THE FRACTAL RESEARCH AND PREDICATING ON THE TIME SERIES OF SUNSPOT RELATIVE NUMBER

In this paper, with the theory of nonlinear dynamic systems, It is analyzed that the dynamic behavior and the predictability for the monthly mean variations of the sunspot relative number recorded from January 1891 to December 1996. In the progress, the fractal dimension (D = 3.3 +/- 0.2) for the variation process rt as computed. This helped us to determine the embedded dimension [2 x D + 1] = 7. By computing the Lyapunov index (lambda(1) = 0.863), it was indicated that the variation process is a chaotic system. The Kolmogorov entropy (K = 0.0260) was also computed, which provides, theoretically, the predicable time scale. And at the end, according to the result of the analysis above, an experimental predication is made, whose data was a part cut from the sample data.

HC浓度对EGR冷却器沉积层表面微观结构的影响

不同试验条件下沉积在EGR(exhaust gas recirculation)冷却器换热管内表面的颗粒物会形成不同表面微观结构的沉积层。为了量化分析沉积处表面微观结构的分布特征和三维表面的起伏特征,提出采用沉积层表面结构特征面积占比和表面分形盒维数两个参数分析沉积层的表面微观结构变化规律,并利用其分析碳氢化合物(HC,hydrocarbons)浓度对沉积层表面微观结构的影响。结果表明:试验气体中的HC等挥发性物质的析出会影响EGR气体中颗粒物的尺寸,改变沉积层表面凹坑和凸起结构的数量和尺寸分布;随着HC浓度的增加,沉积层表面凸起结构所占的面积百分比逐渐增加,凹坑结构所占面积百分比变化较小;用于表征沉积层表面起伏程度的沉积层表面分形盒维数随试验气体中HC浓度的增加而逐渐增加。

基于复合分形的路面抗滑随机森林评估模型

路面抗滑性能直接影响着道路交通安全,而基于路表纹理特征的路面抗滑性能评估方法目前存在着可解释性差、准确度不高的问题.该研究使用精度为0.05 mm的便携式三维激光表面分析仪采集了185组路面纹理数据,通过动态摩擦因数测试仪获得了相应路段0~80 km/h速度范围内的路面摩擦数据,构建了综合表征路面纹理空间、横剖、深度方向复杂度的复合分形维数指标,建立了10 km/h和70 km/h速度下的路面抗滑性能随机森林评估模型.研究结果表明:复合分形维数具备独立描述纹理复杂程度的能力,但与路面动态摩擦因数之间不存在线性关系;复合分形维数对70 km/h速度下动态摩擦因数预估的准确度为0.78,可用于评价轮胎橡胶快速滑动状态下的路面抗滑性能;复合分形指标中的空间、横剖、表层、浅层、深层剖面分形特征共同影响着路面抗滑性能,在进行路面纹理形貌评价时,应从多种空间视角下进行纹理特征综合分析.

碎石压碎值指标与分形维数的关系研究

本文研究了碎石多次压碎对压碎值指标的影响,并利用分形维数探讨了不同复压次数的碎石分形维数的变化规律,建立了分形维数与压碎值指标间的回归方程。结果表明,对于同一种类的碎石,随着压碎次数的增加,压碎值指标逐渐减小,分形维数也逐渐减小。对于同一母岩的碎石,其分形维数和压碎值指标有正相关性。

Mass Constituents of a Flat Lattice Multiverse: Conclusion from Similarity between Two Universal Numbers, the Rocksalt-Type 2<i>D</i>Madelung Constant and the Golden Mean

In fairly good agreement with the consensus range of dark energy to matter this ratio of the critical density is suggested to be connected with the golden mean &phi;=0.6180339887, yielding for dark energy to matter mass fractions .?Assuming the baryonic matter to be only 4.432%, the ratio of matter to baryonic matter would be , and further the ratio of dark matter to baryonic one . If one subtracts from the dark matter a contribution of antimatter with the same mass of baryonic matter, according to the antigravity theories of Villata respectively Hajdukovic, the remaining mass ratio would yield . Replacing the “Madelung” constant α of Villata’s “lattice universe” by &phi;, one reaches again 1 + &phi;as the ratio of the repulsive mass contribution to the attractive one. Assuming instead of a 3D lattice a flat 2D one of rocksalt type, the numerical similarity between the Madelung constant and φ&minus;1 could not be just coincidence. The proposed scaling of the cosmological mass fractions with the square of the most irrational universal number &phi;may indicate that the chaotic cosmological processes have reached a quite stable equilibrium. This may be confirmed by another, but similar representation of the mass constituents by the Archimedes’ constant &pi;, giving for respectively for the dark components . However, the intimate connection of φ with its reciprocal may ignite the discussion whether our universe is intertwined with another universe or even part of a multiverse with the dark constituents contributed from there.

