稳定分量过程象集的一致测度和一致维数

令X(t)=(X_1(t),…,X_N(t))为一d-维过程,其中X_i(t)为α_i-阶d_i-维稳定过程.设0<α_n<…<α_1≤2,d=d_1 … d_N.本文中,我们获得了,当α_1≤d_1时稳定分量过程X(t)关于Borel集E的象X(E)的Hausdorff测度和Packing测度的一致上界和一致下界,当α_1>d_1时得到了相应测度的一个一致上界.同时我们给出了一致维数结果.     

关于双曲线的一种方程

1　关于双曲线的一种方程设在平面直角坐标系中有两条相交直线l1 和l2 ,它们的方程分别是l1 :a1 x+b1 y+c1 =0 ,　l2 :a2 x+b2 y+c2 =0 .因为是相交直线 ,所以当然满足条件a1 b2 -a2 b1 ≠ 0 ( 1 )则凡以这两条相交直线作为渐近线的双曲线的方程总能写成(a1 x+b1 y+c1 ) (a2 x+b2 y+c2 ) =d ( 2 )其中d是任一非零常数 .反之 ,方程 ( 2 )当d≠ 0并且满足上述条件( 1 )时 ,就表示以l1 和l2 为渐近线的一条双曲线 .关于这一结论可以查阅高等学校的解析几何教材 ,比如吕林根、许子道等人编著的由高教出版社出版的《解析几何》[1 ] (第三版 ) .其…     

R^(1)上莫朗测度关于几何平均误差的最优Voronoi分划北大核心CSCD

设E是R^(1)上由有界闭区间J,(nk)_(k)=1∝和C_(k)=(ck,j)j=1nk1)k≥1确定的莫朗集.μ是E上由正概率向量序列(P_(k))k≥1所确定的一个莫朗测度.μ关于几何平均误差的所有n-最优集组成的集簇记为Cn(μ).设αn∈Cn(μ)及αn对应的任一Voronoi分划{Pa(αn)}a∈αn.证明了■对于每个aαn,Pa(αn)包含一个以a为中心,半径为d2|Pa(αn)∩E|的闭区间,其中d2是一个常数,|B|是集合B?R^(1)的直径.记en(μ)是μ上的n-级几何平均误差及ên(μ):=logen(μ),证明了ên(μ)-ên+1(μ)■n-1.     

对称稳定过程的不变测度

对R~d(d≥1)中指标a,0相似文献   

广义α-stable过程自相交局部时增量的Holder律及重点

文研究了 N 指标 d 维广义α-stable过程自相交局部时增量的Holder律. 并利用所得自相交局部时的性质, 证明了该过程重点的存在性, 得到了该过程多重时的Hausdorff维数及测度的下界.所得结论包含并推广了广义布朗单及stable单相应的结果.     

巧证线面垂直的判定定理

线面垂直的判定定理,是立体几何中的重点与难点.教材利用镜面对称的方法,给出了该定理的一个几何证明.本文将从代数角度给出该定理的一个巧证.定理设aα,bα,a∩b=O,l⊥a,l⊥b,则l⊥α.证在平面α内任取一条直线g,根据异面直线所成角的定义,不妨设g,l都过点O.当g与a(或b)重合时     

两条相交直线的轴对称命题

定理1 如果两条相交直线l1,l2的斜率分别为k1,k2,那么: (1)l1,l2的对称轴的斜率为±1的充要条件是k1k2=1; (2)l1,l2的对称轴的斜率为k(≠±1)的充要条件是证明设a1,a2分别为相交直线l1,l2的倾斜角.先证条件(1),(2)的必要性.再证条件(1),(2)的充分性.     

谈谈到两异面直线距离相等的点的集合

在空间到两条平行直线等距离的点的集合是一个平面 ;在空间到两条相交直线等距离的点的集合是两个互相垂直的平面 ,但是在空间到两条异面直线等距离的点的集合是什么呢 ?本文特对此进行一番探究 ,供大家欣赏 .我们先证明以下引理 .引理　设直线l1,l2 平面α ,直线l1∩l2 =O ,则平面α到直线l1,l2 的距离的平方差为定值d(d >0 )的动点的轨迹为等轴双曲线 ,且以直线l1,l2 相交所成角的平分线为渐近线 .证　建立如下直角坐标系 :以l1与l2 交点O为原点 ,以直线l2 到直线l1的角的平分线为x轴 ,以直线l1到直线l2 的角的平分线为 y轴 ,则直线l1,l…     

带有单侧共振的Duffing方程解的存在性

对于α,β∈L(0,1),如果α(t)≤β(t)对a.e.t∈(0,1)成立,则记α≤β;如果α≤β,而且α(t)<β(t)在(0,1)的一个正测度集上成立,则记α<β.任意x∈C~1(0,1)记x满足下述的(2)式,KerL_p=.考虑周     

一类(a+1,3)型的距离正则图

设Γ是直径为d且型为(α 1,3)的距离正则图,其中α≥2.用l(c,a,b)表示交叉阵列l(Γ)中列(c,a,b)~t的个数,记r=r(Γ)=l(c_1,a_1,b_1),s=s(Γ)=l(c_(r 1),a(r 1),b_(r 1)).那末,若c_(r 1)=3且a_(r 1)=3a,则d=r s 1,c_d=4且Γ为正则拟2d边形.     

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.     

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].     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.      

Best approximation by downward sets with applications

We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X     

Boundedness of multilinear operators on weighted herz type spaces

In this paper, the author establishes the boundedness of multilinear operators on weighted Herz spaces and Herz-type Hardy spaces. The author also obtains their weak estimates on endpoints. As a special case, the conclusions may lead to the weighted estimates for multilinear Calderon-Zygmund operators.     

THE EXACT CONVERGENCE RATE AT ZERO OF LAGRANGE INTERPOLATION POLYNOMIAL TO |x|α

In this paper we present a generalized quantitative version of a result due to M. Revers concerning the exact convergence rate at zero of Lagrange interpolation polynomial to f(x) = |x|α with on equally spaced nodes in [-1, 1].