名优产品与劣质产品，孰优孰劣——消费品市场的博弈分析

由于信息不对称,买者通过逆向选择,在消费品市场上形成’伪劣产品”驱逐“名优产品”,类似于货币史上“劣币驱逐良币”,从而伪劣产品泛滥,而在信息畅通的情况下,消费者的选择是购买名优产品,不买劣质产品,厂商的选择是生产名优产品,或者长期生产劣质产品,但产品无人问津.     

On a non-abelian invariant on complex surfaces of general type

In this paper, we give certain homotopy and diffeomorphism versions as a generalization to an earlier result due to W.S. Cheung, Bun Wong and Stephen S. T. Yau concerning a local rigidity problem of the tangent bundle over compact surfaces of general type.     

Carathéodory bounds for integer cones

We provide analogues of Carathéodory's theorem for integer cones and apply our bounds to integer programming and to the cutting stock problem. In particular, we provide an NP certificate for the latter, whose existence has not been known so far.     

非线性二阶中立型时滞微分方程正解的存在性

考虑非线性二阶中立型微分方程,[a(t)x(t)-∑ from i=1 to m (p_i(t)x(τi(t)))]″-∫from n=a to b (f(t,ξ,x[g(t,ξ)])dσ(ξ))=0,t≥t_0,和相应不等式[a(t)x(t)-∑ from i=1 to m (p_i(t)x(τi(t)))]″-∫from n=a to b (f(t,ξ,x[g(t,ξ)])dσ(ξ))≥0,t≥t_0.存在正解是相互等价的.其中a(t),pi(t)∈C([t0,∞),R+),a(t)>0,τi(t)∈C(R~+,R~+),τi(t)t,limt→∞τi(t)=∞(i=1,2,…,m).g(t,ξ)∈C([t_0,∞)×[a,b],R+).g(t,ξ)是分别关于t和ξ的增函数.g(t,ξ)t,ξ∈[a,b],limt→∞,ξ∈[a,b]g(t,ξ)=∞.f(t,ξ,x)∈C([t_0,∞)×[a,b]×R,R+).当x>0时,xf(t,ξ,x)>0.σ(ξ)∈C([a,b],R),且σ(ξ)非减.     

一类非齐次A-调和方程组很弱解的性质

该文应用Hodge分解定理，得到了非齐次A—调和方程组-Di(A^ij(x,Du)) Difj(i(x)=0,j=1,…，m的很弱解是弱解，进一步，利用Morrey空间法与Campanato空间法以及齐次化方法，作者得出了该方程的很弱解是局部Hoelder连续的，并且得出了Hoelder连续指数μ与λ之间的多值函数关系式．     

Bernstein theorems and transformations of correlation measures in statistical physics

We study the class of endomorphisms of the cone of correlation functions generated by probability measures. We consider algebraic properties of the products (·, ?) and the maps K, K ^?1 which establish relationships between the properties of functions on the configuration space and the properties of the corresponding operators (matrices with Boolean indices): F(γ) → F?(γ) = {F(α?β)}α,β?γ. For the operators F?(γ) and F?(γ), we prove conditions which ensure that these operators are positive definite; the conditions are given in terms of complete or absolute monotonicity properties of the function F(γ).     

Dependence of the Convergence Domain of Spectral Expansions on the Geometry of the Set of Discontinuity of the Function Being Expanded

For piecewise smooth functions, we indicate their domains of convergence and Riecz summarizability of their spectral expansions related to the Laplace operator in ? ⁿ , depending on the geometry of points of discontinuity of the function being expanded.     

Large deviations for the two-dimensional Navier–Stokes equations with multiplicative noise

A Wentzell–Freidlin type large deviation principle is established for the two-dimensional Navier–Stokes equations perturbed by a multiplicative noise in both bounded and unbounded domains. The large deviation principle is equivalent to the Laplace principle in our function space setting. Hence, the weak convergence approach is employed to obtain the Laplace principle for solutions of stochastic Navier–Stokes equations. The existence and uniqueness of a strong solution to (a) stochastic Navier–Stokes equations with a small multiplicative noise, and (b) Navier–Stokes equations with an additional Lipschitz continuous drift term are proved for unbounded domains which may be of independent interest.     

新的不动点定理及应用

本文获得了几个压缩型映射的不动点定理,改进了相应文献的结果．应用该定理,给出了一类时滞积分方程的正概周期解的存在性结果．推广了已有的结果．