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 $k=3$

Algebraic characteristic classes for idempotent matrices

This paper contains the algebraic analog for idempotent matrices of the Chern-Weil theory of characteristic classes. This is used to show, algebraically, that the canonical line bundle on the complex projective space is not stably trivial. Also a theorem is proved saying that for any smooth manifold there is a canonical epimorphism from the even dimensional algebraic de Rham cohomology of its algebra of smooth functions onto the standard even dimensional de Rham cohomology of the manifold

Radio interferometric observations of candidate water-maser-emitting planetary nebulae

We present Very Large Array (VLA) observations of H2O and OH masers, as well as radio continuum emission at 1.3 and 18 cm toward three sources previously cataloged as planetary nebulae (PNe) and in which single-dish detections of H2O masers have been reported: IRAS 17443-2949, IRAS 17580-3111, and IRAS 18061-2505. Our goal was to unambiguously confirm their nature as water-maser-emitting PNe, a class of objects of which only two bona-fide members were previously known. We detected and mapped H2O maser emission toward all three sources, while OH maser emission is detected in IRAS 17443-2949 and IRAS 17580-3111 as well as in other two objects within the observed fields: IRAS 17442-2942 (unknown nature) and IRAS 17579-3121 (also cataloged as a possible PN). We found radio continuum emission associated only with IRAS 18061-2505. Our results confirm IRAS 18061-2505 as the third known case of a PN associated with H2O maser emission. The three known water-maser-emitting PNe have clear bipolar morphologies, which suggests that water maser emission in these objects is related to non-spherical mass-loss episodes. We speculate that these bipolar PNe would have ``water-fountain'' Asymptotic Giant Branch (AGB) and post-AGB stars as their precursors. A note of caution is given for other objects that have been classified as OHPNe (objects with both OH maser and radio continuum emission, that could be extremely young PNe) based on single-dish observations, since interferometric data of both OH masers and continuum are necessary for a proper identification as members of this class.Comment: 33 pages, 10 figures. Accepted by The Astronomical Journa

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