二维单边截断分布族中经验Bayes估计的收敛速度

本文考虑二维单边截断型分布族中经验Ｂａｙｅｓ估计的收敛速度，在一定的条件下给出了相应的速度，并说明了在较强的条件下收敛速度可充分接近１。     

更新过程的叠对数律

本文利用独立同分布随机变量序列部分和的叠对数律收敛速度结果,在一定条件下,研究了一般更新过程的叠对致律及其收敛速度。     

一维双边截断型分布族中参数函数的经验Bayes估计及其收敛速度

对一维双边截断型分布族构造了参数函数的经验 Ｂａｙｅｓ 估计,在适当的条件下给出了相应的收敛速度,并说明此收敛速度可充分接近 １２ ．     

Linex损失及PA样本下单边截断型分布族参数函数的EB估计

在Linex损失函数下,运用同分布PA样本密度函数的核估计方法,构造了一类单边截断型分布族参数函数的EB估计,并建立了它的收敛速度.在一定条件下,证明了这个收敛速度可充分接近1.     

NA样本下截断型分布族参数的经验Bayes估计

运用NA样本密度函数核估计构造了一类截断型分布族参数的经验Bayes估计，建立了它的收敛速度，证明了在适当条件下该收敛速度可以任意接近于1，文中还给出了适合定理条件的例子。     

Linex损失下二维单边截断型分布族参数的经验Bayes估计

在linex损失函数下,讨论边二维单边截断型分布族参数的经验Bayes(EB)估计问题,文中构造了参数的EB估计,在适当的条件下给出了该估计的收敛速度。并说明在较强条件下收敛速度可充分接近1。     

NA样本及Linex损失下截断族参数的经验EB估计

在Linex损失及NA样本下 ,对一类双边截断型分布族 ,构造了参数的经验Bayes(EB)估计 ,建立了它的收敛速度 .在一定的条件下证明了该收敛速度可以任意接近于 1 ,并给出满足定理条件的例子 .     

单边截断型分布族位置参数的经验Bayes估计的收敛速度

本文对一般的单边截断型分布族,构造了位置参数θ的经验Beyes估计,并建立了它的收敛速度,在一定条件下这个收敛速度可任意接近1/2。最后也给出了满足定理1和定理 2条件的一些例子。     

Linex损失下单边截断型分布族参数的EB估计

本文在Linex损失函数下,讨论单边截断型分布族参数的经验Bayes(EB)估计,并建立了它的收敛速度,并说明了在较强的条件下,收敛速度可充分接的于1。     

均匀分布族 U(0,θ)中经验 Bayes 检验的渐近特征

关于经验 Bayes 检验的研究,目前在文献上能见到一些结果,其中部分是讨论经验Bayes 检验的渐近最优性及其收敛速度,参见[1—4,6,7,9];最近 stijnen 讨论了连续型单参数指数族中经验 Bayes 检验的条件 Bayes 风险的渐近分布,从而得到了精确的收敛速度.本文我们将讨论均匀分布族{U(0,θ),θ>0)中经验 Bayes 检验的条件 Bayes 风险的极限分布,从而得到了经验 Bayes 检验的渐近最优性及其收敛速度.     

Degenerate boundary conditions for the diffusion operator

We describe all degenerate two-point boundary conditions possible in a homogeneous spectral problem for the diffusion operator. We show that the case in which the characteristic determinant is identically zero is impossible for the nonsymmetric diffusion operator and that the only possible degenerate boundary conditions are the Cauchy conditions. For the symmetric diffusion operator, the characteristic determinant is zero if and only if the boundary conditions are falsely periodic boundary conditions; the characteristic determinant is identically a nonzero constant if and only if the boundary conditions are generalized Cauchy conditions.     

Necessary conditions for stochastic dominance: A general approach

In this paper a general method for developing necessary conditions for all degrees of stochastic dominance is derived. The method, a minimization of the expected value of certain functions of the random variable, is used to rederive known necessary conditions for dominance and is then used to derive new necessary conditions. Some of the old and new conditions are then compared empirically using a data set of security returns.     

