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This project also obtained several limit theorems for some important dependent random variables and stochastic processes, such as the Strassen law of the iterated logarithm for negatively dependent random variables, strong limit theorems for mixing random vectors in Banach spaces, sample path properties for two-parameter fractional Wiener processes, and so on.

随机环境中的随机变量与随机过程的研究在国内外相当活跃，本项目主要研究它们的极限性质，着重研究了随机风景中随机变量与随机过程的极限性质，主要取得了以下几个结果：首先对简单对称的Kesten-Spitzer随机游动在低阶矩的条件下给出了强逼近，大大减弱了前人要求任意阶矩的条件，然后对独立风景中的一般随机变量给出了强逼近的一般性结果，由此导出在风景和随机变量都只具有低阶矩的条件下的独立但不同分布、混合相依变量的强逼近，在只有弱高于二阶矩的条件下得到了重相对数律和弱收敛；给出了连续时间参数的Brown风景中Brown运动和稳定风景中稳定过程的滞后增量和连续模等精确样本轨道性质；同时给出了一些重要的相依随机变量和过程的若干极限定理，如负相关随机变量的Strassen重对数律、抽象空间上混合相依变量的一些强极限定理成立的充分必要条件、两参数分数Wiener过程的样本轨道性质等。

The physical mechanism of soil water transportation is explained using fractional Brownian motion. Quantitative mathematical-physical analysis model is proposed. The analytical solution demonstrates fractal characteristics of Lévy distribution.

通过对土壤中水分输运的物理机制的分析，利用分数布朗运动解释了土壤内水分输运的物理机制，得出土壤内水分输运的定量数理解析模型，模型的解析解是具有分形特征的列维分布。

Characteristic data have been worked out, including the maximum Lyapunov index λ, fractional dimension D, lacunarity Λ and eight energies of various frequency bands. After being normalized, they can function as the characteristic vectors. Then, they are transmitted into an artificial neural network to perform pattern recognition.Starting from the mechanism of ultrasonic generating, initial ultrasonic pulses are calibrated. A stylish discharge source is directly coupled with the ultrasonic sensors, and work out actual discharge magnitude.

利用非线性和非平稳的方法对超声波信号进行了分析处理，对于局部放电模型得到的信号，计算了超声波信号的Lyapunov指数、分维数D、空缺率、小波包分解的8个频带能量，得到了11个特征数据，归一化处理后形成特征向量，由人工神经网络进行识别，实现了对局部放电典型模型的模式识别，显著提高了模式识别的正确率，并分析了传播途径对识别的影响。

The substitution model of RBF neural network was made respectively by 3 different test functions. The error analyses indicate that the fractional steps experiment design method is very practical for the substitution model needed large scale test sample points.

对3个测试函数建立RBF神经网络替代模型，其误差分析表明，分步试验设计方法对于需要大规模试验样本点的替代模型是非常实用的。

Comparing these deviation values and the colligate error controllable limit of the ferrography technical and analysis the amount of deviation, the method of fractional precipitation is feasible in actual operation .

通过比较这些偏差值与铁谱技术的综合误差控制限度，并分析误差原因，来判定铁谱技术中磨粒分步沉积方法在实际操作中的可行性。

This paper presents the interconnection structure and its linear fractional transformation of a class of parameter perturbed systems.

对参数摄动系统的互联结构阵及其线性分式变换给出了可在统一框架下进行处理的方法。

Linear and nonlinear uncertainties are handled by a unified linear fractional transformation model with Popov multipliers.

用带有Popov乘子的线性分式变换模型对线性和非线性不确定性进行了统一处理。

The Linear Fractional Transformation representation of the uncertain aeroelastic system is formulated to perform model validation and robust flutter analysis.

分别使用基于Carathe-dory- Fejer插值定理和Nevanlinna-Pick插值定理的模型集检验方法进行了模型确认，在时间域和频率域中对模型集的有效性进行了验证，确定了不确定性的幅值。

The linear fractional transformation representation of an uncertain aeroelastic system is formulated to perform model validation and robust flutter analysis.

建立不确定气动弹性系统的线性分式变换模型，给出了频域的模型有效性检验方法，对有效模型集进行参数化并将不确定性幅值最小的模型集求解归结为优化问题。

The generalized stability margin and the linear fractional transformation are introduced. A new method with μ-analysis is proposed to appraise a flight control law.

本文介绍了系统广义稳定裕度概念及模型的线性分式变换表达，给出了μ分析评估方法的相关概念、性质，并使之相结合评估飞行控制律。

In contrast to the ubiquitous rising-sun-with-rays military flag of the Japanese, Chinese banners and ensigns feature a range of designs.

与遍地都是的太阳军旗不同，中国人的旗帜和徽章设计得各式各样。

From their small corner of Feng's Guangzhou headquarters -- a jumble of pink leashes, squeezable rubber steaks, and plastic doggy Santas for Fido's stocking -- Soleil's designers come up with at least five new products a month.

从Feng 设在广州总部的产品展示柜台上可以看到，Soleil的设计师每月至少设计出5件新产品。