各种随机Koch曲线岛统计维数的分析

研究了随机变量分布区间（ａ，１／３）对三类随机Ｋｏｃｈ曲线岛系列的统计维数的影响，初始图形边长的扩大倍数Ｍ（Ｍ≥１或＜１）同组合岛系列统计维数和相应ｌｇＰ－ｌｇＡ回归直线截距的关系，及初始图形为正ｎ边形的岛系列的统计维数和回归直线的截距随ｎ的变化规律。

各种随机Koch曲线岛统计维数的分析

研究了随机变量分布区间（ａ，１／３）对３类随机Ｋｏｃｈ曲线岛系列的统计维数的影响，初始图形边长的扩大倍数Ｍ（Ｍ≥１或〈１）同组合岛系列统计维数和相应ｌｇＰ－ｌｇＡ回归直线截距的关系，及初图形为正ｎ边形的岛系列的统计维数和回归直线的截距随ｎ的变化规律。

岩石介质的分形空隙模型及其维数解析

为了探讨岩石介质的空隙结构及分布机理,从分形几何学的角度建立了一种更接近实际情况的岩石介质空隙结构的统计自相似分形模型,并通过随机破碎个数与自相似比的数学期望,给出了岩石介质中空隙分布的分形自相似维数的计算公式.讨论了岩石初始结构的分布维数与破碎后块度的分布维数之间的关系及其意义,为岩石初始结构的探讨和破碎机理的研究奠定了理论基础.

Statistical analysis of pressure fluctuations during unsteady flow for low-specific-speed centrifugal pumps

A three-dimensional transient numerical simulation was conducted to study the pressure fluctuations in low-specific-speed centrifugal pumps. The characteristics of the inner flow were investigated using the SST k-ω turbulence model. The distributions of pressure fluctuations in the impeller and the volute were recorded, and the pressure fluctuation intensity was analyzed comprehensively, at the design condition, using statistical methods. The results show that the pressure fluctuation intensity increases along the impeller streamline from the leading edge to the trailing edge. In the impeller passage, the intensity near the shroud is much higher than that near the hub at thc inlet. However, the intensity at the middle passage is almost equal to the intensity at the outlet. The pressure fluctuation intensity is the highest at the trailing edge on the pressure side and near the tongue because of the rotor-stator interaction. The distribution of pressure fluctuation intensity is symmetrical in the axial cross sections of the volute channel. However, this intensity decreases with increasing radial distance. Hence, the pressure fluctuation intensity can be reduced by modifying the geometry of the leading edge in the impeller and the tongue in the volute.

Reliability modeling of hydraulic system of drum shearer machine

The hydraulic system plays an important role in supplying power and its transition to other working parts of a coal shearer machine. In this paper, the reliability of the hydraulic system of a drum shearer was analyzed. A case study was done in the Tabas Coal Mine in Iran for failure data collection. The results of the statistical analysis show that the time between failures （TBF） data of this system followed the 3-parameters Weibull distribution. There is about a 54% chance that the hydraulic system of the drum shearer will not fail for the first 50 h of operation. The developed model shows that the reliability of the hydraulic system reduces to a zero value after approximately 1 650 hours of operation. The failure rate of this system decreases when time increases. Therefore, corrective maintenance （run-to-t^ailure） was selected as the best maintenance strategy for it.

Evaluation of properties for lubricant filter in diesel engines

The properties of lubricant filters in diesel engines directly affect operation of the lubricant system, and lubricant filters are apt to be impacted by many factors. Therefore, scientific and sensible methods evaluating the properties for lubricant filter diesel engines are necessary to monitor filter properties on line and dynamically. This paper applies ferrographic techniques and adopts sampling methods that oil specimens are synchronously obtained in front of and behind filter elements to monitor the filters of ISUZU DA-220 diesel engine in two FD50 forklifts. Results show that the combination of ferrographic techniques and above sampling methods is effective in analyzing the whole operating process of filters used in diesel engines. The service life and ruined type of filter can be estimated through the relationship between ferrographic readings in front and behind of filter and operation time. Furthermore, through a great deal of tests, a series of experimental curves of readings and time and characteristic parameters for filters used in different machines can be gained, which has guiding significance to the selection and maintenance of the filters. But because of the limitation of the ferrographic technique, the debris on the substrate prevents determination of sizes. It is difficult to judge accurately the size of debris that a filter can filter.

Study on the chaotic behavior of mining rock seepage system

One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit's orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.

An Interactive Model for Analyzing the Development of the Communication Discipline： Israel as a Case Study

Our paper presents an interactive four-dimensional model for studying the long- and short-term development of the communication discipline with Israel serving as a case study： institutional-contextual, institutional-in-field, intellectual-contextual, and intellectual-in-field. Our empirical analysis utilized personal interviews, archive documents, and statistical data. Four main processes were discerned： transition from integration to alienation between institutions of higher learning and the larger political and ideological context; a shift from Hebrew University Institute of Communication＇s institutional monopoly to a multiplicity of increasingly competitive communication schools/departments; transition from intellectual hegemony to limited intellectual diversity; and gradually improving status for the communication field among social science disciplines. Our case-study analysis validated the interactive relationship among the model＇s conceptual dimensions, calling for future cross-national comparisons.

Maximal Dimension of Invariant Subspaces to Systems of Nonlinear Evolution Equations

In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.

ONEOptimal:A Maple Package for Generating One-Dimensional Optimal System of Finite Dimensional Lie Algebra

We present a Maple computer algebra package, ONEOptimal, which can calculate one-dimensional optimal system of finite dimensional Lie algebra for nonlinear equations automatically based on Olver's theory. The core of this theory is viewing the Killing form of the Lie algebra as an invariant for the adjoint representation. Some examples are given to demonstrate the validity and efficiency of the program.