共查询到20条相似文献,搜索用时 93 毫秒
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设m是正整数,f(X,Y)=a0Xn+a1X(n-1)Y+...+anYn∈Z[X,Y]是Q上不可约化的叫n(n≥3)次齐次多项式。本文证明了:当gcd(m,a0)=1,n≥400且m≥10(35)时,方程|f(x,y)|=m,x,y∈z,gcd(x,y)=1,至多有6nv(m)组解(x,y),其中v(m)是同余式F(z)=f(z,1)≡0(modm)的解数。特别是当gcd(m,DF)=1时,该方程至多有6n(ω(m)+1)组解(x,y),其中DF是多项式F的判别式,ω(m)是m的不同素因数的个数. 相似文献
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设n≥3,定义Tf(x,xn)=P.V.∫R^n-1b(t)K(t)f(x=t,xn-Г(│t│))dt,其中x∈R^n-1,b(t)为R^n-1上的有界函数,K(t)为R^n-1上满足Hormander条件的函数,且Г(s)为〔0,∞)上的任意函数。本文给出了T为(L∞(R^n),BMO(R^n))一型,或等价地(H^1(R^n),L^1(R^n))一型时,b所应满足的充分必要条件。 相似文献
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§1. IntroductionWeconsiderthefollowingoptimizationproblem:(P) minx∈Xf(x)(1)whereX={x|x∈En,gj(x)≤0,j=1,2,…,m;gj(x)=0,j=m+1,…,m+l},letI={1,2,…,m},L={m+1,…,m+l}.Fortheproblem(P)withL=,manyefficientprojectiontypealgorithms[1-11]havebeenproposed.In[12],… 相似文献
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设n,s1,s2,…,sn为正整数及M(s1,s2,…,sn)={(x1,x2,…,xn)|0xisi,且xi为正整数}.若FM(s1,s2,…,sn)满足:对任何a,b∈F,都至少有t个i使ai∧bi=min(ai,bi)>0,则称F为M(s1,s2,…,sn)中的一个t-相交序列族.对x=(x1,x2,…,xn)∈M(s1,s2,…,sn),称r(x)=∑ni=1xi为x的秩.本文讨论并得到当s1=s2=…=sn时M(s1,s2,…,sn)中秩为k的有限序列最大相交族,从而获得了由Engel和Frankl提出的一个关于有限序列相交族的公开未解问题在kn+t-1情形下的解. 相似文献
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设a,b是非零整数,p1,…,pr是不同的素数,P={±|m1,…,mr是非负整数}.设K是n(n≥3)次代数数域,α1,…,αm∈k(1<m<n),△(α1,…,αm)是α1,…,αm的判别式,f(x1,…,xm)=αNk/Q(α1x1+…+αmxm)∈z[x1,…,xm].本文证明了:当f(x1,…,xm)非退化且Pi△(α1,…,αm)(i=1,…,r)时,方程f(x1,…,xm)=by,x1,…,xm∈z,gcd(x1,…,xm)=1,y∈P至多有(4Sd2)(Sd)组解(x1,…,xm,y),其中d=n!,S=r+ω是b的不同素因数的个数,hA是K的类数. 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
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ZHENG ShiJun 《分析论及其应用》2004,20(3)
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
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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
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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
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Pankaj Mathur 《分析论及其应用》2006,22(2)
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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《高校应用数学学报(英文版)》2014,29(4)
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 相似文献
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《数学研究及应用》2014,(6)
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. 相似文献
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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]. 相似文献