Fractal characteristics of filamentous bacteria in activated sludge and its significance

On the basis of fractal theory, the fractal characteristics of filamentous bacteria in activated sludge are studied by image dissector system. The results show that the spatial distribution structure of filamentous bacteria in activated sludge has high self similarity in statistics and the filamentous bacteria have clear phenomenon of fractal growth. The critical fractal dimension values of filamentous bacteria bulking such as Eikelboom 021N, Eikelboom 1701, Sphaerotilus natans and Eikelboom 0041 are determined initially. The fractal dimensions can be taken as a parameter to describe filamentous bacteria of activated sludge quantitatively and bring to light the disorder in appearance and the rule in inherence of filamentous bacteria system.

The Precision Estimate of Multi-Fractal Methods of Time Sequence of Earthquakes

At present,there are many methods of calculating seismic time-fractal.However,there isn’t aquantitative result about the precision of every method.So,in this Paper,we use the digitalimitation of theoretic model to solve precision estimate problems of calculating the precision ofone dimension distribution of theoretic models with Cantor multi-fractal set,we obtained someresults as follows:(1)There exists many problems such as rules,numbers of samples,basicpoint selection,the diffence resulted from different methods and so on.(2)The fixed-massmethod(MAS)and the minimal spanning tree method(MST)can give good structure charac-teristics with different q value,while the counting-boxes method can’t.And the error of thefixed-radius method(RAD)in the range of-q is too big.(3)There are scale problems of rulesfor multi-fractal,it is objective reflection for non-rule area.(4)MST has the boundary prob-lem,while MAS and RAD don’t.(5)With increasing sample number,the precision of allfractal-dimension values

Self-Similarities of Pulmonary Arterial Tree and a New Integrated Model of Pulmonary Circulation with the Name of Fractal Phasic Perfusion (FPP) Model

Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular arteries and correlate with hemodynamic measurements. However, it still remains to be shown how pathological changes of the small arteries in the lobule develop to PAH. Based on both fractal properties of pulmonary arterial tree and asynchronous phasic contractions of lobular arterial muscles under the evenness of the pulmonary capillary pressure (PCP) in the lung, the author has constructed an integrated model of pulmonary circulation which has produced a mathematical relationship between the mean pulmonary arterial pressure (MPAP) and the cardiac output (CO). By use of the expression between MPAP and CO, it has been able to explain the pathogenesis of PAH in terms of statistical changes among regional and temporal perfusions in the lung. In order to detect clinically the early stage of PAH, the author has suggested that it is important to establish the pulmonary functional imaging of regional and temporal perfusions.

The Fractal and the Recurrence Equations Concerning the Integer Partitions

This paper introduced a way of fractal to solve the problem of taking count of the integer partitions, furthermore, using the method in this paper some recurrence equations concerning the integer partitions can be deduced, including the pentagonal number theorem.

The “3 Genomic Numbers” Discovery: How Our Genome Single-Stranded DNA Sequence Is “Self-Designed” as a Numerical Whole

This article proves the existence of a hyper-precise global numerical meta-architecture unifying, structuring, binding and controlling the billion triplet codons constituting the sequence of single-stranded DNA of the entire human genome. Beyond the evolution and erratic mutations like transposons within the genome, it’s as if the memory of a fossil genome with multiple symmetries persists. This recalls the “intermingling” of information characterizing the fractal universe of chaos theory. The result leads to a balanced and perfect tuning between the masses of the two strands of the huge DNA molecule that constitute our genome. We show here how codon populations forming the single-stranded DNA sequences can constitute a critical approach to the understanding of junk DNA function. Then, we suggest revisiting certain methods published in our 2009 book “Codex Biogenesis”. In fact, we demonstrate here how the universal genetic code table is a powerful analytical filter to characterize single-stranded DNA sequences constituting chromosomes and genomes. We can then show that any genomic DNA sequence is featured by three numbers, which characterize it and its 64 codon populations with correlations greater than 99%. The number “1” is common to all sequences, expressing the second law of Chargaff. The other 2 numbers are related to each specific DNA sequence case characterizing life species. For example, the entire human genome is characterized by three remarkable numbers 1, 2, and Phi = 1.618 the golden ratio. Associated with each of these three numbers, we can match three axes of symmetry, then “imagine” a kind of hyperspace formed by these codon populations. Then we revisit the value (3-Phi)/2 which is probably universal and common to both the scale of quarks and atomic levels, balancing and tuning the whole human genome codon population. Finally, we demonstrate a new kind of duality between “form and substance” overlapping the whole human genome: we will show that—simultaneously with the duality between genes and junk DNA—there is a second layer of embedded hidden structure overlapping all the DNA of the whole human genome, dividing it into a second type of duality information/redundancy involving golden ratio proportions.

