收入分布曲线的线性正态插值函数拟合方法

用样本数据的分组均值与总体方差为参数的正态函数作为插值基函数,构造出线性正态插值函数曲线以拟合中国城乡居民收入的概率分布函数曲线,并论证了这样构造的线性正态插值函数存在且唯一,此插值函数任意阶可微.利用拟合的正态插值函数曲线计算出拟合的函数面积估计值并与相应的样本数据直方图面积做比较,进而得出正态插值函数拟合曲线面积与样本数据直方图的面积误差比率.     

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.     

Maxima of entries of Haar distributed matrices

Let _n=(_ij) be an n×n random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W_n:=max_1i,jn|_ij|. We obtain the limiting distribution and a strong limit theorem on W_n. A tool has been developed to prove these results. It says that up to n/( log n)² columns of _n can be approximated simultaneously by those of some Y_n=(y_ij) in which y_ij are independent standard normals. Similar results are derived also for the unitary group U(n), the special orthogonal group SO(n), and the special unitary group SU(n).Mathematics Subject Classification (2000):15A52, 60B10, 60B15, 60F10     

Large deviation for the empirical eigenvalue density of truncated Haar unitary matrices

Let U_m be an m×m Haar unitary matrix and U_[m,n] be its n×n truncation. In this paper the large deviation is proven for the empirical eigenvalue density of U_[m,n] as m/n→λ and n→∞. The rate function and the limit distribution are given explicitly. U_[m,n] is the random matrix model of quq, where u is a Haar unitary in a finite von Neumann algebra, q is a certain projection and they are free. The limit distribution coincides with the Brown measure of the operator quq.     

Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models

In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.     

The affine Plateau problem

In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.

     

Boundedness of admissible area function on nonisotropic Lipschitz space

Let be the unit ball in , let be the unit sphere, and let be the admissible area function. In this paper, we show that if , then and there exists a constant such that .

     

Concentration of area in half-planes

For the standard class of normalized univalent functions analytic in the unit disk , we consider a problem on the minimal area of the image concentrated in any given half-plane. This question is related to a well-known problem posed by A. W. Goodman in 1949 that regards minimizing area covered by analytic univalent functions under certain geometric constraints. An interesting aspect of this problem is the unexpected behavior of the candidates for extremal functions constructed via geometric considerations.

     

An Area Modulus of Elasticity: Definition and Properties

A new modulus of elasticity is defined to be the ratio of an equibiaxial stress to the relative area change in the planes in which the stress acts. This area modulus of elasticity is intermediate in properties between Young's modulus and the bulk modulus. Expressions for the area modulus are computed in isotropic elasticity. A simple, convenient expression for the compliance tensor of transverse isotropy is found in terms of, amongst others, the longitudinal (axial) area modulus and this leads to a new, concise condition for positive definiteness of the compliance tensor. The limits of incompressibility, inextensibility and constant area are briefly considered. This revised version was published online in August 2006 with corrections to the Cover Date.     

一类非牛顿系统弱解的长时间性态

本文讨论一类非牛顿系统弱解的长时间性态,证明解在L2 范数下的衰减速率为(1 t)-n/4 达到和线性热方程一致.