空中交通流的多重分形特征实证分析

空中交通系统是复杂非线性系统,分形是非线性系统的典型特征之一.为了对空中交通流进行合理建模、精确预测和精准管控,首先在实测数据基础上构建了空中交通流时间序列,采用KS方法对其非线性进行识别;其次,利用MF-DFA方法,从多个不同角度对空中交通流的多重分形性质进行了实证分析.结果显示随着阶数的增加,广义Hurst指数从0.7167逐渐减少到0.3149,说明空中交通流具有多重分形特征,且从正相关性过渡到负相关性.标度尺度随着阶数变化而变化,呈现明显的非线性,说明空中交通流具有多重分形特征.多重分形谱函数曲线呈现钟形,峰值对应的奇异性指数有2个,分别为0.578和0.4943,谱宽度为0.52,谱高度为-0.3163,说明空中交通流具有较强的多重分形性质,并且文中的交通流时间序列向低流量方向发展的概率较大.多项式拟合的阶数会影响多重分形谱参数,但不会改变交通流变化趋势.打乱顺序后的时间序列,大部分广义Hurst指数减小,且更接近于0.5,说明交通流的多重分形性质是由长相关性和肥尾分布共同决定的,并且长相关性发挥主要作用,但与概率分布有一定的关系.统计尺度对多重分形性质有较大影响,分形方法适...     

巴丹吉林沙漠东缘不同粒级砂土空间分布的多重分形研究

为了探讨不同粒级砂土(细砂,中砂,粗砂)空间变化的特点,引入多重分形理论,揭示粒级砂土随着土层深度空间变化情况.针对土壤属性做了空间变异性分析,利用Pearson相关系数考察了不同深度下粒级砂土分布密度之间的关系,进一步做了多重分形特征判断,表明不同粒级砂土空间分布存在多重分形的变化特征.又利用广义分形谱探讨了相应的多重分形特点.多重分形谱表明,不同土层深度下,粒级砂土空间变异性增强,同时密度空间分布的变异性依赖高密度分布区的程度增强.     

求多重分形谱的滑动格子法在深浅地表元素分布中的应用研究

在多重分形理论和特征判定法的基础上,构造了求多重分形谱的滑动格子计算法,计算出了研究区域4种元素深、浅层的多重分形谱f(α)的图像.结果显示浅层元素的分布不具备多重分形特征;深层元素分布符合多重分形特征.就三种分形维数——格子维数、信息维数、关联维数对深层元素的分布做出了大小排序解释;后就多重分形谱f(α)的跨度、对称性和两端差值Δf做出了对应于深层元素分布概率分布集中差异、高低浓度分布差异、稳定性的解释.最后根据上述分析的结果指出应用求多重分形谱的滑动格子法研究深浅地层元素分布是一快速、实用、有效的方法,具有良好的应用前景.     

中国股指期货市场流动性非线性特征分析与波动趋势预测

针对中国股指期货市场的流动性问题,利用多重分形去趋势波动法研究股指期货市场流动性非线性特征及其成因,并对比分析不同期限下期货市场流动性多重分形程度的差异;进一步,采用趋势熵维数方法识别期货市场流动性的变化趋势,还利用识别正确率和随机识别正确率验证该方法有效性和准确性。研究发现,中国股指期货市场具有明显的多重分形特征;与合约期限较短的股指期货相比,合约期限较长的股指期货流动性多重分形程度更低;股指期货市场流动性多重分形特征主要是流动性时间序列的相关多重分形和分布多重分形造成的;趋势熵维数方法可有效预测期货市场流动性的变化趋势。     

产业集群的分形结构—基于演化的观点

以宏观的视角来研究企业的地理分布,并在地理空间与社会网络结构的基础上建立一个产业集群模型;该模型显示出产业集群的分形结构进而揭示出产业集群是一种自组织系统,即在生产交易过程中自发形成有序的结构或状态的现象.根据该模型,运输成本或者禀赋只是形成产业集群的所有充分条件中的一个;影响产业集群的最重要指标是关系网络空间的分形维度,它显示了经济系统的层次结构性.网络密度很大的集群的关系网络可能是接近紊乱的,即分形维度接近于零;而紊乱将会导致这个集群效益下降,甚至促使集群崩溃.     

基于MF-DCCA方法的香港股市与大陆股市交叉相关及多重分形研究

通过研究香港恒生指数和深成指数价格的交叉相关关系来确定两者的协同效应.首先,采用交叉相关统计量Q_(cc)(m)和DCCA交叉相关系数法,发现恒生指数和深成指数收盘价存在显著的交叉相关关系.然后,采用去趋势多重分形交叉相关分析法(MF-DCCA),发现恒生指数和深成指数收盘价之间具有长程交叉相关性,两个序列均呈现出反持续性和多重分形特征,恒生指数的价格变化对于深成指数变化的趋同作用非常明显.     

贝塔系数变动性的多重分形特征及其量化方法

针对CAPM模型中贝塔系数的时变性观点,本文提出了多重分形去趋势贝塔分析法(MFDBCA),运用该方法检验上证综合A股指数、上证综合B股指数、深圳综指、深圳综合A股指数及深圳综合B股指数的贝塔系数变动性,并对其多重分形程度进行了量化分析,分析了其在投资实践中应用。研究结果表明:它们的贝塔系数变动性呈现出多重分形特征,上证综合A股指数的多重分形程度最小,而上证综合B股指数的多重分形程度最大。本文研究为量化系统风险及利用贝塔投资实践提供了一种新方法,为改进贝塔系数提供了一种猜想。     

基于R/S分析的我国股票市场标度特性研究

应用重标度极差分析法(R/S),对我国股票市场不同时间间隔的收盘指数进行实证分析,研究我国股票市场的标度特性.结果表明我国股票市场具有长期记忆性和标度不变性,分别存在244天(上海)和190天(深圳)的非周期循环,并呈现多重分形特征.     

多重胞元和规则多重分形

以超级分形纤维和双重分形纤维的研究结果为基础,达成了如下目标:首先,归纳、抽象出了多重胞元概念;其次,基于多重胞元概念,证实:具有严格自相似性的规则多重分形,不仅是可构造的,而且其构造模式具有普遍性;再者,通过分析构造模式,发现:任何规则多重分形,都可以在多重胞元意义下,被精确地等价成具有多重精细结构的广义单重分形．而基于这种等价性,单重分形维数公式就能够推广至规则多重分形维数公式,单重分形几何就能够推广至规则多重分形几何;最后,借助规则多重分形,构造了几种黄金分形．     

多重分形的统计物理方法在证券市场中的应用

本文研究了多重分形的统计物理方法,以上证综合指数长达四年的一分钟高频数据为研究对象,计算了实际交易数据的多重分形谱及其特征参数,并确定了权重因子的取值范围。结果表明奇异指数和相应的谱函数作为多重分形谱的重要参数,一定程度上反映了股指本身的变化范围和高低价位出现频率的变化,然而谱函数可以预测股市趋势的断言在沪市并不成立。     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

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.     

On a class of Riemann surfaces

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.     

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.