Eigenvalue problems for nonlinear third‐order m‐point p‐Laplacian dynamic equations on time scales

This work deals with the existence and uniqueness of a nontrivial solution for the third‐order p‐Laplacian m‐point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when λ is in some interval. The proofs are based on the nonlinear alternative of Leray–Schauder. To illustrate the results, some examples are included. Copyright © 2014 John Wiley & Sons, Ltd.     

Closed inflationary universe in patch cosmology

In this paper, we study closed inflationary universe models using the Gauss–Bonnet Brane. We determine and characterize the existence of a universe with Ω>1, with an appropriate period of inflation. We have found that this model is less restrictive in comparison with the standard approach where a scalar field is considered. We use recent astronomical observations to constrain the parameters appearing in the model.     

相对湿度对空调中翅片管蒸发器性能的影响

基于换热器几何结构参数以及流路布置等相同的3HP商用空调,在空调工况下,研究了相对湿度对R22替代制冷剂R407C、R410A、R32以及R290在蒸发器内的流动和传热性能的影响规律。研究表明:在一定的条件下,增加环境相对湿度,这五种制冷剂对应蒸发器换热量、压降和质量流量均增加,其中R407C蒸发器换热量最大,R290和R32蒸发器压降和制冷剂质量流量均小于R22蒸发器。在低湿度环境下(约20—30%相对湿度),显热换热占主导因素。随着相对湿度的增加,显然换热减少,潜热换热增强且起主导因素。在满足换热量的要求下,R290在协调压降与质量流量具有一定的优势且满足现行工质替代理念,可以作为现有商用空调的环保型替代工质。     

On the existence of conically self-similar free-vortex solutions to the Navier-Stokes equations

In this paper a proof of existence and non-existence of theconically self-similar free-vortex solutions to the Navier-Stokesequations, originally found by Yih et al. (1982, Phys. Fluids.25, 2147-2158), is presented. This proof clearly establishesthat these solutions do not have any kind of singularity atthe symmetry axis. This analysis gives considerably improvedexistence and non-existence bounds and it is shown that thesebounds are close to optimal in the low-swirling limit. Thisapproach links the questions of existence and non-existencefor the swirling case and for the non-swirling case. The proof,which is an extension of techniques developed by Serrin (1972,Phil. Trans. R. Soc. Lond. 271, 325-360), is based on Schauder'sFixed Point Theorem and is, therefore, non-constructive. Therefore,the paper ends with a brief discussion of the question of howto compute the conically self-similar free-vortex solutionsto the Navier-Stokes equations.     

A General Gordan Alternative Theorem with Weakened Convexity and Its Application

In this paper, we present a general Gordan alternative theorem for presubconvexlike functions in a Hausdorff topological linear space. This is then applied to discuss the saddle point theorem, concave-convex condition and minimax theorem for vector extremum problems.     

Disease control in a food chain model supplying alternative food

Necessity to find a non-chemical method of disease control is being increasingly felt due to its eco-friendly nature. In this paper the role of alternative food as a disease controller in a disease induced predator–prey system is studied. Stability criteria and the persistence conditions for the system are derived. Bifurcation analysis is done with respect to rate of infection. The main goal of this study is to show the non-trivial consequences of providing alternative food in a disease induced predator–prey system. Numerical simulation results illustrate that there exists a critical infection rate above which disease free system cannot be reached in absence of alternative food whereas supply of suitable alternative food makes the system disease free up to certain infection level. We have computed the disease free regions in various parametric planes. This study is aimed to introduce a new non-chemical method for controlling disease in a predator–prey system.     

Predator interference in a Leslie–Gower intraguild predation model

The aim of this paper is to analyze general dynamics features of a new Intraguild Predation (IGP) model where the top predator feeds only on the mesopredator and also affects its consumption rate. Important dynamical aspects of the model are described. Specifically, we prove that the trajectories of the associated system are bounded and defined for all positive time; there is a trapping domain; there are open subsets of parameters, such that the system in the first octant has at most five equilibrium solutions and at most three of them are of co-existence. Here we characterize the existence of Hopf bifurcations and we prove that this model exhibits either one, two or three small amplitude periodic solutions which arise from a zero-Hopf bifurcation. We prove the existence of alternative stable states. Finally, some numerical computations have been given in order to support our analytical results. The importance of some parameters of the model is discussed, in particular the role of the interference rate. The numerical exploration suggests that the equilibrium biomass of each of the three species grows as the level of interference grows.