n阶泛函微分方程边值问题

本文研究下列n阶RFDE边值问题:x⁽ⁿ⁾(t)=f(t,x_t,x(t),x′(t),…,x^(n-1)(t)),　t∈［0,T ］,x(t)=φ(t),t∈［-r,0］;x′(0)=η,x″(0)=η₂,…,x^(n-2) (0)=η_n-2,x^(j)(T)=A,其中j∈I={0,1,2,…,n-1},得到了解的存在性和唯一性新的结果.     

多元Szász—Mirkjan算子的一致逼近

本文研究了多元Szása—Mirakjan算子在C_2B(T)中的逼近性质,利用K—泛函,建立了等价的逼近定理.主要结果如下 定理设f∈C_2B(T),0a) ;(ii)‖S_n,m(f)-f‖_∞ =0(n^-a);(iii)a)‖f(x+tφ(x),y)-2f(x,y)+f(x-tφ(x),y)‖_∞ =0(t<     

一类非线性波方程初边值问题解的爆破

该文研究如下具有非线性阻尼项和非线性源项的波方程的初边值问题 u_tt -u_xxt -u_xx -(σ(u²_x)u_x)_x+δ|u_t|^p-1u_t=μ|u|^q-1u, 0 < x <1, 0≤ t ≤T, (0.1) u(0, t)=u(1, t)=0, 0≤t≤ T, (0.2) u(x, 0)=u₀(x), u_t(x, 0)=u₁(x),0≤x≤1.(0.3) 文章将给出问题(0.1)--(0.3)的解在有限时刻爆破的充分条件, 同时将证明问题的局部广义解和局部古典解的存在性和唯一性.     

非线性项有非线性增长的2阶泛函微分方程边值问题

本文考虑下述２阶泛函微分方程边值问题：x″(t)=f(t,x_t,x′(t))(00=φ,x(b)=B.对于ｆ有非线性增长的情况，得出了上述问题可解的某些充分条件。     

重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

无穷时滞Liénard方程的周期解(英文)

讨论具有无穷时滞Liénard型方程x+(?²F(x))/(?x²)x+g(t,x_t)=p(t)的周期解问题, 利用重合度理论得到了周期解存在的充分条件.     

Clifford分析中双正则函数的非线性边值问题 *

讨论Clifford分析中的双正则函数,研究它的Coxo-Plemelj公式和一个非线性边值问题:A(t₁,t₂)φ⁺⁺(t₁,t₂)+B(t₁,t₂)φ^+-(t₁,t₂)+C(t₁,t₂)φ^-+(t₁,t₂)+D(t₁,t₂)φ^--(t₁,t₂)=g(t₁,t₂)f[t₁,t₂,φ⁺⁺(t₁,t₂),φ^+-(t₁,t₂),φ^-+(t₁,t₂),φ^--(t₁,t₂)].利用积分方程方法和Schauder不动点定理证明了问题解的存在性,并给出了解的积分表示式以及线性情况下解的存在唯一性.     

拟线性抛物方程组第一边界问题的有限差分法 ——Ⅲ.稳定性

讨论如下拟线性抛物组第一边值问题的显式、弱隐式和强隐式差分解u_t=(-1)^M+1A(x,t,u,…,u_x^M-1)u_x^2M+f(x,t,u,…,u_x^2M-1(x,t)∈Q_T={O<x<l,0<t≤T.}，u_x^k(0，t)=u_x^k(l，t)=0 (k=0，1，…，M -1)，0<t≤T，u(x，0)=φ(x)，0≤x≤l，其中u，φ和f是m维向量值函数，A是m×m正定矩阵，u_t=∂u/∂t，u_x^k=∂^ku/∂x^k.在以下意义下证明了该问题的一般有限差分格式的稳定性：即离散向量解在W₂^(2M，M)(Q_T)中的离散范数是连续地依赖于初始数据的H^M离散范数，以及矩阵A与自由项f的相应的离散范数.     

