CONSERVATION OF ENDANGERED ENDEMIC SEABIRDS WITHIN A MULTI‐PREDATOR CONTEXT: THE BARAU'S PETREL IN RÉUNION ISLAND

Abstract Seabirds breeding on islands are vulnerable to introduced predators, such as rats and cats, and the removal of such predators is generally viewed as a priority for seabird conservation and restoration. However, multiple invasive mammal species interacting may generate unexpected outcomes following the removal (eradication) of one species. Generally these indirect interactions are not well understood or demonstrated. We propose and study a prey (seabird)‐mesopredator (rat)‐superpredator (cat) model, taking into account the juvenile stages in the prey population, in order to direct conservation management for seabird conservation. We give a more biologically realistic differential system than those studied before (Courchamp et al. [1999] ; Fan et al. [2005] ), in particular for long‐lived seabird species. We present a theoretical study and show existence and uniqueness of a positive solution as well as a qualitative study of the equilibria that may appear. Because standard numerical methods, usually implemented in scientific softwares, can fail to give the right biological approximations ( Anguelov et al. [2009] ), we propose a reliable algorithm that preserves most of the qualitative properties of the continuous system, using the theory of nonstandard finite difference methods. Finally, we use biologically realistic parameters available for the representative Barau's petrel (Pinet et al. [2008] ), an endemic species from Réunion island, to present numerical simulations that support the theoretical study. Cats play the major role in seabird prey population dynamics. Seasonality in seabird breeding delays but does not prevent extinction. In all scenarios, cat control (or preferably eradication) is imperative to prevent extinction of vulnerable long‐lived seabirds, like the Barau's petrel.     

An axiomatization of minimal curb sets

Norde et al. [Games Econ. Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent. A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games. The minimal curb sets of Basu and Weibull [Econ. Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.     

NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY

In this article, we study the nonlinear stochastic heat equation in the spatial domain R~d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z~d to that on R~d. Then,we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.     

Mathematical modelling of plastic deformation instabilities with two delays

In this paper we present a new model describing the temporal evolution for multi-instabilities of plastic deformation of stressed monocrystal. This model generalizes that with a single delay presented in [12] and [13]. The plastic instability is due to the increase in dislocation density and the mutual interaction between dislocations, and can be explained by a phase shift, characterized by a time delay between the nucleation and the propagation of dislocations. Here, we consider the general case when several deformation-mechanisms are active, leading to several delays. Using a linear analysis, we deduce a differential equation with two delays. We present some results on existence and stability of the solution according to the characteristics of material and the two delays. Numerical examples for stability and instability of material close to a mean stress using the MATLAB software are also investigated.     

Weakly Nonlocal Solitary Waves in a Singularly Perturbed Nonlinear Schrödinger Equation

We consider the nonlinear Schrödinger equation perturbed by the addition of a third-derivative term whose coefficient constitutes a small parameter. It is known from the work of Wai et al. [1] that this singular perturbation causes the solitary wave solution of the nonlinear Schrödinger equation to become nonlocal by the radiation of small-amplitude oscillatory waves. The calculation of the amplitude of these oscillatory waves requires the techniques of exponential asymptotics. This problem is re-examined here and the amplitude of the oscillatory waves calculated using the method of Borel summation. The results of Wai et al. [1] are modified and extended.     

Martingale solutions and Markov selection of stochastic 3D Navier-Stokes equations with jump

In this paper, we study the existence of martingale solutions of stochastic 3D Navier-Stokes equations with jump, and following Flandoli and Romito (2008) [7] and Goldys et al. (2009) [8], we prove the existence of Markov selections for the martingale solutions.     

Ranking decision-making units using common weights in DEA

Data envelopment analysis (DEA) is a linear programming technique that is used to measure the relative efficiency of decision-making units (DMUs). Liu et al. (2008) [13] used common weights analysis (CWA) methodology to generate a CSW using linear programming. They classified the DMUs as CWA-efficient and CWA-inefficient DMUs and ranked the DMUs using CWA-ranking rules. The aim of this study is to show that the criteria used by Liu et al. are not theoretically strong enough to discriminate among the CWA-efficient DMUs with equal efficiency. Moreover, there is no guarantee that their proposed model can select one optimal solution from the alternative components. The optimal solution is considered to be the only unique optimal solution. This study shows that the proposal by Liu et al. is not generally correct. The claims made by the authors against the theorem proposed by Liu et al. are fully supported using two counter examples.     

