有限uM,D-正交指数函数系的一个充分条件

设$\mu_{M,D}$是由仿射迭代函数系$\{\phi_{d}(x)=M^{-1}(x+d)\}_{d\in D}$唯一确定的自仿测度, 它的谱与非谱性质与Hilbert空间$L^{2}(\mu_{M,D})$中正交指数函数系的有限性和无限性有着直接的关系. 本文将利用矩阵的初等变换给出$\mu_{M,D}$\,{-}\!\!正交指数函数系有限性的一个充分条件. 由于这个条件只与 矩阵$M$的行列式有关, 因此, 它在$\mu_{M,D}$的非谱性的判断方面便于直接验证.     

On the Asymmetry for Convex Domains of Constant Width

The extremal convex bodies of constant width for the Minkowski measure of asymmetry are discussed. A result, similar to that of H. Groemer＇s and of H. Lu＇s, is obtained, which states that, for the Minkowski measure of asymmetry, the most asymmetric convex domains of constant width in R2 are Reuleaux triangles.     

Asymptotic analysis of the Krawtchouk polynomials by the WKB method

We analyze the Krawtchouk polynomials K _n (x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N→∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0,N]×[0,N], involving some special functions. We give numerical examples showing the accuracy of our formulas.      

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.     

5-桥图F(2,a,a,b,c)的色等价刻画

设P(G，λ)是图G关于变量λ的色多项式，P(G，λ)=P(H，λ)，称G和H色等价，由连接两个顶点的S条内部不交的路组成的图叫S-桥图。本讨论了5-桥图F(2,a,a,b,c)(c≥b≥a 1，a≥2)的色性，完整刻画了这类图的色等价图。     

The Newton Polygon and Elliptic Problems with Parameter

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well-known Agmon-Agranovich-Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis-Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis-Nirenberg was introduced by A. KOZHEVNIKOV [K2].     

The Regular Near Polygons of Order (s, 2)

In this note we classify the regular near polygons of order (s, 2).     

二维卷积及其在色谱峰纯度鉴定中的应用

光电二极管阵列检测器与色谱仪的联用 ( HPLC- DAD)为复杂体系中多组分的定性定量分析提供了可能 .Savitzky等 [1]提出了以简单的卷积运算完成数值微分方法 .Gorry等 [2 ]曾以 Gram正交多项式替代幂级数拟合 ,让卷积技术可以覆盖到谱图包括起讫部分的任一点 .Edwards[3]与 Kuo[4 ]等提出的二维卷积法对处理和利用二变量数据矩阵具有普遍意义 ,但理论推导繁琐 .我们曾完善了推求二维卷积整数的普遍方法 [5] ,并研究和解决了一维和二维卷积中的信息丢失问题 [6 ,7] .本文提出了一种简化的求算二维卷积整数的方法 .理论推导表明 ,二维卷积…