四阶奇异边值问题的正解

本文利用上下解方法和极大值原理给出了四阶微分方程的奇异边值问题有C2[0,1]和C3[0,1]正解存在的充分必要条件.     

三阶常微分方程的某些非线性特征值问题的正解

研究了三阶常微分方程的某些非线性特征值问题. 通过考察非 线性项在有界集上的性质建立了这些问题的正解的存在性与多解性.     

具无限时滞的周期系统的持久性与正周期解

本文利用比较定理,控制收敛定理和积分平均的方法,讨论一类具有无限时滞的非自治,非卷积的捕食者-食饵系统的一致持久性和正周期解。     

一类n维非球谐振子势的精确解

严格求解一类n维非球谐振子势的定态薛定谔方程，获得了归一化径向波函数和能谱的 精确解.在此基础上导出径向矩阵元r,L_n｜r^s｜n′ ₄,L′_n>的通项公式. 关键词： n维非球谐振子 精确解 径向矩阵元 通项公式     

The Index of Cusp Operators on Manifolds with Corners

We recall a Fredholm criterion for fully elliptic cusp(pseudo)differential operators on a compact manifold with corners ofarbitrary codimension, acting on suitable Sobolev spaces. Then we give aformula for the index in terms of regularized `trace' functionalssimilar to the residue trace of Wodzicki and Guillemin.     

Positivity preserving finite element approximation

We consider finite element operators defined on ``rough' functions in a bounded polyhedron in . Insisting on preserving positivity in the approximations, we discover an intriguing and basic difference between approximating functions which vanish on the boundary of and approximating general functions which do not. We give impossibility results for approximation of general functions to more than first order accuracy at extreme points of . We also give impossibility results about invariance of positive operators on finite element functions. This is in striking contrast to the well-studied case without positivity.

     

正线性算子对无穷区间上有界变差函数的点态逼近度

用ＢＶ［０，∞）表示在［０，∞）的每一有限子区间上为有界变差函数的函数构成的空间。用表示ＢＶ［０，∞）上的正线性算子，其中ｄｔＫｎ（ｘ，ｔ）是非负测度且，则有定理如果Ｌｎ（｜ｔ－ｘ｜β，ｘ）≤Ｃ（ｘ）／ｎｖ，，这里β＞０，ｖ≥１，Ｃ（ｘ）是一个与ｘ有关的常数，对ｆ∈ＢＶ［０，∞）和ｘ∈（０，∞）有这里作为应用，给出算子的逼近估计．     

The ?-positive center figure

Based on Gage's notion of a “positive center” of a planar convex set, an ε-positive center figure is defined, constructed, and illustrated through example. The existence of an ε-positive center point, and the convexity of the ε-positive center figure, is conjectured.     

On Overspill Principles and Axiom Schemes for Bounded Formulas

We study the theories I?_n, L?_n and overspill principles for ?_n formulas. We show that IE_n ? L?_n ? I?_n, but we do not know if I?_n L?_n. We introduce a new scheme, the growth scheme Crγ, and we prove that L?_n ? Cr?_n? I?_n. Also, we analyse the utility of bounded collection axioms for the study of the above theories. Mathematics Subject Classification: 03F30, 03H15.     

On the choice of the initial value of a quadratic spline in positive interpolation

Any quadratic spline with coinciding interpolating points and breakpoints can be uniquely determined by one initial condition. We examine how to choose the initial value in positive interpolation by using a norm of the spline. Monotone interpolation is also considered. The results are illuminated by numerical examples and by an application.