On time flows of minimizers of general convex functionals of linear growth with variable exponent in BV space and stability of pseudosolutions

Here we examine a method of selective smoothing in image restoration in BV space using a variable exponent functional of linear growth. Variable exponent growth was suggested in P. Blomgren et al. (1997) [6], and in Y. Chen et al. (2006) [8] the notion of a pseudosolution of the minimization problem is discussed, as well as the proof of existence and uniqueness of the solution of the time flow for the associated time dependent PDE. Here we prove stability for pseudosolutions, while also discussing the case for more general convex functionals of linear growth and variable exponent for use as an approximation for the time flow other than that which is used in Y. Chen et al. (2006) [8].     

Formal first integrals for periodic systems

In the present paper, we give an elementary proof for the result of Li et al. (2003) [6] about nonexistence of formal first integrals for periodic systems in a neighborhood of a constant solution. Moreover, we present a criterion about partial existence of formal first integrals for the periodic system, by using the Floquet's theory.     

Deformation Argument under PSP Condition and Applications

In this paper we introduce a new deformation argument, in which C~0-group action and a new type of Palais-Smale condition PSP play important roles. This type of deformation results are studied in [17, 21] and has many different applications [10,11, 17, 21] et al. Typically it can be applied to nonlinear scalar field equations. We give a survey in an abstract functional setting. We also present another application to nonlinear elliptic problems in strip-like domains. Under conditions related to [5,6], we show the existence of infinitely many solutions. This extends the results in [8].     

Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation

In this paper, the traditional inventory lot-size model is extended to allow not only for general partial backlogging rate but also for inflation. The assumptions of equal cycle length and constant shortage length imposed in the model developed by Moon et al. [Moon, I., Giri, B.C., Ko, B., 2005. Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European Journal of Operational Research 162(3), 773–785] are also relaxed. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established. The theoretical results here amend those in Yang et al. [Yang, H.L., Teng, J.T., Chern, M.S., 2001. Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Naval Research Logistics 48(2), 144–158] and provide the solution to those two counterexamples by Skouri and Papachristos [Skouri, K., Papachristos, S., 2002. Note on “deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand” by Yang et al. Naval Research Logistics 49(5), 527–529.]. Finally we propose an algorithm to find the solution, and obtain some managerial results by using sensitivity analyses.     

关于非协调位移元与杂交应力元的对应性

本文阐明了E.L.Wilson[3]等的非协调移位元与卞学鐄的杂交应力元之间所存在的对应性.     

Comment on “HAM solutions for boundary layer flow in the region of the stagnation point towards a stretching sheet” [Comm. Nonlinear Sci. Numer. Simul. 15 (2010) 475–481]

Recently, Nadeem et al. [1] discussed the HAM solution for the boundary layer flow in the region of the stagnation point towards a stretching sheet. Crucial flaws in [1] are pointed out in this comment.     

Classification of nonoscillatory solutions of second order self-adjoint neutral difference equations

This paper deals with existence of positive solutions of nonlinear elliptic singular boundary value problems in a ball. It is shown that results of Grandall et al. [1] and [2] follow as special cases of our results proved in this article.     

Nonlinear instability of Phillips model

We investigate the instability of two-layer Phillips model in this paper, which is a prototypical geophysical fluid model. Using the results of Guo and Strauss et al, we obtained linear instability implies nonlinear instability provided the linearized system has an exponentially growing solution.     

On recent developments in the theory of abstract differential equations with fractional derivatives

This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6] and [7], Mophou (2010) [8] and [9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.     

Existence of invariant tori for differentiable Hamiltonian vector fields without action-angle variables

We proved the theorem for existence of invariant tori in differentiable Hamiltonian vector fields without action-angle variables. It is a generalization of the result of de la Llave et al. [4] that deals with analytic vector fields.     

Multiobjective programming in optimization of interval objective functions — A generalized approach

We generalize known concepts (those introduced by Ishihuchi and Tanaka [1] and Rommerlfanger et al. [2]) of the solution of the linear programming problem with interval coefficients in the objective function based on preference relations between intervals. We unify all the discussed concepts as well as the corresponding solution methods into one general framework.     

A note on a Cauchy problem for the Laplace equation: Regularization and error estimates

In this paper, a Cauchy problem for the Laplace equation is investigated. Based on the fundamental solution to the elliptic equation, we propose to solve this problem by the truncation method, which generates well-posed problem. Then the well posedness of the proposed regularizing problem and convergence property of the regularizing solution to the exact one are proved. Error estimates for this method are provided together with a selection rule for the regularization parameter. The numerical results show that our proposed numerical methods work effectively. This work extends to earlier results in Qian et al. (2008) [14] and Hao et al. (2009) [5].