多变量的

These problems can be seen : the number of variables broken down by the huge market, many variables breakdown between strong relevance to the effective impact of the marketing work; In the face of new economic forms, and more detailed variables needed; By the development of methods and tools needed to be further strengthened.

可以看出其中存在的问题：细分市场中的细分变量数目巨大，许多细分变量之间存在较强的相关性，影响了营销工作的有效开展；面对新的经济形式，更多的细分变量需要提出；细分方法和工具的开发需要进一步加强。

The simulation of design has been conducted by matrix method combined with iterative method.

操作型模型分别以T_0、T_K、处理量F_0、出料浓度x_等不同控制变量为未知变量并采用矩阵法结合迭代法进行操作模拟计算；在操作模拟计算的基础上，建立了复杂多效蒸发系统操作优化模型，该模型以浓缩成本最小为优化目标，以T_K和F_0为决策变量，采用遗传算法结合矩阵法求解。

First, the partial derivative is defined, based on the convergence in probability measure in the probability measure space.

本文首先在概率测度空间上，利用依概率测度收敛，定义了多随机变量函数的偏导数，并且偏导数的计算式可以通过替换实值函数的对应的偏导数中所有的实变量替换为随机变量得到。

The main results are as follows:We review the existing Monte Carlo control variates estimators of the price of Asian options and propose a new one. According to pratical needs, we define efficiency as the inverse of the product of the variance of an estimator and its computational time and make it a standard for comparisons to draw the following conclusions: Firstly, the more control variates correlate with arithmetic average Asian options, the larger is the efficiency of an estimator with these control variates, but among which the geometric average option plays the most important role; Secondly, an estimator with more control variates is better than one with less ones only when the time to maturity is long and the volatility is high.

在综合已有研究工作的基础上，本论文的主要创新成果如下：（1）我们回顾了已有的亚洲期权价格的蒙特卡罗控制变量估计，并提出了一个新的控制变量估计，且从客观实际出发，将估计值的方差和计算时间的乘积的倒数定义为效率并以它为标准比较各估计，得到以下结论：与算术平均亚洲期权相关程度越大的控制变量构成的估计的效率越大，而其中起主要作用的控制变量为几何平均亚洲期权的价格；只有在到期时间较长且标的资产的波动率较大时，元素多的多元控制变量估计比元素少的效率大。

In the global variable, the source variable is referenced on primal space and the configure variable on dual space.

首次将全局变量中的源变量定义在原剖分网格上，将全局变量中的形态变量定义在映射剖分网格上，提高了在区域边界不规则的情况下多介质区域中磁场计算精度，和编程效率。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

To a one-dimension case, the solution to the distribution of non-monotone function is given; to a two-dimension case, the transformation of random variable and the computation formula of its probability density are given when inverse transform has one value and multiple value, meanwhile, several deductive conclusions are obtained.

从一维与二维随机变量函数的分布的一般求法出发，对一维情形，给出了当随机变量函数非单调时其分布的求法；对二维情形，用随机变量变换的方法分别给出了当逆变换单值与多值时其分布密度的计算公式，并得到了若干推论。

The substitution of triangle: used for conditions inequality proof, when given condition is relatively complex, a variable to use another variable representation, then can consider triangle substitution, the two variables are the same parameters.

1三角代换法：多用于条件不等式的证明，当所给条件较复杂，一个变量不易用另一个变量表示，这时可考虑三角代换，将两个变量都有同一个参数表示。

Twelve variables with prognostic value for mortality that were included in the final model were Activities of Daily Living score of 28, male sex, cancer, the need for oxygen therapy, congestive heart failure, shortness of breath, intake of not more than 25% of food provided at most meals, unstable condition, bowel incontinence, bedfast state, age older than 83 years, and sleeping during most of the day.

住在安养院的六个月期间内，28.3%的纽约受试者和35.1%的密西根受试著死亡；12个对死亡率有预后价值的变量被包括在最后的model，这些变量是Activities of Daily Living评分28、男性、癌症、需要吸氧、充血性心脏衰竭、呼吸急促、每餐吃进的食物不超过提供量的25%、病情不稳定、大便失禁、卧床不起、超过83岁、一天大部分时间都在昏睡；病人拥有这些变量越多，在六个月内死亡的危险将越高。

A special real-time data exchange model was proposed and established, which can explain multiple relationships between dependent variables and independent variables in developing model systems in forestry and ecology fields through vectored expression evaluation.

提出和实现了一种独特的实时数据交换模型，它通过矢量化的表达式求值，解决了在林业和生态学等方面的研究中，建立模型系时，解释变量和被解释变量之间的多对多的关系。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。