NA样本下一般形式的密度估计

Campos和Dorea(2001)在独立同分布样本下讨论了一般形式的核密度估计,得到了与连续型密度和离散型密度类似的结果,并将他们作为特例.本文则在NA样本下给出了类似的结果.     

复流形上（p，q）形式的带权因子的积分表示

本文在[1]的基础上，通过构造带权的Cauchy—Leray核，得到了一般复流形上的(p,q)形式的带权因子的积分表示和带权子的Koppelman—Lerey—Noryuet公式．     

考虑病毒DNA核衣壳和细胞间传播的一般HBV扩散模型

该文综合考虑了诱发HBV感染的两类途径、一般发生率函数和HBV病毒及其核衣壳的扩散效应,建立了一般性的HBV扩散模型.证明了模型解的适定性,两类平衡态的存在唯一性和模型的一致持久性,然后通过构造Lyapunov函数,得出模型的阈值动力学行为.最后结合数值模拟验证理论结果的同时,揭示了扩散对各状态变量的影响,结果显示:扩散影响HBV感染,且扩散系数越大,HBV感染的空间区域越大.     

一个具有混合核的Hilbert型积分不等式

引入参数及估算权函数,建立一个具有混合核的H ilbert型积分不等式.作为应用,考虑了逆向形式、相应的等价形式及一些特殊结果.     

一般多值混合隐拟变分不等式的解的存在性与算法

引入了实Hilbert空间中一类新的一般多值混合隐拟变分不等式.它概括了丁协平教授引入与研究过的熟知的广义混合隐拟变分不等式类成特例.运用辅助变分原理技巧来解这类一般多值混合隐拟变分不等式.首先,定义了具真凸下半连续的二元泛函的新的辅助变分不等式,并选取了一适当的泛函,使得其唯一的最小值点等价于此辅助变分不等式的解.其次,利用此辅助变分不等式,构造了用于计算一般多值混合隐拟变分不等式逼近解的新的迭代算法.在此,等价性保证了算法能够生成一列逼近解.最后,证明了一般多值混合隐拟变分不等式解的存在性与逼近解的收敛性.而且,给算法提供了新的收敛判据.因此,结果对M.A.Noor提出的公开问题给出了一个肯定答案,并推广和改进了关于各种变分不等式与补问题的早期与最近的结果,包括最近文献中涉及单值与集值映象的有关混合变分不等式、混合拟变不等式与拟补问题的相应结果.     

凸度量空间中拟压缩映象具误差的Ishikawa型迭代序列的收敛性

对凸度量空间中非线性拟压缩映象具误差的Ishikawa型迭代序列的收敛性问题证明了几个新的收敛性定理,结果不仅改进和推广了L.B.Ciric,Q.H.Liu,H.E.Rhoades,H.K.Xu等人的相应结果,而且对Rhoades-Naimplally-Singh所提出的公开问题,在凸度量空间的框架下给出了肯定的答复.     

具一般边界条件的细菌种群模型的谱问题

在L_1空间上研究了一般边界条件下一类具结构化的细菌种群模型,讨论了这类模型相应的迁移算子的谱分析,得到了该迁移算子的谱在右半平面上仅由有限个具有限代数重数的离散本征值组成等结果.     

附加广义函数的一般形式

作者证明了两两次数不同的附加广义函数组的线性无关性，接着给出了附加广义函数的一般形式。     

一类具一阶奇性核的奇异积分方程

当(?)是复平面C上的光滑封闭曲线,k（z）是在(?)所围成的有界闭区域上连续.在其内部解析的函数时.借助于奇异积分算子的广义逆.讨论了具一阶奇性核的正则型奇异积分方程:　在H类中的求解问题.作为应用,作者给出了当k（z）是一类有理函数时的具体解法,从而统一并推广了 Cauchy核和Hilbert核奇异积分方程的经典结果.     

