Periodic Eigenvalues of One-Dimensional p-Laplacian with Indefinite Weights

Rotation numbers are used in this paper to study the periodic and anti-periodic eigenvalues of the one-dimensional p-Laplacian with a periodic weight which changes sign. The analysis proves that for any nonnegative integer n, ρ^-1(n/2) is the union of two closed intervals, one of which lies in R^ and the other in R^-, and the endpoints of these intervals yield the corresponding periodic and anti-periodic eigenvalues.     

Calculation of non－mono chromatic reflectance of Co／Sb multilayer

It is well known that the structure defects, such as the interfacial roughness, interdiffusion and chemical reaction at interface, can degrade the optical properties for soft X-ray multilayer[1—5]. For example, the interfacial rough-ness can lead to a loss of spectral reflectance, which has been investigated for many years, and number theories for the scattering of electromagnetic radiation by interfacial roughness have been formulated[6,7]. In addition, the fluc-tuation of the period can als…     

Solution and order number methods for multiple ob－jective decision making with incomplete knowledge

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Approximate solution for nonlinear model of the second and half order reactions in porous catalyst by decomposition method

The problem of the process of coupled diffusion and reaction in catalyst pellets is considered for the case of second and half order reactions. The Adomian decomposition method is used to solve the non-linear model. For the second, half and first order reactions, analytical approximate solutions are obtained. The variation of reactant concentration in the catalyst pellet and the effectiveness factors at φ＜10 are determined and compared with those by the BAND's finite difference numerical method developed by Newman. At lower values of φ, the decomposition solution with 3 terms gives satisfactory agreement with the numerical solution; at higher values of φ, as the term number in the decomposition method is increased, an acceptable agreement between the two methods is achieved. In general, the solution with 6 terms gives a satisfactory agreement.     

Robust predictive control of uncertain intergrating linear systems with input constraints

This paper presents a two-stage robust model predictive control (RMPC) aigorithm named as IRMFC for uncertain linear integrating plants described by a state-space model with input constraints. The global convergence of the resulted closed loop system is guaranteed under mild assumption. The simulation example shows its validity and better performance than conventional Min-Max RMPC strategies.     

Preparation of 3-D porous fibroin scaffolds by freeze drying with treatment of methanol solutions

In this study, silk scaffolds with appropriate porous structures were prepared by adjusting solution concentrations and providing treatment with methanol solutions in the way of freeze drying. The effects of the preparation conditions on the microstructures and properties of the scaffolds were discussed. Fibroin solutions with different concentrations of 4, 6, 8, 10 wt% were used respectively to prepare the scaffolds. The effects of the addition of 20 vol% methanol before or after freeze drying to the 4 wt% fibroin solution were investigated. As demonstrated by Scanning Electron Microscope (SEM), the fib-roin scaffolds prepared without methanol had porous microstructures composed of thin sheets, and the sizes of the pores decreased with the increase of the fibroin solution concentrations, while the scaffolds prepared in the presence of methanol showed porous microstructures formed by fine-particle aggregates. The porosities and mechanical properties of the prepared fibroin scaffolds under different conditions were tested. The crystalline structures and conformations of the fibroin scaffolds were detected by Fourier transform infrared spectroscopy (FT-IR) and X-ray diffraction (XRD).     

Linear stability of numerical methods for systems of functional differential equations with a proportional delay

The numerical solution of functional differential equations with a proportional delay is considered. The stability of general linear methods for linear systems of neutral type is investigated. It is shown that a general linear method with strict stability at infinity can preserve the asymptotic stability of the underlying system if we employ an appropriate equi-stage interpolation to approximate the delay argument.     

