Landesman-Lazer conditions at half-eigenvalues of the p-Laplacian

We study the existence of solutions of the Dirichlet problem {gather} -\phi_p(u')' -a_+ \phi_p(u^+) + a_- \phi_p(u^-) -\lambda \phi_p(u) = f(x,u), \quad x \in (0,1), \label{pb.eq} \tag{1} u(0)=u(1)=0,\label{pb_bc.eq} \tag{2} {gather} where $p>1$, \phi_p(s):=|s|^{p-1}\sgn s for $s \in \mathbb{R}$, the coefficients $a_\pm \in C^0[0,1]$, $\lambda \in \mathbb{R}$, and $u^\pm := \max\{\pm u,0\}$. We suppose that $f\in C^1([0,1]\times\mathbb{R})$ and that there exists $f_\pm \in C^0[0,1]$ such that $\lim_{\xi\to\pm\infty} f(x,\xi) = f_\pm(x)$, for all $x \in [0,1]$. With these conditions the problem \eqref{pb.eq}-\eqref{pb_bc.eq} is said to have a `jumping nonlinearity'. We also suppose that the problem {gather} -\phi_p(u')' = a_+ \phi_p(u^+) - a_- \phi_p(u^-) + \lambda \phi_p(u) \quad\text{on} \ (0,1), \tag{3} \label{heval_pb.eq} {gather} together with \eqref{pb_bc.eq}, has a non-trivial solution $u$. That is, $\lambda$ is a `half-eigenvalue' of \eqref{pb_bc.eq}-\eqref{heval_pb.eq}, and the problem \eqref{pb.eq}-\eqref{pb_bc.eq} is said to be `resonant'. Combining a shooting method with so called `Landesman-Lazer' conditions, we show that the problem \eqref{pb.eq}-\eqref{pb_bc.eq} has a solution. Most previous existence results for jumping nonlinearity problems at resonance have considered the case where the coefficients $a_\pm$ are constants, and the resonance has been at a point in the `Fucik spectrum'. Even in this constant coefficient case our result extends previous results. In particular, previous variational approaches have required strong conditions on the location of the resonant point, whereas our result applies to any point in the Fucik spectrum.Comment: 14 page

Collider Constraints on Dipole-Interacting Dark Matter

Dark matter which interacts through a magnetic or electric dipole moment is an interesting possibility which may help to resolve the discrepancy between the DAMA annual modulation signal and the null results of other searches. In this article we examine relic density and collider constraints on such dark matter, and find that for couplings needed to explain DAMA, the thermal relic density is generically in the right ballpark to account for cosmological measurements. Collider constraints are relevant for light WIMPs, but less constraining that direct searches for masses above about 10 GeV.Comment: 11 pages, 2 figures, extended discussion, added references, conclusion unchange

The role of recent experience and weight on hen's agonistic behaviour during dyadic conflict resolution.

Recent victory or defeat experiences and 2-hour familiarity with the meeting place were combined with size differences in order to better understand their effects on the behaviour leading to the establishment of dyadic dominance relationships between hens not previously acquainted with each other. Three kinds of encounters were videotaped: (i) a previous winner unfamiliar with the meeting place met a previous loser familiar for 2 hours with the meeting place (n = 12 dyads); (ii) as in (i) but both were unfamiliar with the meeting place (n=12); (iii) as in (i) but the previous winner was familiar with the meeting place while the previous loser was unfamiliar (n=13). The weight asymmetry was combined with these three types of encounters by selecting hens of various weight differences: in 29 dyads the recent loser was heavier than the recent winner and in 8 dyads it was the reverse. Recent experience had a major influence upon both agonistic behaviour and dominance outcome. Hens that were familiar with the meeting site initiated attacks more frequently than their unfamiliar opponent but did not win significantly more often. Recent experience and site familiarity could be used to identify 80% of future initiators. Once the first aggressive behaviour had been initiated, it led to victory of its initiator in 92% of cases. Weight was not found to influence agonistic behaviour nor dominance outcome. However, hens with superior comb and wattles areas won significantly more initial meetings than opponents with smaller ones. In the final encounters, victory also went more frequently to the bird showing larger comb and wattles, which happened also to be the previous dominant in a majority of cases. The use of higher-order partial correlations as an ex post facto control for comb and wattles indicates that they were not influential upon agonistic behaviour nor on dominance outcome, but were simply co-selected with the selection of victorious and defeated birds in the first phase of the experiment designed to let hens acquire recent victory/defeat experience

A simple preconditioned domain decomposition method for electromagnetic scattering problems

We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single layer operator restricted to the fictitious interface between the two subdomains.Comment: 23 page

The role of hen's weight and recent experience on dyadic conflict outcome

This study simultaneously varied experiences of recent victory or defeat, 2-hour familiarity with the meeting place, and hen weight in order to understand their combined effects on the establishment of dyadic dominance relationships between hens not previously acquainted with each other. Three kinds of encounters were arranged: (i) a previous winner unfamiliar with the meeting place met a previous loser familiar with the meeting place (n =28 dyads); (ii) a previous winner met a previous loser, both unfamiliar with the meeting place (n=27); (iii) a previous winner familiar with the meeting place encountered a previous loser unfamiliar with the meeting place (n=28). The weight asymmetry was combined with these three types of encounters by selecting hens showing various weight differences, in favour of the recent loser in 54 dyads and of the recent winner in 29 dyads. Results indicate that recent victory or defeat experience significantly affected the outcome. Even an important weight asymmetry, or familiarity with the meeting place were not sufficient for a hen recently defeated to overcome an opponent that was previously victorious. A 2-hour period of familiarization with the meeting place did not provide any significant advantage over unfamiliarity. Although a significant relationship was found to exist between comb and wattles areas and the initial and final statuses, examination of partial correlations indicates that the influence was from initial status to final status, rather than from comb and wattles to final status. These results suggest that more importance should be attributed to recent social experience in comparison to intrinsic factors in determining dyadic dominance in the hen

The low Sr/Ba ratio on some extremely metal-poor stars

It has been noted that, in classical extremely metal-poor (EMP) stars, the abundance ratio of Sr and Ba, is always higher than [Sr/Ba] = -0.5, the value of the solar r-only process; however, a handful of EMP stars have recently been found with a very low Sr/Ba ratio. We try to understand the origin of this anomaly by comparing the abundance pattern of the elements in these stars and in the classical EMP stars. Four stars with very low Sr/Ba ratios were observed and analyzed within LTE approximation through 1D (hydrostatic) model atmosphere, providing homogeneous abundances of nine neutron-capture elements. In CS 22950-173, the only turnoff star of the sample, the Sr/Ba ratio is, in fact, found to be higher than the r-only solar ratio, so the star is discarded. The remaining stars (CS 29493-090, CS 30322-023, HE 305-4520) are cool evolved giants. They do not present a clear carbon enrichment. The abundance patterns of the neutron-capture elements in the three stars are strikingly similar to a theoretical s-process pattern. This pattern could at first be attributed to pollution by a nearby AGB, but none of the stars presents a clear variation in the radial velocity indicating the presence of a companion. The stellar parameters seem to exclude any internal pollution in a TP-AGB phase for at least two of these stars. The possibility that the stars are early-AGB stars polluted during the core He flash does not seem compatible with the theory.Comment: Accepted for publication in Astronomy and Astrophysic