具有性质cr+1=3,ar+1=3a+1或 4a的(a+1,3)型距离正则图

设г是直径为d且型为(a 1,3)的距离正则图,其中a≥2.用l(c,a,b)表示交叉阵列ι(г)中列(c,a,6)t的个数,记r=r(г)=l(c1,a1,b1),8=8(г)=l(Cr 1,ar 1,br 1)及t=t(г)=l(cr s 1,ar s 1,br s 1).那末,若Cr 1=3,ar 1=4a或3a 1,则d=r t 2.     

具有性质cr 1=3,ar 1=3a 1或 4a的(a 1,3)型距离正则图

设г是直径为d且型为(a 1,3)的距离正则图,其中a≥2.用l(c,a,b)表示交叉阵列ι(г)中列(c,a,6)t的个数,记r=r(г)=l(c1,a1,b1),8=8(г)=l(Cr 1,ar 1,br 1)及t=t(г)=l(cr s 1,ar s 1,br s 1).那末,若Cr 1=3,ar 1=4a或3a 1,则d=r t 2.     

三角形方程的简化及分类

已知△ABC三顶点坐标为A(a,b),B(c,d),C(e,f),则其绝对值方程可写成如下形式: |a_1x b_1y c_1| |a_2x b_2y c_2| |a_3x b_3y c_3|=0 其中系数a_i,b_i,c_i=1,2,3可由顶点坐标确定。     

一个猜测的否定

对第43届普特南数学竞赛题“△~(1/2)(a_1,b_1,c_1)+△~(1/2)(a_2,b_2,c_2)≤△~(1/2)(a_1+a_2,b_1+b_2,c_1+c_2)”(其中△(a,b,c)表示以a,b,c为边长的三角形面积),该刊1989年第4期“一道竞赛题引起的猜测”一文中提出如下猜测:     

一道IMO预选题的溯源及推广

第28届国际数学奥林匹克有如下一道预选题: 试证:若a、b、c是三角形的三边,且2s=a b c,则(1) 运用契贝雪夫不等式: 若序列a_1和b_1(i=1,2,…,n)为同序,即满足a_2≤a_2≤…≤a_m且b_1≤b_2≤…≤b_n或a_1≥a_2≥…≥a_n且b_1≥b_2≥…≥b_n 则若序列a_1和b_1(i=1,2,…,n)为反序,则上式中的不等号反向。     

非负全连续算子的谱模

设 A=(a_(ij))是 l_2中一个全连续算子,其中a_(i_1j)≥0.当 A~*A 为不可约时,本文证明了|||A|||+2=min{r(B)c_1(C)∶A=BoC},其中 A=BoC 表示对一切 i,j,a_(ij)=b_(ji)c_(ji),r(B)=sup(sum from j=1 to ∞ |b_(ij)|~2)~(1/2),c_1(C)=(sum from i=1 to ∞ (c_(ji)~2)~(1/2),并给出极小解的具体形式.文中所有结果均适用于 A_(mn)为一 m×n 矩阵的情形     

用行列式证三数成等差数列

定理如果a_1、b_1、c_1、三数成等差数列(a_1、b_1、c_1为互不相等的三数),那么a_2、b_2、c_2三数成等差数列的充要条件是证明 (充分性):设a_1、b_1、c_1三数成等差数列的公差为d,则b_1-a_1=d=c_1-b_1,c_1-a_1=2d。     

利用矩阵初等变换求非奇线性对应的表示式

1 问题的提出非奇线性对应即是由表示式确定的齐次坐标(x_1,x_2,x_3)和(x'_1,x'_2,x'_3)之间的对应,在高等几何中,二维射影变换是非奇线性对应。怎样由给定的两组无三点共线的四点a=(a_1,a_2,a_3),b=(b_1,b_2,b_3),c=(c_1,c_2,c_3),d=(d_1,d_2,d_3)和a'=(a'_1,a'_2,a'_3),b'=(b'_1,b'_2,b'_3),c'=(c'_1,c'_2,c'_3),d'=(d'_1,d'_2,d'_3)计算出非奇线性对应(1),使得     

分式线性迭代数列的敛散性及收敛速度

若a_i,b_i0(i=1,2),|a_1 a_2b_1 b_2|≠0,则数列x_10,x_(n+1)=a_1x_n+a_2/b_1x_n+b_2收敛.若迭代过程中,xn(n=1,2,…)全不是φ(x)=a1x+a2/b1x+b2的不动点,则迭代数列{xn}线性收敛.     

二元二次式因式分解的一个简便方法

形如Ax~2+Bxy+Cy~2+Dx+Ey+F的二元二次式的因式分解,一般可用求根公式法,待定系数法等方法进行分解,但计算都比较复杂。下面我们介绍一种简便的分解方法——取零凑尾法。这个方法的理论根据是定理二元二次多项式f(x,y)=Ax~2+Bxy+Cy~2+Dx+Ey+F能分解为一次式之积(a_1x+b_1y+c_1)(a_2x+b_2y+c_2)的充要条件是对 B=a_1b_2+a_2b_1, (1)使得 f(x,o)=(a_1x+c_1)(a_2x+c_2) (2) f(o,y)=(b_1y+c_1)(b_2y+c2) (3)证明:条件的充分性。设上三式同时成立,     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].