Asymptotic Dynamics of a Single-species Model with Resource-dependent Dispersal in One Dimension

In this paper,we study the asymptotic dynamics of a single-species model with resource-dependent dispersal in one dimension.To overcome the analytical difficulties brought by the resource-dependent dispersal,we use the idea of changing variables to transform the model into a uniform dispersal one.Then the existence and uniqueness of positive stationary solution to the model can be verified by the squeezing argument,where the solution plays a crucial role in later analyses.Moreover,the asymptotic behavior of solutions to the model is obtained by the upper-lower solutions method.The result indicates that the solutions of the model converge to the corresponding positive stationary solution locally uniformly in one dimension as time goes to infinity.

一类含有位势的快扩散方程组的Fujita指标

研究带有位势的快扩散方程组ut=Δum-Ф(x)um+vp,vt=Δvn-ψ(x)vn+uq的Fujita指标的存在性,其中空间维数N≥2,p,q>1,pq>1,0<m,n<1.主要利用比较原理、试验函数法以及上、下解法得到它的Fujita指标为pc=[2+m(mα1+N)]/(N+nα2),qc=[2+n(nα2+N)]/(N+mα1).

Banach空间中二阶Volterra型积分微分方程边值问题解的存在性

利用上、下解法在正规锥上证明了二阶非线性Volterra型积分微分方程边值问题解的存在性。

A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems

This paper presents new existence results for singular discrete boundary value problems. In particular our nonlinearity may be singular in its dependent variable and is allowed to change sign.

An Approach to Underwater Image Enhancement Based on Image Structural Decomposition

Underwater imaging posts a challenge due to the degradation by the absorption and scattering occurred during light propagation as well as poor lighting conditions in water medium Although image filtering techniques are utilized to improve image quality effectively, problems of the distortion of image details and the bias of color correction still exist in output images due to the complexity of image texture distribution. This paper proposes a new underwater image enhancement method based on image struc- tural decomposition. By introducing a curvature factor into the Mumford_Shah_G decomposition algorithm, image details and struc- ture components are better preserved without the gradient effect. Thus, histogram equalization and Retinex algorithms are applied in the decomposed structure component for global image enhancement and non-uniform brightness correction for gray level and the color images, then the optical absorption spectrum in water medium is incorporate to improve the color correction. Finally, the en- hauced structure and preserved detail component are re.composed to generate the output. Experiments with real underwater images verify the image improvement by the proposed method in image contrast, brightness and color fidelity.

Existence Theorems for a Fifth-Order Boundary Value Problem

Abstract： In this paper, we study the existence of a solution for fifth-order boundary value problem{u（5）（t）＋f（t,u（t）,u＂（t）=0,0〈t〈1）/u（0）=u＇（0）=u＇（1）=u＂（1）=u（4）（0）=0 Where f ∈ C（[0,1] × R2, R）. By placing certain restrictions on the nonlinear term f, we prove the existence of at least one solution to the boundary value problem with the use of the lower and upper solution method and Schauder fixed-point theorem. The construction of lower or upper solution is also present.ed. Boundary value problems of very similar type are also considered.

Practical Application of Two-Way Multiple Overlapping Relationships in a BDM Network

Today, most construction projects in urban environments are complex high-rise buildings that present unique challenges, including local building ordinances and restrictions, adjoining public and residential areas, narrow sidewalks and streets, and underground utilities, all of which require extensive planning and tight schedules. A major problem facing such projects is to formulate realistic schedules that will make it possible to meet contractual completion dates with limited resources and budgets. The scheduling software products currently used in construction projects, which include Primavera P6, Microsoft Project, etc., are not actually applied as a scheduling tool in practical construction projects, which instead generally depend on Microsoft Excel or a bar-chart. This is because the existing scheduling programs cannot provide more user-oriented schedule format such as representing two-way multiple overlapping relationships. To overcome this deficiency, the BDM （beeline diagramming method） is proposed as a new networking technique in 2010. But two-way multiple overlapping relationships generate the loop in a conventional schedule computation process. This paper addresses the loop phenomenon of two-way multiple overlapping relationships in a BDM network as well as proposes the solutions of them, and then presents a practical application of two-way multiple overlapping relationships at a real project.

Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation

This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.

Global dynamics of a nonlocal population model with age structure in a bounded domain:A non-monotone case

We study the global dynamics of a nonlocal population model with age structure in a bounded domain. We mainly concern with the case where the birth rate decreases as the mature population size become large. The analysis is rather subtle and it is inadequate to apply the powerful theory of monotone dynamical systems. By using the method of super-sub solutions, combined with the careful analysis of the kernel function in the nonlocal term, we prove nonexistence, existence and uniqueness of positive steady states of the model.Moreover, due to the mature individuals do not diffuse, the solution semiflow to the model is not compact. To overcome the difficulty of non-compactness in describing the global asymptotic stability of the unique positive steady state, we first establish an appropriate comparison principle. With the help of the comparison principle,we can employ the theory of dissipative systems to obtain the global asymptotic stability of the unique positive steady state. The main results are illustrated with the nonlocal Nicholson's blowflies equation and the nonlocal Mackey-Glass equation.