A Note on the Multifractal Decomposition of Directed Graph Self Similar Sets

We investigated the directed graph self similar sets under some weak overlapping condition. We get the multifractal decomposition formulas for these sets, i. e.,dim Ku^a DimKu^a =f(a), where fis the multifractal spectral function of the directed graph self similar measure. Especially, the results improve that of Edgar and Mauldin to the case which allows certain overlapping.     

Some polar sets for the generalized Brownian sheet

Let (t)(t ∈ R ₊ ^N ) be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for (t). It is proved that for any a ∈ R ^d , P{ (t) = a, for some t ∈ R _> ^N } = and the probability that (t) has k-multiple points is 1 or 0 according as whether 2kN > d(k − 1)β or 2kN < d(k−1)α. These results contain and extend the results of the Brownian sheet, where R _> ^N = (0,+∞) ^N ,R ₊ ^N =[10,+∞) ^N ,0< α≤1 and β≥1. Biography: LI Huiqiong (1966–), female, Associate professor, research direction: stochastic process and random fractal.     

Some Results about the Sample Path Properties of Markov Processes with Independent Self-Similar Components

This paper considers a special class of operator self-similar processes Markov processes {X（t）, t≥0} with independent self-similar components, that is, X （ t ） =（X^1（t）,…,X^d（t））, where {X^i（t）,t≥0}, i=1,2,…,d are d independent real valued self-similar Markov processes. By means of Brel-Cantelli lemma, we give two results about asymptotic property as t→∞ of sample paths for two special classes of Markov processes with independent self-similar components.     

Estimation of soil water retention curve: An asymmetrical pore-solid fractal model

The soil water retention curve is an important hydraulic function for the study of flow transport processes in unsaturated soils. The objective of this study was to develop a soil water retention function using a generalized fractal approach. The model exhibits asymmetry between the solid phase and pore phase, which is in marked contrast to the symmetry between phases present in a conventional fractal model. The retention function includes 4 parameters: the saturated water content θs, the air entry value ha, the fractal dimension Df, and an empirical parameter β, characterizing the complicated soil pore structures. Sixty one data sets, covering a wide range of soil structure and textural properties, were used to evaluate the applicability of the proposed soil water retention function. The retention function is shown to be a general model, which incorporates several existing retention models. The values of β/θs and (θs-θr )/β were used as indexes to quantify the relationships between the proposed retention function and the existing retention models. The proposed function fits all the data very well, whereas other tested models only match about 16%-48% of the soil retention data.     

The classification of statistically recursive sets

The main aim of this paper is to make a classification of random setsK _m (ω) constructed in theorem 2. 1 and theorem 2. 1′ in [1]. We provide five criterions for the classification. Many kinds of random sets such as Hawkes constructed in [2], Graf constructed in [3] and Mauldin constructed in [4] are the special cases ofK _m (ω) constructed in [1], and then these random sets belong to some model respectively according to our classification. Supported by the National Natural Science Fundation and the Doctal Programme Fundation of China Hu Dihe: born in May 1935, Professor     

q - 覆盖及其空间

利用 q - 开集定义了 Q_i( #em/em# = 0, 1, 2, 3, 4) 空间, 讨论了它们的性质及 Q_i 空间同 T_i( i = 0, 1, 2, 3, 4) 空间的关系.给出了, q- 覆盖的定义,即拓扑空间 X 的q- 开集簇{Aα |α∈I } 称为 q- 覆盖, 当且仅当∪_α∈IAα = X .继而定义了一种新的紧致空间--Q- 紧致空间, 讨论它的性质及 Q - 紧空间同 Q_i 空间的关系, 得到一些性质.     

单群O_5(4)和O_5(9)的新刻画

有限群的特征标给出了群结构的许多重要信息.利用特征标的维数来刻画有限群的结构是群论研究中一个重要的课题, Huppert猜想要求考虑群的所有不可约特征标维数,条件较强.只用群的阶和群的至多两个高维不可约特征标维数成功地刻画了单群O_5(4)和O_5(9).     

On the limiting behavior of weighted partial sums for<Emphasis Type="Italic">B</Emphasis> valued martingale difference sequences

Let {X_n, n≥1} be a martingale difference sequence and {a _nk , 1⩽k⩽n,n⩾1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ _k=1 ⁿ a _nk X _k is investigated and some new results are obtained. Foundation item: Supported by the National Natural Sciene Foundation of China (No. 10071058 and No. 10071019) Biography: Gan Shi-xin (1939-), male, Prof lessor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

A new class of harmonic univalent functions by the generalized Salagean operator

A complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h ＋ g^-, where h and g are analytic in U. We define and investigate a new class SHPλ（α,β）by generalized Salagean operator of harmonic univalent functions. We give sufficient coefficient conditions for normalized harmonic functions in the class SHPλ（α,β） These conditions are also shown to be necessary when the coefficients are negative. This leads to distortion bounds and extreme points.     

Convergence in the<Emphasis Type="Italic">r</Emphasis>-th mean and the Marcinkiewicz type weak law of large numbers for weighted sums of<Emphasis Type="Italic">L</Emphasis><Subscript>q</Subscript>-mixingale arrays

L _r convergence and convergence in probability for weighted sums ofL _q-mixingale arrays have been discussed and the Marcinkiewicz type weak law of large numbers forL _q-mixingale arrays has been obtained. Foundation item: Supported by the National Natural Science Foundation of China (10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction; martingale theory, probability limiting theory and Banach space geometry theory.     

A preliminary exploration of the mechanism for the occurrence of two types of various magnetic structures in the magnetotail

As well known, the magnetic cross-tail component B_y in the magnetotail is in direct proportion to the in-terplanetary magnetic field (IMF) B_y component. And the polarity of IMF and plasmoid / flux rope B_y components do indeed agree. This results indicate that the IMF B_y penetrates plasmoids and the magnetic structures must therefore be three-dimensional. In this note, the dynamical processes of magnetotail in the course of a substorm are studied using a MHD code with two-dimensions and three components on the basis of two types of initial equilibrium solutions of the quiet magnetotail. The numerical results of two cases illustrate various features of time evolution of B_y component that correspond to two kinds of plasmoid-like structures: one is associated with a flux rope core and the other resembles a “closed loop” plamoid. Therefore, the occurrence of various magnetic structures in the magnetotail might be related to nonsteady driven reconnection with different distributions of the B_y component.     

Important properties of alternating groupA 6

By using electric computer machine, via computation method, we obtained some important properties of alternating groupA ₆, as below: 1)A ₆ has 501 subgroups in total, and for each subgroup we give its generators; 2) the index ofA ₆’s subgroup can only be 1,2,3,4,5,6,8,9,10,12,18,24,36,60,360; 3) all subgroups ofA ₆ are separated into 22 conjugate classes, and the subgroups contained in each class are listed. Foundation item: Supported by the Natural Science Foundation of Hubei Province (99J165) Biography: HUANG Ben-wen(1948-), male, Associate professor, research interest is in computation group.     

Some fractal properties of a class of self-similar Markov processes

LetX=(Ω,F,F _t ,X _t , θ _t ,P ^x be a self-similar Markov process on (0, ∞). The exact Hausdorff measure function of the level sets are obtained. An appropriate condition is given under which the self-similar Markov process corresponds to a stable process, and some more fractal properties of the sample path ofX are obtained in this case. Supported by the National Natural Science Foundation of China Huang Lihu: born in March 1972, Ph. D graduate student     

关于Banach空间中集的局部接近一致光滑性(英文)

本文，首先定义了Banach空间中奥的局部接近一致光滑性的概念。其次。讨论了集或其权是局部接近一致光滑的条件。在适当的情况，在征了局部接近一致光滑性，最后．给出了结果的应用。     

样条子空间逼近周期可微函数的最佳逼近度

样条函数类与周期函数类的逼近问题是函数逼近论的重要内容。为了在较大范围内研究最佳逼近问题,在Lp空间内研究最佳逼近方法的基础上,利用最佳逼近的对偶原理、Holder不等式等工具,借助抽象逼近的方法和技巧,研究了样条子空间在Orlicz空间内的最佳逼近问题,给出了最佳逼近度的估计式。研究结果对误差估计、精度分析可提供必要的理论分析依据和参考数据。     

Characterization of type<Emphasis Type="Italic">p</Emphasis> Banach spaces by the weak law of large numbers

For weighted sums of the form where {a _nj , 1 ⩽j⩽k _n ↑∞,n⩾1} is a real constant array and {X _aj , 1≤j≤k _{n, n}≥1} is a rowwise independent, zero mean, random element array in a real separable Banach space of typep, we establishL ^r convergence theorem and a general weak law of large numbers respectively, conversely, we characterize Banach spaces of typep in terms of convergence inr-th mean and probability for such weighted sums. Foundation item: Supported by the National Natural Science Foundation of China (No. 10071058) Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.     

Davis’s inequalities for two-parameter Banach space valued strong martingales and geometrical properties of Banach spaces

In this paper we investigated theL ₁ norm inequalities of theP square and the maximal functions of two-parameterB-valued strong martingales, which can be applied to characterizep-smoothness andq-convexity of Banach spaces. Foundation item: Supported by the National Natural Science Foundation of China Biography: YE Chen (1974-), male, Master candidate, Research interest is in stochastic processes.     

弱C-倾斜对

给出了弱C-倾斜对的概念,它是倾斜对的一个推广,进而给出了弱C-倾斜对的若干性质及等价刻画。     

聚类集成中的外部有效性指标评估研究

基于提供的11种聚类外部指标来组合多个聚类,通过单个对象的簇标记变化递增地更新目标函数来求出共识聚类,并利用模拟退火优化算法框架来解决局部最优问题。在UCI和TREC数据库中选取10个数据集进行几种算法的外部指标聚类性能评估实验,从实验数据的归一化角度和排序角度评估不同外部指标的聚类性能,结果表明:M_SS3指标从整体性能表现上最适合用于引导聚类集成,可以作为算法默认的共识函数;基于模拟退火优化算法的聚类集成算法在7个数据集上优于其他聚类方法,而DBSCAN、MCLA、Kmearns算法则在其余3个数据集上表现最好。     

Almost sure convergence and complete convergence for the weighted sums of martingale differences

Let {(D _n, FFF_n),n/->1} be a sequence of martingale differences and {a _ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption. Foundation item: Supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation of China Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate. Research interest is in stochastic processes and random fractal.