污染分布的近邻估计

本文研究了污染分布中污染系数和未知主体分布密度的估计问题.利用近邻估计法得到了它们的估计量,并且证明了此估计量均满足一致弱相合性,同时对污染系数的估计进行了统计模拟,并与用核密度估计得出的结果作比较.结果显示估计的好坏与样本量的多少和参数的选取有关.     

Large Deviations for Random Sums on Some Kind of Heavy-tailed Classes in Risk Models

This paper is a further investigation into the large deviations for random sums of heavy-tailed,we extended and improved some results in ref. [1] and [2]. These results can applied to some questions in Insurance and Finance.     

Abel-Poisson type kernel on dyadic field

In this paper, we discuss the Abel-Poisson type kernel over dyadic field, prove that it is an approximation identity kernel and give some results on its approximation properties. It can be regarded as a complement of [1], [2] and [3]. Supported by National Natural Science Foundation of China.     

Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices

The paper is related to the norm estimate of Mercer kernel matrices.The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on[0,1]×[0,1]based on the Bernstein-Durrmeyer operator kernel ale obtained,with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2-norm for general Mercer kernel matrices on[0,1]×[0,1]are provided.     

On some properties of the ε-core of games with coalition structure

Chang [1991] stated some inclusion relation about kernel, reasonable set, and ε-core of games with coalition structure. We give counterexamples and modify erroneous results. Received: May 1997/Revised version: January 1999     

Some remarks on reverse Hilbert and Hardy-Hilbert type inequalities

In this paper we obtain an extension of discrete Hilbert’s inequality, by using some numerical methods. We shall obtain, in a similar way as Yang did in [10], that the parameter from the kernel can be taken from the interval [3/2, 3). We also compare our findings with existing results, known from the literature.     

Spectral approximation for compact integral operators by degenerate kernel methods

We establish a new improved error estimate for the solution of the integral equation eigenvalue problem by degenerate kernel methods. In [6] these estimates were proved under the assumption of normality of the original kernel as well as of the approximating degenerate kernel. Now we consider any compact integral operator and a general Banach space situation, in contrast to the Hilbert space setting in [6], This will be done by combining the techniques in [6] with the suitably transformed estimates of [5]. Our results show that degenerate kernel methods have, besides their overall property of furnishing easy approximations to eigenfunctions, for eigenvalues an order of convergence comparable to quadrature methods.     

当绝热指数很大时气体的一种非定常平面平行运动的渐近解

文献[1]在气体的速度分量只与极角θ及时间t有关,而与极距r无关的条件下求解理想气体的非定常平面平行具势运动方程组(1.2)～(1.3).文献[1]指出,在一般的情况下,不能得到解的显式表示式,只是对于二种特殊情况得到了显式解.本文研究了文献[1]的同样问题.第一部分,对音速作了一些补充限制,从而得到了方程组的显式解.第二部分,假设气体的绝热指数γ>>1,求得了方程组的一级近似解.     

Existence for a doubly nonlinear Volterra equation

We consider a doubly nonlinear Volterra equation involving a nonsmooth kernel and two possibly degenerate monotone operators. By exploiting an implicit time-discretization procedure, we obtain the existence of a global strong solution and extend to the nonlocal in time situation some former results by Colli [P. Colli, On some doubly nonlinear evolution equations in Banach spaces, Japan J. Indust. Appl. Math. 9 (2) (1992) 181-203].     

自重作用下的圆环薄壳

本文得到了等厚度圆环薄壳在自重荷载下一种简化形式的Новожилов方程,用Fourier级数求得了方程的特解.利用文[2]已有的齐次解结果,从而给出了问题的一般解.作为结果的应用,文中给出了两个算例.     

A new method for solving singular fourth-order boundary value problems with mixed boundary conditions

In [1], [2], [3], [4], [5], [6], [7] and [8], it is very difficult to get reproducing kernel space of problem (1). This paper is concerned with a new algorithm for giving the analytical and approximate solutions of a class of fourth-order in the new reproducing kernel space. The numerical results are compared with both the exact solution and its n-order derived functions in the example. It is demonstrated that the new method is quite accurate and efficient for fourth-order problems.