitigates thermal expansion, reducing cracks and defects in upper layer CrAlSiN

Noncommutative Differential Forms on the kappa-deformed Space

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo

Kappa-Minkowski spacetime, Kappa-Poincar\'{e} Hopf algebra and realizations

We unify kappa-Minkowki spacetime and Lorentz algebra in unique Lie algebra. Introducing commutative momenta, a family of kappa-deformed Heisenberg algebras and kappa-deformed Poincare algebras are defined. They are specified by the matrix depending on momenta. We construct all such matrices. Realizations and star product are defined and analyzed in general and specially, their relation to coproduct of momenta is pointed out. Hopf algebra of the Poincare algebra, related to the covariant realization, is presented in unified covariant form. Left-right dual realizations and dual algebra are introduced and considered. The generalized involution and the star inner product are analyzed and their properties are discussed. Partial integration and deformed trace property are obtained in general. The translation invariance of the star product is pointed out. Finally, perturbative approach up to the first order in $a$ is presented in Appendix.Comment: references added, typos corrected, acceped in J. Phys.

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal