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1.
反差分计算在数列求和上的应用常丰(蚌埠教育学院,蚌埠233010)一、差分设f(n)是非负整数n=0,1,2,3,…的函数,其差分Δf(n)定义为Δf(n)=f(n+1)-f(n).例如,设阶乘幂f(n)=n(k)=n(n-1)…(n-k+1),k≥...  相似文献   

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关于f(f~(k)~n-a(z)的零点   总被引:5,自引:0,他引:5  
本文讨论了杨重骏和杨乐等提出的一个猜想:设f是一超越整函数,n,k是两个正整数,则当n2时,f(f(k)n取任何非零有限值无穷多次,并证明了这个猜测,而且证明了,当f是亚纯函数时的情形也成立,即有,设f是超越亚纯函数,n,k是两个正整数,则当n2时,f(f(k)n-a(z)有无穷多个零点,其中a(z)是f的一个小函数  相似文献   

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胡克 《数学杂志》1993,13(4):413-418
设f(z)=z+Σanz^n为单位园|z|<1内解析且平均单叶,记其族为M又设{f(z)/z}^λ=1+Σ^∞n=1Dn(λ),λ>0,本文说明了:定理一 若f∈M,λ>0,则:Σ^∞k=1{||Dk(λ)|-|Dk-1(λ)||/dk(λ)}^2≤An,n=2,3,…其中A为绝对常数。dk(h)=h(h+1)…(h+k-1)/k!当λ=1/2,f∈s时为I.V.Milm所证明。定理二 若f∈M并  相似文献   

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齐型空间上的Lipschitz函数与Littlewood-Paley g-函数   总被引:1,自引:0,他引:1  
在θ阶正规齐型空间上,如果算子列{Sk}k∈Z是恒等逼近,Dk=Sk-Sk-1;本文给出一个用{Dk}k∈Z表达的f∈Lipα(Lipschitz函数类,0<α<θ)的充分必要条件.作为其推论得到,对于f∈LIpα,其Littlewood-Paleyg函数g(f)(X)或者处处为无穷大,或者在Lipα上有界.  相似文献   

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△(G)=3的外平面图的邻强边染色   总被引:2,自引:0,他引:2  
对图G(V,E),一正常k-边染色f称为G(V,E)的一邻强边染色,当且仅当对任意uv∈E(G)有f[u]≠f[v].其中f[u]={f(uw)|uw∈E(G)},f(uw)表示染边uw的色,并称xas(G)=min{k|存在C的一k种色的郁强边染色}为G的邻强边色数.本文证明了对△(G)=3的2-连通外平面图,有xas(G)=4.  相似文献   

6.
齐型空间上的Lipschitz函数与Littlewood-Paley g-函数   总被引:3,自引:0,他引:3  
常心怡 《数学学报》1996,39(5):629-636
在θ阶正规齐型空间上,如果算子列{Sk}k∈Z是恒等逼近,Dk=Sk-Sk-1;本文给出一个用{Dk}k∈Z表达的f∈Lipα(Lipschitz函数类,0<α<θ)的充分必要条件.作为其推论得到,对于f∈LIpα,其Littlewood-Paleyg函数g(f)(X)或者处处为无穷大,或者在Lipα上有界.  相似文献   

7.
设函数f(z)在区域D={z∈C|z|<R≤∞}内解析,(n+k/n)f(z)是f(z)的以(1+)n为分母的Pade型逼近。本用初等方法证明了:当n→∞时,(n+k/n)f(z)在D的任一紧子集上一致收敛于f(z)。  相似文献   

8.
具有与任意图正交的(g,f)-因子分解的子图   总被引:2,自引:0,他引:2  
设g和f分别是定义在图G的顶点集合V(G)上的整数位函数且对每个x∈V(G)有0≤g(x)≤f(x).证明了:若G是一个(mg+k,mf-k)-图,1≤k<m,H是G中一个给定的有k条边的子图,则G有一个子图L使得L有一个(g,f)-因子分解与H正交.  相似文献   

9.
给出了一个有用的有判断Hermite-Fejer插值算子Hn(f,x)平均收敛准则,即Hn(f,x)依范数收敛于f(x)的充分必要条件是:Hn(f,x)一致 有界(对一切n)并且Hn(F,x^k)依范数收敛于x^k(k=1,2)。  相似文献   

10.
设{αk}∞k=-∞为正数缺项序列,满足infkαk+1/dk=α>1,Ω(y′)为Besov空间B0,11(Sn-1)上的函数,其中Sn-1为Rn(n2)上的单位球面.本文证明:若∫Sn-1Ω(y′)dσ(y′)=0,则离散型奇异积分TΩ(f)(x)=∑∞k=-∞∫Sn-1f(x-αky′)Ω(y′)dσ(y′)和相关的极大算子TΩ(f)(x)=supN∑∞k=N∫Sn-1f(x-αky′)Ω(y′)dσ(y′)均在L2(Rn)上有界.上述结果推广了Duoandikoetxea和RubiodeFrancia[1]在L2情形下的一个结果  相似文献   

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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.  相似文献   

13.
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.  相似文献   

14.
张丽娜  吴建华 《数学进展》2008,37(1):115-117
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  相似文献   

15.
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.  相似文献   

16.
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).  相似文献   

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<正>Aims and Scope Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,is one of the transactions of China Society for Industrial and Applied Mathematics,and is a bimonthly journal.JMRA is dedicated to publishing first-rate original research papers in all areas of mathematics with applications,and making research findings available to a wide scientific world,as JMRE has for many years.In line with the name change,the new scope of Journal of Mathematical Research with Applications will not include the articles on mathematical methodology and mathematical philosophy.Copyright Information  相似文献   

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