Multiple solutions for fourth-order boundary value problem

In this paper, we study the existence and multiplicity of nontrivial solutions for the fourth-order two point boundary value problems. Making use of the theory of fixed point index in cone and Leray-Schauder degree, under general conditions on nonlinearity, we prove that there exist at least six different nontrivial solutions for the fourth-order two point boundary value problems. Furthermore, if the nonlinearity is odd, we obtain that there exist at least eight different nontrivial solutions.     

Time periodic solution of the viscous Camassa-Holm equation

This paper discusses the viscous Camassa-Holm equation with a periodic boundary condition. The existence and uniqueness of a time periodic solution are investigated by using the Galerkin method and Leray-Schauder fixed point theorem.     

制冷剂替代物相平衡性质的分子动力学模拟

本文利用分子动力学模拟算法研究制冷剂替代物的气液相平衡性质。通过将制冷剂替代物作为极性的2CLJ流体处理,建立了针对它们的 2CLJD 势能模型。利用 NPT+Test Particle 算法对五种制冷剂替代物 (HFC-152a,HFC-143a,HFC-134a,HCFC-142b和HFC-227ea)的气液相平衡性质进行了计算,同时验证了计算结果的热力学一致性。模拟结果与 NIST 的 REFPROP 数据库的最大相对偏差在2％以内。     

Novel extracellular polymeric substances produced by Cupriavidus necator IPT 027 grown on glucose and crude glycerol originated from biodiesel

The aim of this study was to evaluate the production and properties of novel extracellular polymeric substances (EPS) from glucose (EPS 1) and crude glycerol (CG) from castor beans oil (EPS 2). Cupriavidus necator IPT 027 cultivated with glucose and CG (35 °C, 150 rpm, 72 hr, pH 7, shaker) produced approximately 1.60 ± 0.01 and 2.83 ± 0.02 g l^?1 EPS, respectively, with high‐molecular weight (3.89 × 10⁵ and 1.89 × 10⁷ Da) and constituted of different functional groups such as uronic acid, monosaccharides (glucose, mannose, arabinose, and fucose) and primary amine group. The composition of the fermentable substrate influenced the melting temperature (221.11 and 230.18 °C), crystallinity (34.36% and 37.11%), degradation temperature (255.06 and 296.62 °C) and morphology. EPS showed pseudoplastic non‐Newtonian fluid behavior in the aqueous solutions, presenting potential applicability biotechnological and industrial mainly in food industry as emulsifiers and biosurfactants. This is the first study on the production and characterization of EPS obtained by C. necator IPT 027 in culture with glucose and CG. Copyright © 2016 John Wiley & Sons, Ltd.     

奇异超线性半正定二阶周期边值问题的正解

基于格林函数理论,主要利用Lerray-Schauder抉择定理和上下解方法针对半正定条件下,奇异超线性二阶周期边值问题正解的存在性进行推理证明,获取了奇异超线性二阶周期边值问题的一个正解.     

Phragmen-Lindelöf alternative results for the initial boundary problem of stokes equation

In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation, i. e. we show that the energy expression for the solution of the initial boundary problem must either grow exponentially or decay exponentially with axial distance from the end of a semi-infinite strip. For the case of decay, we also establish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.Project supported by the National Natural Science Foundation of China and Zhongshan University Science Foundation     

Two positive nontrivial solutions for a class of semilinear elliptic variational systems

We obtain existence and localization results of positive nontrivial solutions for a class of semilinear elliptic variational systems. The proof is based on variants of Schechter's localized critical point theorems for Hilbert spaces not identified to their duals and on the technique of inverse-positive matrices. The Leray-Schauder boundary condition is also involved.     

An intermediate wavelength, weakly nonlinear theory for the evolution of capillary gravity waves

A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity.     

多元分布下单边备择假设的两步检验

x~2检验是熟知的拟合优度检验.它适用于任意的备择假设,尤其是适用于一般的备择假设"H_0不真"的情况.但是,当备择假设是一个单边假设时,x~2检验没有用到单边假设所提供的信息.因此,一个充分利用单边备择假设信息的检验是有可能优于传统的x~2检验的.本文就是利用单边备择假设的信息给出了一个两步检验,并通过一个例子,详细介绍了两步检验法的实施,说明了其应用.     

一类非局部Cahn-Hilliard方程弱解的存在唯一性

研究一类对流非局部Cahn-Hilliard方程的Neumann问题.通过一致Schauder估计和Leray-Schauder不动点定理,得到了该问题经典解的存在唯一性.进而,利用弱收敛方法得到了该问题弱解的存在唯一性.