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Jacobian, Hessian Matrix Properties, Sensitivity Analysis w.r.t Design Variables, Fixed Parameters and Constraints, Normalization, Finite Difference Approximation, Automatic Differentiation, ANOVA, Adjoint Methods, Examples

Jacobian， Hessian矩阵属性，灵敏度分析w.r.t设计变量，固定参数和约束，归一化，有限差分逼近算法，自动差分算法，ANOVA，伴随矩阵法，举例

College of Guandong Business, Guanzhou 510320, China）Abstract: Since large-scale vertical quench furnace is voluminous, whose working condition is a typically complex process with distributed parameter, nonlinear, multi-inputs/multi-outputs, close coupled variables, etc, dynamically decoupling control algorithm of temperature distributed parameter system in the furnace was presented, by which the whole system was decoupled to several subsystems and the implementation of controller was simplified. With finite difference approximation, the space and time step size was solved to ensure the convergency of finite difference approximation. After decoupling, the subsystems were controlled with self-learning PID control algorithm. The results show that the temperature control precision and homogeneity are improved; the overshoot and process in temperature rising period are reduced simultaneity.

摘 要：针对大型立式淬火炉体积庞大，工况复杂，炉内温度分布呈本征非均匀性，具有多输入/多输出、非线性、强耦合等特性，难以实现炉内温度高精度高均匀性控制目标等问题，提出一种温度分布参数系统动态解耦控制算法，其原理是：采用有限维逼近方法将对象解耦为多个独立的子系统，简化控制器的实现过程；通过分析有限维逼近方法的收敛性，获得保证收敛性的空间和时间步长应满足的条件；解耦后的子系统采用自学习PID控制算法，实现炉内温度高精度和高均匀性控制以及升温过程的快速性和小超调。

To find the partition function at finite temperature, go to imaginary time, t →-it, and integrate over the anticommuting variables and

为了找出有限温度下的配分函数，在虚时间下t→-it，对反对易变数和，积分

A finite set of variables.

一个变量的有限集合。

On the contrary, the obstruction to the first four variables and the unsuitable system are all obstructive factors, which lead to the slow-down of the economic growth.

相反，即对前4大变量的增长的阻碍，以及制度的不适应，都是经济增长的阻滞因素，并导致经济增长速度的减慢。

This paper describes the least one-power method of estimating the parameters in linear regression model of two variables,which is used in the solving method by fixed point, general solving method,two points method and simplex method.

论述了用最小一乘法估计两变数线性回归模型中的参数。计算方法为：通过定点的解法，一般解法，两点法和单纯形法。

Scheduling variables being time varying, the controllers designed by the fixed point method often made the closed systems act with lower performance than the fixed point .

在此，揭示了定点法所存在的问题及其实质，并针对这些问题说明利用现代调参设计方法对时变系统控制器的设

In theory this paper creates 6 independent variables to figure a corporation's debt structure by the generalized concept of capital structure with floating debt. Taking the improved Tobin's Q as the explained variable, this paper works out 4 expressions after regression estimation.

首先理论上，本文从一个新的角度在广义资本结构的概念下，将流动负债纳入负债结构的研究范围，将企业负债按照对象结构——既债权人类型分类，在此基础上设计了6个解释变量表征负债结构。

Secondary variables included fluorescein angiography and optical coherence tomography.

次要变量包括荧光血管造影术和光学相干层析技术。

Inside of foo it could see all of these variables a, b, and c

如果我们在foo中定义另一个函数，它将可以调用所有的这些变量

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。