Development of Compact Standing－wave Guides with on－Axis Coupler of Electron Linac for Medical Radio

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Algebraically explicit analytical solutions of unsteady conduction with variable thermal properties in cylindrical coordinate

The analytical solutions of unsteady heat conduction with variable thermal properties(thermal conductivity,density and specific heat are functions of temperature or coordinates)are meaningful in theory.In addition,they are very useful to the computational heat conduction to check the numerical solutions and to develop numerical schemes,grid generation methods and so forth.Such solutions in rectangular coordinates have been derived by the authors.Some other solutions for 1-D and 2-D axisymmetrical heat conduction in cylin drical coordinates are given in this paper to promote the heat conduction theory and to develop the relative computational heat conduction.     

具有次可加位势的二阶系统的周期解

通过使用最小作用原理,对于具有次可加位势的非自治二阶系统,获得了一个周期解的存在性定理.     

一类阻尼振动问题的变分原理及周期解的存在性定理

对如下的阻尼振动问题:{ü(t) g(t) (u) (t) = ▽F(t,u(t) ),a.e.t∈[0,T],u(0) -u(T) = (u) (0) - (u) (T) =0.此处,T＞0,g∈L1(0,T,;R),G(t)=∫1 0 g(s)ds,G(T)=0,F:[0,T]×RN→R,给出其变分原理,并得到2个周期解的存在性定理.     

一类非自治二阶差分方程的周期解

研究一类二阶差分方程-Δ2x(t-1)=Fx(t,x),t∈Z,其中,f∈C(Z×Rm,R),xF(t,x)=■∈C(Z×Rm,Rm)为F关于x的梯度,且存在一个正整数M使得F(t M,x)=F(t,x).应用临界点理论,结合环绕的方法,给出了这个方程的非常数周期解存在性的一个充分条件,改进了已有文献中的结果.     

含有次凸位势的二阶Hamilton系统周期解

研究非自治的二阶Hamilton系统:±u= F(t,u(t)),a.e.t∈[0,T],u(0)-u(T)=u(0)-u(T)=0的周期解.当位势函数是一个(λ,μ)次凸函数与一个次二次函数的和时,利用极小作用原理和鞍点定理得到了非平凡周期解存在的几个充分条件.更全面地讨论了含有(λ,μ)次凸位势的Hamilton系统的周期解,推广和补充了某些已知的结果.     

非自治共振二阶离散Hamilton系统的周期解

研究了非自治二阶离散Hamilton系统周期解的存在性问题。在非线性项是次线性增长时,将这类Hamil-ton系统的周期解转化为定义在一个适当空间上泛函的临界点,然后利用临界点理论建立了此类系统周期解的存在性结果。     

非自治二阶系统周期解的存在性

这篇文章的目的是研究非自治二阶系统¨u(t)=F(t,u(t)),a.e.t∈[0,T]u(0)-u(T)=u(0)-u(T)=0周期解的存在性,通过最小作用原理获得一些存在性定理。     

一类推广的二阶Hamilton系统的周期解

分别利用极小作用原理及鞍点定理在势泛函为一次线性泛函和次二次泛函之和的条件下讨论了一类非自治二阶Hamilton系统周期解的存在性.     

某类非自治二阶系统具鞍点特征的周期解的存在性

研究一类非自治二阶系统周期解的存在性问题．利用鞍点约化方法,证明了该系统具鞍点特征的周期解的存在性,得到了一些新的可解性条件．     

一类二阶非Hamiltonian系统的变分原理及周期解的存在性定理

研究了阻尼振动问题{ü（t）＋g（t）u（t）=△F（t,u（t））,a.e.t∈[0,T]; u（0）-u（T）=u（0）-u（T）=0其中,T＞0,g（t）∈L^∞（0,T,R）,G（t）=∫^tog（s）ds,G（T）=0,F;[0,T]×R^N→R,给出了其变分原理和2个周期解的存在性定理,即使在g（t）=0特殊情况下,所得结果也是新的。     

非自治二阶系统周期解的存在性

将鞍点归约方法应用于非自治二阶系统,得到了非自治二阶系统在次线性增长条件下的周期解的存在性定理.