Is the Approximation Rate for European Pay-offs in the Black–Scholes Model Always 1/ \sqrt{n}

For a Borel-function , we consider the approximation of a random variable f(W ₁) with by stochastic integrals with respect to the Brownian motion and the geometric Brownian motion, where the integrands are piecewise constant within certain deterministic time intervals. In earlier papers it has been shown that under certain regularity conditions the optimal approximation rate is 1/ , if one optimizes over deterministic time-nets of cardinality n. We will show the existence of random variables f(W ₁) such that the approximation error tends as slowly to zero as one wishes.     

ON NEWMAN-TYPE RATIONAL INTERPOLATION TO ｜x｜ AT THE CHEBYSHEV NODES OF THE SECOND KIND

Recently Brutman and Passow considered Newman-type rational interpolation to ｜x｜ induced by arbitrary set of symmetric nodes in [-1,1] and gave the general estimation of the approximation error.By their methods one could establish the exact order of approximation for some special nodes. In the present paper we consider the special case where the interpolation nodes are the zeros of the Chebyshev polynomial of the second kind and prove that in this case the exact order of approximation is O（1/n｜nn）     

Modified Taylor approximation of functions with periodic behaviour

We approximate a function with periodic behaviour by means of a small modification of its Taylor polynomial. This modification is based on the work of Scheifele and will simplify the construction of special numerical methods for differential equations with near periodic solutions.     

On (q 2 + q + 2, q + 2)-arcs in the Projective Plane PG(2, q)

A (k,n)-arc in PG(2,q) is usually defined to be a set of k points in the plane such that some line meets in n points but such that no line meets in more than n points. There is an extensive literature on the topic of (k,n)-arcs. Here we keep the same definition but allow to be a multiset, that is, permit to contain multiple points. The case k=q ²+q+2 is of interest because it is the first value of k for which a (k,n)-arc must be a multiset. The problem of classifying (q ²+q+2,q+2)-arcs is of importance in coding theory, since it is equivalent to classifying 3-dimensional q-ary error-correcting codes of length q ²+q+2 and minimum distance q ². Indeed, it was the coding theory problem which provided the initial motivation for our study. It turns out that such arcs are surprisingly rich in geometric structure. Here we construct several families of (q ²+q+2,q+2)-arcs as well as obtain some bounds and non-existence results. A complete classification of such arcs seems to be a difficult problem.     

一类树并的补图的色唯一性

彻底解决了一类不可约树并的补图是色唯一的 ,并得到了一些图的伴随多项式的最小根的重要规律 .     

Liénard-Chipart稳定性准则的一个初等证明

ＡｎｏｔｈｅｒＥｌ§１．　ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＦｒｏｍ［１］,ａｒｅａｌｐｏｌｙｎｏｍｉａｌｆ（ｚ）＝∑ｎｉ＝０αｉｚｉ,ｉｓｃａｌｌｅｄａＨｕｒｗｉｔｚｐｏｌｙｎｏｍｉａｌ,ｉｆａｌｌｉｔｓｒｏｏｔｓｈａｖｅｎｅｇａｔｉｖｅｒｅａｌｐａｒｔｓ．Ｉｎｔｈｉｓｐａｐｅｒ,ｓｅｖｅｒａｌｎｅｃｅｓｓａｒｙａｎｄｓｕｆｆｉｃｉｅｎｔｃｏｎｄｉｔｉｏｎｓｏｆＨｕｒｗｉｔｚｐｏｌｙｎｏｍｉａｌａｒｅｇｉｖｅｎ,ａｓａｂｙｐｒｏｄｕｃｔ,ｔｈｅｓｔａｂｉｌｉｔｙｃｒｉｔｅ…     

扩充的Hermite—Fejer插值算子平均收敛性

讨论了以Ｊａｃｏｂｉ正交多项式零点为插值结点的扩充Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子在Ｌｕ＾ｐ空间的平均收敛性。首先给出了算子加权平均收敛的条件,进一步得到了收敛阶。     

两类新的广义Ball曲线

本文提出两类新的广义Ｂａｌｌ曲线,一类介于Ｗａｎｇ（王国瑾）和Ｓａｉｄ广义Ｂａｌｌ曲线之间,另一类介于Ｂｅｚｉｅｒ和Ｓａｉｄ曲线之间,同时给出有关的升阶公式、递推算法及转化成Ｂｅｚｉｅｒ形式的系数公式。     

关于一个反应扩散方程的两个结果

本文讨论了一个反应扩散方程的行波解以及一个平面三次系统的全局相图．     

不同尺度下多项式滤波器的优化算法

１　　引　言 在小波分析的应用中,紧支撑正交对称的小波是非常可贵的．尤其是对称性,它在实际应用中具有非常重要的意义．但Daubechies的具有紧支撑正交小波无任何对称性和反对称性（除Haar小波外）．为了克服这一不足,崔锦泰和王建忠［１］提出了样条小波,样条小波用失去正交性换来了小波的对称性．A.Cohen［２］等引入了双正交小波似乎解决了这一问题,但它需要两个对偶的小波．匡正［３］等采用了小波的分式滤波器构造出了既正交又对称的小波,但却没有有限的支撑区间．本文欲采用优化的方法给出了一种构造具有任意正则性的多项式…