Regularized collocation method for Fredholm integral equations of the first kind

In this paper we consider a collocation method for solving Fredholm integral equations of the first kind, which is known to be an ill-posed problem. An “unregularized” use of this method can give reliable results in the case when the rate at which smallest singular values of the collocation matrices decrease is known a priori. In this case the number of collocation points plays the role of a regularization parameter. If the a priori information mentioned above is not available, then a combination of collocation with Tikhonov regularization can be the method of choice. We analyze such regularized collocation in a rather general setting, when a solution smoothness is given as a source condition with an operator monotone index function. This setting covers all types of smoothness studied so far in the theory of Tikhonov regularization. One more issue discussed in this paper is an a posteriori choice of the regularization parameter, which allows us to reach an optimal order of accuracy for deterministic noise model without any knowledge of solution smoothness.     

关于纤维锥的Hilbert系数

Let （R, m） be a Cohen-Macaulay local ring of dimension d, I an mprimary ideal and K an ideal containing I. Assuming that I has minimal （almost minimal） mixed multiplicity with respect to K, we get some results on the Hilbert coefficients of fiber cones.     

The L resolvents of elliptic operators with uniformly continuous coefficients

We consider the strongly elliptic operator A of order 2m in the divergence form with bounded measurable coefficients and assume that the coefficients of top order are uniformly continuous. For 1<p<∞, A is a bounded linear operator from the L^p Sobolev space H^m,p into H^−m,p. We will prove that (A−λ)⁻¹ exists in H^−m,p for some λ and estimate its operator norm.     

Representation of measurable functions in Franklin general system

The paper proves that every almost everywhere finite measurable function is representable by an absolute convergent series in the Franklin systems generated by quasi-dyadic, weakly regular partitions.     

Functional inequalities involving special functions II

This paper is motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen. We prove a chain of inequalities for hypergeometric functions, generalized and normalized Bessel functions, Kummer functions and for some general power series. Some particular cases and refinements are given.     

平面热传导方程Douglas交替方向隐格式的稳定性与收敛性

1 引言 解抛物方程的交替方向差分方法产生于本世纪五十年代,由于其稳定性好、易编制计算程序,几十年来在科学与工程计算中得到了广泛的应用,最早的交替方向差分格式由Peace- man,D.W.和Rachford,H.H.以及Douglas,J,Jr.和Rachford,H.H.给出,Douglas,J.Jr.于1962年提出了后人称之为Douglas格式的一类交替方向隐格式,其特点是有二阶截断误差而且适用于三维情形.下面简要给出其格式。 考虑平面方形区域上热传导方程 (1.1) (1.2) (1.3)其中Ω=(0,1)×(0,1),为其边界,t为时间变量,以及u_o为已知函数. 令x与y方向网格步长均为h,x_i=ih,y_j=jh,N=1/h为正整数;时间步长为△t,t~n=n△t,记w_(ij)~n=w(x_i,y_j,t~n)以及     

时间赢余过程的构造及其破产理论

本文提出了一种研究风险模型的新思路，并构造了一个时间孕余过程，从另外一个新的侧面给出了破产概率的定义，并在此方面做了初步的探讨。     

ON THE EXISTENCE OF GLOBAL GENERAL SOLUTIONS OF POLYNOMIAL SYSTEMS

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＧＥＮＥＲＡＬＳＯＬＵＴＩＯＮＳＯＦ　ＰＯＬＹＮＯＭＩＡＬＳＹＳＴＥＭＳＺＨＡＯＸＩＡＯＱＩＡＮＧ（赵晓强）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏ...     

零级狄里克莱级数的增长性

首先研究了全平面上零级狄里克莱级数的系数和增长性之间的关系，然后证明了对于本级随机狄里克莱级数所确定的随机整函数，在每条水平直线上的增长性几乎必然（ａ．ｓ．）与相应的狄里克莱级数所确定的整函数的增长性相同．     

关于停止损失再保险的调节系数最大化问题

停止损失再保险作为一种再保险方式,在具有相同保费的前提下,能使保险人的期望效用最大,并能使其自留风险方差最小.另外在保费和费率相等的前提下,停止损失再保险的调节系数不可能比其他再保险方式的调节系数小.本论文在此基础上作了相应推广,讨论了在保费相等的前提下,停止损失再保险的费率满足时,其调节系数不小于其他再保险方式的调节系数.