球面Schr?dinger算子的迹

Let S be a unit sphere in R³,Δ_θ,φ be the spherical Laplasian and q(θ,φ) be a continuous function on S. The following trace formulae are proved for the eigenvalues μ_n of L₀=-Δ_θ,φ and λ_n of L=L₀+q.     

从属过程的样本轨道的填充测度函数

设随机过程x(t)(t∈[0,∞))是一个从属过程,X[0,1]=|x∈R:t∈[0,1],X(t)=x}.通过对x(t)的指标函数g(u)(u≥0)的细致分析得到了关于X[0,1]填充测度函数的判别准则.事实上,若φ(s)(s∈(0,1))为任一测度函数,记h(s)=φ(s)/g(1/s),则有:h-p(x|0,1|= 相应于∫¹₀φ²(s)/s ds{<+∞ =+∞     

N-d维广义Brownian单的像集一致Packing测度和一致Packing维数

我们获得了Ｎ－ｄ维广义Ｂｒｏｗｎｉａｎ单的像集的一致Ｐａｃｋｉｎｇ测度和一致Ｐａｃｋｉｎｇ维数。     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS I

In this paper,authors compute the Packing dimension of statistically selfsimilar sets and obtaine the dimension and dimension distribution of statistically selfsimilar measure.     

FRACTAL PROPERTIES OF STATISTICALLY SELF-SIMILAR SETS

1IntroductionIn1981,J.E.Hutchinson[1]establishedthebasictheoryof(strictly)selfsimilarsets.Foragivenset(={S1,'',SN}ofcontractionmapsonacompleteseparableboundedmetricspaceN(X,d),thereexistsauniquecompactsetKsuchthatK=ZSi(K),andKistheclooureofi=1thesetofallfixedpointssi,,..-,iPoffillitecompositionsSi,o''oSi,(wesayKistheselfsimilarNsetwithrespectto().Illaddition,supposep1,-'tPNE(o,1)andZpi=l,thenthereexistsi=1NauuiqueBorelregularmeasurepoftotalmass1suchthatp=Zpipos;'withsuppp=Ki=1(we…     

N指标d维广义Wiener过程像集的一致维数

研究了N指标d维广义Wiener过程像集的一致维数和测度，得到了其像集的致Hausdorff维数和一致Packing维数。     

Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure

For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error.     

广义α-Stable过程的像集和图集的一致维数

研究了未必具有随机一致Holder条件的N指标d维广义α-stable过程的像集和图集的一致维数问题,并在一定条件下得到了N指标d维广义α-stable过程像集约一致Hausdorff维数和一致Packing维数的上、下界,图集的一致Hausdorff维数和一致Packing维数的上界,包含了多指标α-stable过程和广义布朗单相应的结果．     

Dimension analysis on a class of Bush type fractal surfaces

Abstract. In this paper,the authors construct a class of fractal surfaces,Bush type surfaces,based on the Bush type functions. The Box dimension,Packing dimension and Hausdorff dimen-sion of such surfaces are investigated.     

A circle packing measurable Riemann mapping theorem

We prove a circle packing version of the Measurable Riemann Mapping Theorem in the spirit of Rodin and Sullivan's Circle Packing Riemann Mapping Theorem. We also construct circle packing maps of the plane onto itself with prescribed dilatation.

     

Packing sets of patterns

Packing density is a permutation occurrence statistic which describes the maximal number of permutations of a given type that can occur in another permutation. In this article we focus on containment of sets of permutations. Although this question has been tangentially considered previously, this is the first article focusing exclusively on it. We find the packing density for various special sets of permutations and study permutation and pattern co-occurrence.     

一类分形曲面的维数与可微性

本文构造了一类由迭代函数系统生成的分形曲面。得到了曲面的Ｂｏｘ维数，Ｐａｃｋｉｎｇ维数和Ｈａｕｓｄｏｒｆｆ维数的下界，并指出了该曲面的不可微点类。指出了存在几乎处处可微和处处不可微的分形曲面的实例，使［１］成为本文的一个例子。