级配和密度组合对粗粒土强度特性的影响

颗粒级配和初始干密度是粗粒土强度特性的两个重要影响因素。为建立粗粒土级配、初始干密度指标与强度指标之间的定量规律。首先,基于多重分形级配方程,推导了单位体积内大于某粒径的颗粒个数与多重分形维数、干密度之间的定量表达式,并将其称之为“骨架颗粒数密度指标”;接着,开展了4种不同级配和密度组合的粗粒土三轴固结排水剪切试验,初步得出结论:连续级配粗粒土的破坏剪应力与骨架颗粒数密度指标之间呈线性递增规律;最后,对该结论进行了大量文献数据验证研究。该结论不仅可为粗粒料填筑优化方案的比选提供参考,对粗粒土强度缩尺效应的研究亦有一定启发作用。

基于分形几何的油料火焰图像分割技术研究

在图像火灾探测中,经常需要根据图像的亮度、颜色和纹理对图像进行分割,分割使到的要素越多,分割就越精准。为了提高油料火焰图像分割的精细程度,提高油料火灾探测准确率,论文研究了油焰图像分割中图像的分形特征,提出了一种改进的不需要拟合步骤的图像盒维估计方法,并通过试验验证了其可行性,为油料火焰图像分割技术提供了一定的参考,为油料火灾探测技术的发展指明了新的方向。

用小波和分维数方法处理喘振实验数据

本文针对离心压缩机喘振的实验数据，采用小波分析，发现喘振先兆的频率与后来发生的喘振频率接近，且喘振先兆和喘振均为周期性的脉动．用分维数方法进行处理分析，通过计算压缩机系统不同工况下的关联维数，可以看出关联维数是信号复杂程度的度量．以上工作为实施喘振的主动控制提供了依据．

分形理论在聚合物共混物界面研究中的应用

聚合物界面很难加以定量描述 ,采用一种图形变换的方法可以将界面复杂状态转换成几何特征加以描述 ,文中基于分形理论及 n维分形布朗运动 ,提出用分形数来描述聚合物界面的状态。

多孔介质干燥过程分形孔道网络模型与模拟:Ⅰ.模型建立

目前孔道网络干燥理论中普遍以“人造多孔介质”为孔道网络模拟的研究目标，尚未涉及实际多孔体的应用问题。以农副产品中常见孔隙直径范围（10^-7～10^-4m）的自然多孔介质为研究对象，运用分形几何学、多孔介质渗流物理和传递过程原理。建立了描述多孔介质干燥过程热质传递的分形孔道网络模型和规则孔道网络模型。模型中考虑了多孔介质孔隙内的液相流动、汽相扩散、温度梯度以及孔道微细结构特征等诸多因素对干燥过程热质传递特性的影响。为了更准确地契合自然多孔介质的孔道网络拓扑结构，应用分形孔道网络替代了通常采用的规则孔道网络。

基于分形测度的电压暂降持续时间检测

基于分形技术,提出了一种新型的电压暂降持续时间检测方法。该方法利用分形数计算信号波形的平滑度,识别暂降起止时刻的高频暂态振荡,然后将实时计算的分形数与阈值进行比较,得到起止时间的定位进而求得持续时间。基于PSCAD/EMTDC软件进行故障暂态仿真,在有无谐波畸变的情况下分别进行测试,证明该方法有效可行。同时进一步将此方法与小波变换及有效值法分析比较,表明其具有较好的实时性和准确性。

太阳黑子数时间序列的分形研究及预测

本文应用非线性动力系统理论分析了１８９１年１月至１９９６年１２月间太阳黑子月平均数变化的动力行为及其可预测性·计算了它的分形维数（Ｄ＝３３±０２）·确定了预测的嵌入维数［２×Ｄ＋１］＝７；计算了Ｌｙａｐｕｎｏｖ指数（λ１＝０８６３），揭示了该系统的混沌特性；并计算了Ｋｏｌｍｏｇｏｒｏｖ熵（Ｋ＝００２６０），用以从理论上分析这组数据可预报的时间尺度·最后根据分析的结果。

分形理论在储集层横向预测和油气层判断中的应用

复杂的地质现象具有内部自相似特点，因此，可以用分形理论来进行定量预测。介绍了利用地震数据求取面积、关联、振幅3种维数的方法和原理，并通过建立的理论模型和计算3种维数，可以进行储集层预测和油气判断的工作。通过实例分析，表明分形分维技术能够较准确地反映地震波形特征和油气藏本身的变化，是一种比较好的进行储集层预测等工作的方法。

任意相位子波的分形反褶积方法

通过假设反射系数具有分形特性，并对预测误差滤波器进行修改，即可推导出任意相位的地震子波的反滤波方程，建立未知地震子波情况下求解反滤波因子和地震子波的迭代算法。该方法可以克服传统反褶积方法中假设反射系数为白噪声所带来的问题，能够明显提高剖面目的层段的分辨率，并具有一定的抗干扰能力。

分形方法预测气田数量及其储量

由于油气田数量与储量规模之间具有分形关系 ,本文在对松辽盆地北部已发现气田储量规模 (储量级别 )进行划分的基础上 ,应用分形方法对该区未发现气田的数量和储量进行了预测 ,同时应用截断帕雷托分布模型预测了未发现气田总储量。结果表明 ,分形方法与截断帕雷托分布模型预测的未发现气田储量大小相吻合 ,验证了分形方法是一种预测油气田储量的可靠方法。最后得出以下主要结论 :油气田数量与储量规模之间具有分形关系 ;分形方法在勘探程度较高的盆地或区带应用效果好 ,而在勘探新区有些难度。