随机

A virtual stochastic process is constructed so that the basic random variable becomes the value of the stochastic process at certain instants of time.

在此方法中，构造一个与基本随机变量相关的虚拟随机过程，使得基本随机变量成为该随机过程的截口随机变量。

That not only could be extended to the continuous random varia- ble,but also the theorem of maximum information measure could be extended to the continuous random variable, which unified the measurement arithmetic of information between distributed random variable and continuous ran- dom variable,and gave two validating models to the information entropy of the continuous random variable in the last.

用公理化的方法，推导出了有限分布列的离散型随机变量的信息量系，不仅将它推广到连续型随机变量，而且将信息量系的最大信息量定理推广到连续型随机变量，统一了离散型和连续型随机变量的信息度量算法。最后利用得出的结论对连续型随机变量信息熵给出两个验证性算例。

Furthermore, the paper analyses the randomness of two schemes and test them with FIPS 140-2 and SP 800-22 issued by National Institute of Standards and Technology.

论文详细分析了这两种方法产生的伪随机序列的随机性能，特别是使用美国国家标准和技术局发布的FIPS 140-2及SP 800-22测试标准(来源：A6dBC21论12文网www.abclunwen.com)对时空混沌伪随机比特发生器产生的比特序列进行了检测，结果表明这两种伪随机比特发生器随机性能良好。

Firstly, the article expatiates the concept of fuzzy reliability and the relation between random and fuzzy. It presents a list of random-finite element formula that is suitable for the reliability analysis for mechanical rigid frame system. Secondly, it presents two arrangements' reliability analysis methods that fit for component and fabric system. Finally, according to the characteristic of engineering mechanical, the article first brings forward half random-half fuzzy"stress-intensity intermeddle model"for mechanical intensity analysis, and according to Gerber equation for weariness intensity calculation, the article presents fuzzy number's calculating principle and the fuzzy reliability analysis method for engineering structure weariness intensity.

首先阐述了模糊可靠性概念、随机性与模糊性的关系；在导出摄动随机有限元法随机变量的变分原理、随机有限元控制方程和递归方程组基础上，给出了适合于工程机械刚架系统可靠性分析的随机有限元列式；给出了构件和结构体系两个层次的可靠性分析方法；根据工程机械的特点，首次提出机械强度分析的半随机半模糊"应力-强度干涉模型"，并依据疲劳强度计算的Gerber方程，给出了模糊强度的模糊数运算法则及工程结构疲劳强度模糊可靠性分析计算方法，该方法具有简便实用的特点和普遍意义。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

By employing the local Lipschitz condition and Picard sequence, the local existence-uniqueness of solutions of stochastic functional differential equations of Ito-type is firstly obtained. Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition. Finally, by establishing some delay differential inequalities and using properties of H_m-functions, a stochastic version of Wintner theorem and the global existence-uniqueness of solutions of stochastic functional differential equations of Ito-type are given. The results generalize the earlier publications.

首先，利用局部Lipschitz条件和Picard序列，获得了伊藤随机泛函微分方程解的局部存在唯一性；其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；最后，通过建立一些时滞微分不等式和利用H_m-函数的特性，得到了Wintner定理的随机版本和伊藤随机泛函微分方程解的全局存在唯一性，推广了已有的一些结果。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

Random recursive set; random self-similar set; random sub-self-similar set; random walk in random environment; skew product Markov chain; frac-tal set

随机递归集；随机自相似集；随机次自相似集；随机环境中随机游动；绕积马氏链；分形集

In the study of the stochastic chaos in simple pendulum, the random Melnikov process is derived and the mean-square criterion is used to determine the threshold amplitude of the bounded noise excitation for the onset of the chaos or random chaos in the system. For the coupled simple pendulum and harmonic oscillator, the Melnikov function is used to determine the condition for the onset of chaos in the case of Hamiltonian perturbations. In the case of non-Hamiltonian perturbation, the generalized random Melnikov process and mean-square criterion are used to determine the threshold amplitude of the bounded noise for the onset of random chaos.

在随机混沌研究中，应用随机Melnikov过程的均方准则研究了单摆在有界噪声激励下发生混沌或随机混沌时有界噪声激励的临界幅值；对于耦合的单摆-谐振子系统，先用Melnikov函数研究了在哈密顿扰动下发生混沌的必要条件；然后用推广的随机Melnikov过程方法研究了在非哈密顿扰动下发生随机混沌的必要条件；用最大Lyapunov指数及Poincaré截面方法结果与上述理论结果作了对比。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。