可变量

Two types of new Abel differential equation are structured by method of variation replacement, variation position transformation and compound function derivation law.

借助变量替换法、交换变量位置法及复合函数求导法则，构造出两类新的 Abel型微分方程，论证它们的可积性，提供可积的判据，从而推广有关文献的结论，扩大微分方程的可积范围。

Abstract〕similar to regression analysis,cluster analysis,etc.,correlation analysis is also the basic work for information researches.canonical correlation analysis can be used to analyze the relationship between two groups of variables,and thus worth for using in information science.method of canonical correlation analysis was presented in present study.a java-based network algorithm of canonical correlation analysis was developed,which can be used to calculate the canonical correlation coefficients,canonical variable pairs,and statistical significance of canonical correlation coefficients.the algorithm may be run on java-compatible web browser.at the same time,paper publishing information and citation statistics in information science of china in past years were analyzed using the algorithm,and a number of conclusions were drawn.

摘 要〕与因果分析等一样，相关分析也是信息资料分析的基本工作。典范相关分析用于分析两组变量之间的关系，在情报信息的相关性分析方面有潜在的应用价值。本研究介绍了典范相关分析方法，给出了典范相关分析的java网络算法软件，可用于计算典范相关系数，典范变量对，以及典范相关系数的统计显著性。该软件可在兼容java的网络浏览器上运行。同时，用该算法对国内情报信息论文的发文和引文统计数据进行了分析，得到了一些结论。

As for continuous random variable, the connection of distribution function between random variable and its function -- a new random variable can be obtained first according to the definition of distribution function, then the connection between distribution densities can be obtained by derivation; thus the distribution density is solved.

对于连续型随机变量ξ来说，可由分布函数的定义先求出随机变量ξ和它的函数η=f这个新的随机变量的分布函数之间的联系，然后通过求导，得到密度函数之间的联系，从而求得η的分布密度。

The identity and difference in the expressional patterns between distribution functions of discrete random variables and distribution functions of continuous random variables are elaborated,and the main expressional patterns of distribution functions of continuous random variables are summarized,and the derivability of distribution functions of continuous random variables is discussed.

0引言在概率论中，连续型随机变量分布函数的表达形式及其可导性是一难点。其一，离散型随机变量的分布函数有较明显的性质和统一的表达形式，而连续型随机变量，由于其概率密度函数一般为分段函数，根据其分段区间的差异，表达形式差异较大，不容易总结其规律，本文主要比较连续型随机

Factor analysis is a very popular multivariate statistical analysis method. It can summarize some unobservable factors from the test results which can summarize most of the observed data. The factor analysis suggest the DP, furfuran and CO_X can be divided into insulation aging factor, while the hydrocarbon gas and hydrogen were divided into another group which can be called insulation fault factor. The result of the factor analysis

因子分析作为一种常用的多元统计分析方法，可从众多可观测变量中，概括和推论出少数不可观测的潜变量，用最少的因子去概括和解释大量的观测事实；本文将试验过程中90℃下油中溶解气体、绝缘聚合度、糠醛等参量进行因子分析，结果表明：绝缘聚合度、糠醛、CO_x被分为一类，代表绝缘老化因子：烃类、氢气、被分为一类，代表绝缘故障因子；因子分析结果与现场经验一致，相互印证，具有重要意义。

The problem of PI controller design for the multi-input and multi-output system is transformed to that of static output feedback controller design via the new state variable. As to the problem of the static output feedback, a new LMI-based sufficient condition of the controller is presented in this thesis. We can gain the multivariable PI controllers just solving one LMI inequality. The numerical example is provided to illustrate the proposed design approach. 3.The H_∞ robust control is able to solve the multivariable problem, also the control problem characteristic of the modeling error, parameters uncertainties and unknown perturbation, Its application research in the power electronics is beginning now. Considering the characteristics of the PWM DC-DC converters, a multivariable PI controllers which is based on H_∞ Performance Index is designed.

通过构造新的状态变量，可以将多输入多输出系统的PI控制器设计问题转化为静态输出反馈控制问题，利用后者的成熟理论来设计控制器；本文在问题转化后采用更为简便的算法，只需通过求解一个LMI不等式，就能求取基于H_∞性能指标的多变量PI控制器参数，实例验证了算法的有效性。3.H_∞鲁棒控制具有处理多变量问题的能力，可解决具有建模误差、参数不确定和干扰未知系统的控制问题；它在电力电子学中的应用研究刚刚开始。

The model of principal components is built up by applying a method of principal component analysis and by extracting the principal character of process variable to condense process data of multi-variables in a process of chemical polymeric production.

对聚合生产过程中的操作变量进行主元分析，提取过程变量的主要特徵，建立主元模型，可实现对多变量过程数据的压缩。

The results indicated:（1）the combination of the Markov and spatial logistic models can improve the predictability of each model individually. In macroscopic scale, the total land use amount can be predicted via Markov chain; in microscopic scale, the multi-class multinomial logistic model can be used to implement the combined calculations of categorical variable and continuous variable, qualitative variable and quantitative variable to improve the precision of spatial regression. Meanwhile, the transition probability of each land use unit will be confirmed and the prediction of land use spatial distribution will also be completed.（2）the application system developed in accordance with the integrated model can effectively simulate and predict the land use evolution in Shenzhen City, and the prediction precision of verification system will suffice for recent land use monitoring and the making of annual land supply planning.

研究结果：（1）空间Logistic和Markov模型集成可提升单一模型的应用能力，宏观上利用Markov Chain进行土地利用规模总量预测，微观上利用多分类Multinomial Logistic模型解决分类变量与连续变量，定性变量和定量变量的联合解算提高空间回归精度，同时可以确定每一个土地利用单元转移概率，实现土地利用空间分布的预测；（2）基于集成模型开发出的应用系统能够有效仿真和预测深圳市土地利用演化，通过验证系统预测精度能够满足近期土地利用预警和年度土地供应计划编制。

Trigonometric series is used to simulate stationary, non-stationary, Gaussian andnon-Gaussin stochastic processes by spectral representation in which the non-stationary stochastic processes are expressed as the product of determinate functionsand stationary stochastic processes.

结合随机变量的Monte Carlo模拟法，随机场的局部平均法与随机过程的三角级数模拟法，用均值、方差、相关长度及功率谱等，可有效地描述随机变量、随机场、随机过程，及同时具有场与过程随机的变量。

Considering linear and O-linear predictable variables, the author investigates optimal prediction problems by the trace of matrix. A few necessary conditions are derived and accordingly optimal linear and optimal O-linear unbiased predictors, which are unique with probabitity one, are obtained respectively by the author.

对于一类线性可预测变量和Φ-线性可预测变量，作者在矩阵迹意义下研究了一般增长曲线模型中最优预测问题，找到了其存在最优预测的几个必要条件，并在给定的条件下分别得到了最优线性无偏预测和最优Φ-线性无偏预测，而且还证明了它们在几乎处处意义下的唯一性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。