Two novel classes of solvable many-body problems of goldfish type with constraints

Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints): i. e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited: i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.Comment: 30 pages, 2 figure

Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem (WPT)

An analogue of the Wedderbur principal theorem (WPT) is considered for finite dimensional Jordan superalgebras A with solvable radical N, such that N^2=0 and A/N is isomorphic to Josp_n|2m(F), where F is an algebraicallly closed field of characteristic zero. Let's we prove that the WPT is valid under some restrictions over the irreducible Josp_n|2m(F)-bimodules contained in N, and it is shown with counter-examples that these restrictions can not be weakened.Comment: 13 page

On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$

Field induced multiple order-by-disorder state selection in antiferromagnetic honeycomb bilayer lattice

In this paper we present a detailed study of the antiferromagnetic classical Heisenberg model on a bilayer honeycomb lattice in a highly frustrated regime in presence of a magnetic field. This study shows strong evidence of entropic order-by-disorder selection in different sectors of the magnetization curve. For antiferromagnetic couplings $J_1=J_x=J_p/3$, we find that at low temperatures there are two different regions in the magnetization curve selected by this mechanism with different number of soft and zero modes. These regions present broken $Z_2$ symmetry and are separated by a not fully collinear classical plateau at $M=1/2$. At higher temperatures, there is a crossover from the conventional paramagnet to a cooperative magnet. Finally, we also discuss the low temperature behavior of the system for a less frustrated region, $J_1=J_x<J_p/3$.Comment: revised version - accepted for publication in Physical Review B - 12 pages, 11 figure

An updated catalog of OH-maser-emitting planetary nebulae

Aims. We studied the characteristics of planetary nebulae (PNe) that show both OH maser and radio continuum emission (hereafter OHPNe). These have been proposed to be very young PNe, and therefore, they could be key objects for understanding the formation and evolution of PNe. Methods. We consulted the literature searching for interferometric observations of radio continuum and OH masers toward evolved stars, including the information from several surveys. We also processed radio continuum and OH maser observations toward PNe in the Very Large Array data archive. The high positional accuracy provided by interferometric observations allow us to confirm or reject the association between OH maser and radio continuum emission. Results. We found a total of six PNe that present both OH maser and radio continuum emissions, as confirmed with radio interferometric observations. These are bona fide OHPNe. The confirmed OHPNe present a bipolar morphology in resolved images of their ionized emission at different wavelengths, suggesting that the OH maser emission in PNe is related to nonspherical mass-loss phenomena. The OH maser spectra in PNe present a clear asymmetry, tending to show blueshifted emission with respect to the systemic velocity. Their infrared colors suggest that most of these objects are very young PNe. OHPNe do not form a homogeneous group, and seem to represent a variety of different evolutionary stages. We suggest that OH masers pumped in the AGB phase may disappear during the post-AGB phase, but reappear once the source becomes a PN and its radio continuum emission is amplified by the OH molecules. Therefore, OH maser emission could last significantly longer than the previously assumed 1000 yr after the end of the AGB phase. This maser lifetime may be longer in PNe with more massive central stars, which ionize a larger amount of gas in the envelope.Comment: 16 pages, 5 figures, 4 tables. Accepted for publication by Astronomy & Astrophysic