The sl(2n|2n)^(1) Super-Toda Lattices and the Heavenly Equations as Continuum Limit

The $n\to\infty$ continuum limit of super-Toda models associated with the affine $sl(2n|2n)^{(1)}$ (super)algebra series produces $(2+1)$-dimensional integrable equations in the ${\bf S}^{1}\times {\bf R}^2$ spacetimes. The equations of motion of the (super)Toda hierarchies depend not only on the chosen (super)algebras but also on the specific presentation of their Cartan matrices. Four distinct series of integrable hierarchies in relation with symmetric-versus-antisymmetric, null-versus-nonnull presentations of the corresponding Cartan matrices are investigated. In the continuum limit we derive four classes of integrable equations of heavenly type, generalizing the results previously obtained in the literature. The systems are manifestly N=1 supersymmetric and, for specific choices of the Cartan matrix preserving the complex structure, admit a hidden N=2 supersymmetry. The coset reduction of the (super)-heavenly equation to the ${\bf I}\times{\bf R}^{(2)}=({\bf S}^{1}/{\bf Z}_2)\times {\bf R}^2$ spacetime (with ${\bf I}$ a line segment) is illustrated. Finally, integrable $N=2,4$ supersymmetrically extended models in $(1+1)$ dimensions are constructed through dimensional reduction of the previous systems.Comment: 12 page

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Massive pulsating stars observed by BRITE-Constellation. I. The triple system Beta Centauri (Agena)

This paper aims to precisely determine the masses and detect pulsation modes in the two massive components of Beta Cen with BRITE-Constellation photometry. In addition, seismic models for the components are considered and the effects of fast rotation are discussed. This is done to test the limitations of seismic modeling for this very difficult case. A simultaneous fit of visual and spectroscopic orbits is used to self-consistently derive the orbital parameters, and subsequently the masses, of the components. The derived masses are equal to 12.02 +/- 0.13 and 10.58 +/- 0.18 M_Sun. The parameters of the wider, A - B system, presently approaching periastron passage, are constrained. Analysis of the combined blue- and red-filter BRITE-Constellation photometric data of the system revealed the presence of 19 periodic terms, of which eight are likely g modes, nine are p modes, and the remaining two are combination terms. It cannot be excluded that one or two low-frequency terms are rotational frequencies. It is possible that both components of Beta Cen are Beta Cep/SPB hybrids. An attempt to use the apparent changes of frequency to distinguish which modes originate in which component did not succeed, but there is potential for using this method when more BRITE data become available. Agena seems to be one of very few rapidly rotating massive objects with rich p- and g-mode spectra, and precisely known masses. It can therefore be used to gain a better understanding of the excitation of pulsations in relatively rapidly rotating stars and their seismic modeling. Finally, this case illustrates the potential of BRITE-Constellation data for the detection of rich-frequency spectra of small-amplitude modes in massive pulsating stars.Comment: 17 pages (with Appendix), 15 figures, accepted for publication in A&

Interaction patterns of methoprene-tolerant and germ cell-expressed Drosophila JH receptors suggest significant differences in their functioning

Methoprene-tolerant (Met) and germ cell-expressed (Gce) proteins were shown to be juvenile hormone (JH) receptors of Drosophila melanogaster with partially redundant functions. We raised the question of where the functional differentiation of paralogs comes from. Therefore, we tested Met and Gce interaction patterns with selected partners. In this study, we showed the ability of Gce and its C-terminus (GceC) to interact with 14-3-3 in the absence of JH. In contrast, Met or Met C-terminus (MetC) interactions with 14-3-3 were not observed. We also performed a detailed structural analysis of Met/Gce interactions with the nuclear receptor fushi tarazu factor-1 (Ftz-F1) ligand-binding domain. We showed that GceC comprising an Ftz-F1-binding site and full-length protein interacts with Ftz-F1. In contrast to Gce, only MetC (not full-length Met) can interact with Ftz-F1 in the absence of JH. We propose that the described differences result from the distinct tertiary structure and accessibility of binding sites in the full-length Met/Gce. Moreover, we hypothesize that each interacting partner can force disordered MetC and GceC to change the structure in a partner-specific manner. The observed interactions seem to determine the subcellular localization of Met/Gce by forcing their translocation between the nucleus and the cytoplasm, which may affect the activity of the proteins. The presented differences between Met and Gce can be crucial for their functional differentiation during D. melanogaster development and indicate Gce as a more universal and more active paralog. It is consistent with the theory indicating gce as an ancestor gene

Studying the photometric and spectroscopic variability of the magnetic hot supergiant ζ\zeta Orionis Aa

Massive stars play a significant role in the chemical and dynamical evolution of galaxies. However, much of their variability, particularly during their evolved supergiant stage, is poorly understood. To understand the variability of evolved massive stars in more detail, we present a study of the O9.2Ib supergiant $\zeta$ Ori Aa, the only currently confirmed supergiant to host a magnetic field. We have obtained two-color space-based BRIght Target Explorer photometry (BRITE) for $\zeta$ Ori Aa during two observing campaigns, as well as simultaneous ground-based, high-resolution optical CHIRON spectroscopy. We perform a detailed frequency analysis to detect and characterize the star's periodic variability. We detect two significant, independent frequencies, their higher harmonics, and combination frequencies: the stellar rotation period $P_{\mathrm{rot}} = 6.82\pm0.18$ d, most likely related to the presence of the stable magnetic poles, and a variation with a period of $10.0\pm0.3$ d attributed to circumstellar environment, also detected in the H$\alpha$ and several He I lines, yet absent in the purely photospheric lines. We confirm the variability with $P_{\mathrm{rot}}$/4, likely caused by surface inhomogeneities, being the possible photospheric drivers of the discrete absorption components. No stellar pulsations were detected in the data. The level of circumstellar activity clearly differs between the two BRITE observing campaigns. We demonstrate that $\zeta$ Ori Aa is a highly variable star with both periodic and non-periodic variations, as well as episodic events. The rotation period we determined agrees well with the spectropolarimetric value from the literature. The changing activity level observed with BRITE could explain why the rotational modulation of the magnetic measurements was not clearly detected at all epochs.Comment: 20 pages, 5 tables, 12 figures, accepted for publication in A&

The BRITE-Constellation Nanosatellite Space Mission And Its First Scientific Results

The BRIght Target Explorer (BRITE) Constellation is the first nanosatellite mission applied to astrophysical research. Five satellites in low-Earth orbits perform precise optical two-colour photometry of the brightest stars in the night sky. BRITE is naturally well suited for variability studies of hot stars. This contribution describes the basic outline of the mission and some initial problems that needed to be overcome. Some information on BRITE data products, how to access them, and how to join their scientific exploration is provided. Finally, a brief summary of the first scientific results obtained by BRITE is given.Comment: 5 pages, 1 figure, to appear in the proceedings of "Seismology of the Sun and the Distant Stars 2016. Using Today's Successes to Prepare the Future. Joint TASC2/KASC9 Workshop - SPACEINN/HELAS8 Conference", ed. M. J. P. F. G. Monteir

Supersymmetry for integrable hierarchies on loop superalgebras

The algebraic approach is employed to formulate N=2 supersymmetry transformations in the context of integrable systems based on loop superalgebras $\hat{\rm sl}(p+1,p), p \ge 1$ with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for $p=1$ which solves positive and negative evolution equations of the N=2 supersymmetric model.Comment: Latex, 21 page