两响应Haar小波回归模型最优设计

本文讨论两响应线性Haar小波模型的最优试验设计问题.假定每个响应变量与自变量之间的回归关系可以用一个线性小波多项式表示.本文给出一个设计,它同时具有D-,A-和Q-最优性,并且与两响应变量的协方差阵无关.     

Positive Solutions for Singular Quasilinear Schrodinger Equations with One Parameter,II

We establish the existence of positive bound state solutions for the singular quasilinear Schrodinger equation iψ/t=-div（ρ（｜ψ｜^2） ψ）＋ω（｜ψ｜62）ψ-λρ（｜ψ｜^2）ψ,x∈Ω,t〉0,where ω（τ^2）τ→∞ as τ→ 0 and, λ 〉 0is a parameter and Ω is a ball in ^RN. This problem is studied in connection with the following quasilinear eigenvalue problem with Dirichlet boundary condition -div（ρ（｜ ψ｜^2） ψ）=λ1ρ（｜ψ｜^2）ψ=λ1ρ（｜ψ｜^2）ψ,x∈Ω.Indeed, we establish the existence of solutions for the above Schrodinger equation when A belongs to a certain neighborhood of the first eigenvahie λ1 of this eigenvalue problem. The main feature of this paper is that the nonlinearity ω｜ψ｜^2 is unbounded around the origin and also the presence of the second order nonlinear term. Our analysis shows the importance of the role played by the parameter A combined with the nonlinear nonhomogeneous term div （ρ（｜ ψ｜^2） ψ） which leads us to treat this prob- lem in an appropriate Orlicz space. The proofs are based on various techniques related to variational methods and implicit function theorem.     

Global Weak Solutions to One-Dimensional Compressible Navier-Stokes Equations with Density-Dependent Viscosity Coefficients

We prove the global existence of weak solutions of the one-dimensional compressible Navier-stokes equations with density-dependent viscosity. In particular, we assume that the initial density belongs to L^1 and L^∞, module constant states at x = -∞ and x = ＋∞, which may be different. The initial vacuum is permitted in this paper and the results may apply to the one-dimensional Saint-Venant model for shallow water.     

应用推广的比较法得到的概率估计的几个结果

我们推广了比较法, 提出一个新方法得到 概率$\pr(X\leq t)$的可达的半参数界, 这里$X\in[0,M]$有给定的\, $\ep X=m_1$和$\ep X^2=m_2$. 我们的证明是初等的.     

双曲正弦和双曲余弦函数的幂级数余项的不等式

该文建立了双曲正弦和双曲余弦函数的幂级数余项的若干不等式.     

Green’s Functions of Partial Differential Equations with Involutions

In this paper we develop a way of obtaining Green''s functions of partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat transfer in a conducting plate which is bent in half.     

基于金属有机骨架材料和酶切放大的适配体荧光法检测副溶血性弧菌

基于铜基金属有机骨架(Cu-MOF)的荧光猝灭性质、核酸适配体的选择识别能力及核酸外切酶的水解放大信号作用,建立了一种快速检测副溶血性弧菌(V.P)的适配体荧光法.该文在室温下合成Cu-MOF,对其形貌、结构、荧光猝灭机理进行了系统研究,考察了Cu-MOF的体积、猝灭时间、核酸外切酶用量、恢复时间及试剂加入顺序等分析条...     

一类二阶脉冲微分方程三点边值问题三个非负解的存在性

研究一类二阶脉冲微分方程三点边值问题三个非负解的存在性,利用Leggett-Williams不动点定理得到了方程三个非负解存在的充分条件.     

不含4-圈和5-圈的平面图的非正常2-染色的一个新结果

设d_1,d_2,···,d_k是k个非负整数,若图G=(V,E)的顶点集V能被剖分成k个子集V_1,V_2,···,V_k,使得对任意的i=1,···,k,V_i的点导出子图G[Vi]的最大度至多为di,则称图G是(d_1,d_2,···,d_k)-可染的,本文证明了既不含4-圈又不含5-圈的平面图是(9,9)-可染的.     

不含5-圈和6-圈的平面图的(2,1)-全标号

图G的(2,1)-全标号是对图G的顶点和边的一个标号分配,使得:(1)任意两个相邻顶点标号不同;(2)任意两条相邻边标号不同;(3)任意顶点与其相关联的边标号至少相差2.两个标号的最大差值称为跨度,图G的所有(2,1)-全标号的最小跨度称为(2,1)-全标号数,记为λ_2~T(G).本文证明了如果G是一个?=p+5的平面图,且G不包含5-圈和6-圈,那么λ_2~T(G)=2?-p,p=1,2,3.