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Abstract: We study theoretically the effects of pulse interactions mediated by the gain and absorber dynamics in a passively mode-locked laser containing a slow saturable absorber, and operating in a regime with several pulses coexisting in the cavity. [Copyright &y& Elsevier]

The recent rapid growth of the woodpigeon population in the British Isles is a cause for concern for environmental managers. It is unclear what has driven their increase in abundance. Using a mathematical model, we explored two possible mechanisms, reduced intraspecific competition for food and increased reproductive success. We developed an age-structured hybrid model consisting of a system of ordinary differential equations that describes density-dependent mortality and a discrete component, which represents the birth-pulse. We investigated equilibrium population dynamics using our model. The two hypotheses predict contrasting population age profiles at equilibrium. We adapted the model to examine the impacts of control measures. We showed that an annual shooting season that follows the period of density-dependent mortality is the most effective control strategy because it simultaneously removes adult and juvenile woodpigeons. The model is a first step towards understanding the processes that influence the dynamics of woodpigeon populations. [Copyright &y& Elsevier]

In this paper, we prove the existence of non-radial solutions to the problem − △ u = f (z , u) , u | ∂ D = 0 on the unit disc D ≔ { z ∈ ℂ : | z | < 1 } with u (z) ∈ R k , where f is a sub-linear continuous function, differentiable with respect to u at zero and satisfying f (e i θ z , u) = f (z , u) for all θ ∈ R , f (z , − u) = − f (z , u). Under the assumption that f respects additional (spacial) symmetries on R k , we investigate symmetric properties of the corresponding non-radial solutions. The abstract result is supported by a numerical example with S 4 -symmetry. [ABSTRACT FROM AUTHOR]