Solvabilty of generalized Hammerstein integral equations on unbounded domains, with sign-changing kernels

In this work we study an Hammerstein generalized integral equation u(t)=∫_{-∞}^{+∞}k(t,s) f(s,u(s),u′(s),...,u^{(m)}(s))ds, where k:ℝ²→ℝ is a W^{m,∞}(ℝ²), m∈ℕ, kernel function and f:ℝ^{m+2}→ℝ is a L¹-Carathéodory function. To the best of our knowledge, this paper is the first one to consider discontinuous nonlinearities with derivatives dependence, without monotone or asymptotic assumptions, on the whole real line. Our method is applied to a fourth order nonlinear boundary value problem, which models moderately large deflections of infinite nonlinear beams resting on elastic foundations under localized external loads.

Covariant Spectator Theory of heavy–light and heavy mesons and the predictive power of covariant interaction kernels

The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy–light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The numerical calculations are performed in momentum space, where special care is taken to treat the strong singularities present in the confining kernel. The observed meson spectrum is very well reproduced after fitting a small number of model parameters. Remarkably, a fit to a few pseudoscalar meson states only, which are insensitive to spin–orbit and tensor forces and do not allow to separate the spin–spin from the central interaction, leads to essentially the same model parameters as a more general fit. This demonstrates that the covariance of the chosen interaction kernel is responsible for the very accurate prediction of the spin-dependent quark–antiquark interactions.

Landscape structure shapes carnivore-mediated seed dispersal kernels

Context Seed dispersal is recognized as having profound effects on the distribution, dynamics and structure of plant populations and communities. However, knowledge of how landscape structure shapes carnivore-mediated seed dispersal patterns is still scarce, thereby limiting our understanding of large-scale plant population processes. Objectives We aim to determine how the amount and spatial configuration of forest cover impacted the relative abundance of carnivorous mammals, and how these effects cascaded through the seed dispersal kernels they generated. Methods Camera traps activated by animal movement were used for carnivore sampling. Colour-coded seed mimics embedded in common figs were used to know the exact origin of the dispersed seed mimics later found in carnivore scats. We applied this procedure in two sites differing in landscape structure. Results We did not find between-site differences in the relative abundance of the principal carnivore species contributing to seed dispersal patterns, Martes foina. Mean dispersal distance and the probability of long dispersal events were higher in the site with spatially continuous and abundant forest cover, compared to the site with spatially aggregated and scarcer forest cover. Seed deposition closely matched the spatial patterning of forest cover in both study sites, suggesting behaviour-based mechanisms underpinning seed dispersal patterns generated by individual frugivore species. Conclusions Our results provide the first empirical evidence of the impact of landscape structure on carnivore-mediated seed dispersal kernels. They also indicate that seed dispersal kernels generated strongly depend on the effect that landscape structure exerts on carnivore populations, particularly on habitat-use preferences.