Regular simple geodesic loops on a tetrahedron

A regular simple geodesic loop on a tetrahedron is a simple geodesic loop which does not pass through any vertex of the tetrahedron. It is evident that such loops meet each face of the tetrahedron. Among these loops, the minimal loops are those which meet each face exactly once. Necessary and sufficient conditions for the existence of minimal loops are obtained. These conditions fall naturally into two categories, conditions in the first category being called coherence conditions and conditions in the second category being called separation conditions. It is shown that for the existence of three distinct minimal loops through any point on the face of a tetrahedron it is necessary and sufficient that the tetrahedron be isosceles, which, in turn, amounts to the tetrahedron satisfying three coherence conditions. All other regular simple geodesic loops on an isosceles tetrahedron are then classified. Finally, coherence conditions for the existence of similar loops on an arbitrary tetrahedron are found.     

Conjugate-point conditions for variational problems with delayed argument

A variational problem with delayed argument is investigated. The existing necessary conditions are first reviewed. New results, two conjugate-point conditions, are then derived for this problem. The method of proof is similar to that used by Bliss for the classical problem. An example shows that the two conditions are not equivalent, and that the first-order necessary conditions, the strengthened Legendre conditions, and the conjugate-point conditions do not in general constitute a set of sufficient conditions for the delay problem. It is shown that a special case, referred to as the separated-integrand problem, leads to considerable simplification of the results for the general problem.     

Eine abstrakte Theorie der Kegel- und Segmentbedingungen

We develop an abstract theory of geometric regularity conditions for subsets of normed linear spaces, of the type which occurs in the theory of Sobolev spaces (cone conditions, …). The theory is to systematize the diversity of existing conditions, to replace complicated conditions by simpler ones, and to clarify the interplay between different conditions. Our main result is a very general decomposition theorem.     

带吸收边界条件的声波方程显式差分格式的稳定性分析

１．引言 在进行无界或半无界区域上各种波动方程的数值求解时,需引进入工边界以限制计算范围,在这些边界上应加相应的人工边界条件．这种边界条件应保证所求得的有界区域上的解很好地逼近原来无界区域上的解．对波动方程来说,就是在边界上人工反射应尽可能地小,使之对区域内部解的影响在允许的误差范围以内.因而它们被称为无反射边界条件或吸收边界条件．这种边界条件还应保证所形成的有界区域上的微分方程定解问题是适定的．这也是各种数值方法稳定的必要条件。 近二十多年来,已发展了声波方程的各种类型的吸收边界条件,其中以Ｃｌ…     

No-gap optimality conditions for an optimal control problem with pointwise control-state constraints

An optimal control problem with pointwise mixed constraints of the instationary three-dimensional Navier–Stokes–Voigt equations is considered. We derive second-order optimality conditions and show that there is no gap between second-order necessary optimality conditions and second-order sufficient optimality conditions. In addition, the second-order sufficient optimality conditions for the problem where the objective functional does not contain a Tikhonov regularization term are also discussed.     

Second-order conditions in c1, 1 optimization with applications

Second-order necessary conditions for inequality and equality constrained C^{1, 1} optimization problems are derived. A constraint qualification condition which uses the recent generalized second-order directional derivative is employed to obtain these conditions. Various second-order sufficient conditions are given under appropriate conditions on the generalized second-order directional derivative in a neighborhood of a given point. An application of the secondorder conditions to a new class of nonsmooth C^{1, 1} optimization problems with infinitely many constraints is presented.     

On viscous incompressible flows of nonsymmetric fluids with mixed boundary conditions

In this paper we are concerned with the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions. The considered boundary conditions are of two types: Navier’s slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The Dirichlet boundary condition for the microrotation of the fluid is commonly used in practice. However, the well-posedness of problems with different types of boundary conditions for microrotation are completely unexplored. The present paper is devoted to the proof of the existence, regularity and uniqueness of the solution in distribution spaces.     

The nonlinear bilevel programming problem:formulations,regularity and optimality conditions

In this paper, we study regularity and optimality conditions for the BLPP by using a marginal function formulation, where the marginal function is defined by the optimal value function of the lower problem. We address the regularity issue by exploring the structure of the tangent cones of the feasible set of the BLPP. These regularity results indicate that the nonlinear/nonlinear BLPP is most likely degenerate and a class of nonlinear/linear BLPP is regular in the conventional sense. Existence of exact penalty function is proved for a class of nonlinear/linear BLPP. Fritz-John type optimality conditions are derived for nonlinear BLPP, while KKT type conditions are obtained for a class of nonlinear/linear BLPP in the framework of nonsmooth analysis. A typical example is examined for these conditions and some applications of these conditions are pointed out