辅助变量

Main contributions and achievements are as follows:A general non-equilibrium rigorous model for RDP is developed in this thesis. Based on the pseudo-homogenous assumption, two main factors reaction and separation are de-coupled, and an RDP model with the same format as that for a traditional distillation process is established. To solve the model with a large number of algebraic equations, modified M-K equations with tri-diagonal matrix form are developed based on the improved Separation Efficiency Functions, which greatly increases the iteration efficiency. This thesis also develops a general reactive distillation dynamic model. Through splitting of the differential variables based on SEFS, large-scaled differential algebraic equations can be solved with the improved Gear's algorithm which makes the dynamic model suitable for the on-line application. A simulation platform for the control loop design and evaluation of RDP by introducing control system equations into the dynamic model is also developed.A lactic acid purification pilot-scale RDP is investigated.

论文对热点问题——反应精馏过程的建模与优化控制相关技术进行了深入的研究，取得了一系列成果：1、建立了反应精馏过程机理模型，基于拟均相假设，将反应和分离过程进行解耦，推导出反应精馏过程的非平衡级稳态模型和动态模型，通过引入推广的分离效率函数，对模型变量进行了合理划分，显著提高了模型求解效率；将动态模型和控制系统方程结合，建立了反应精馏过程控制系统研究的辅助工具。2、全面分析了乳酸提纯反应精馏新工艺试验装置，利用本文建立的过程机理模型，对该试验装置进行了稳态和动态性能分析及水力学核算；设计和分析了单边质量控制方案，比较了间接和直接物料平衡控制两种方案的控制性能。

As a result, it shows thatthe static or dynamic subsystem optimum alone is not equal to the system optimum. Three initial value problems met in the optimal design of flying vehicle are studied andconclusions are derived that: orthogonal test method can be adopted to decide the initial valueof static optimization problem, some mathematical techniques can be used to deal with thecostate variables of Maximum Principle and decide the initial value of the costate variable,the indirect method can be used to get the analytical solution under ideal case to guide thechoice of the initial control curve in the direct method. With some numerical examples oftrajectory optimization, it shows that all these methods are useful not only in accelerating theconvergence but also in converging to the global optimum.

针对飞行器优化设计中的三种初始值问题进行了研究，以远程弹道导弹弹道的工程优化为例说明，对于静态优化问题，采用正交试验法选取初始值，不仅可以大大加快收敛的速度，而且更有可能收敛到全局最优解；以气动力辅助变轨问题为例说明，用共态变量的一阶泰勒级数展开可以解决极大值原理中共态变量初值难于确定的问题；以二级弹道导弹的主动段弹道优化为例说明，利用间接法在理想情况下得到的解析解来指导直接法初始控制曲线的选择，将大大有利于提高直接法的收敛速度。

In order to assist Boost converter design, the working process of the converter at discontinuous current mode was analyzed and a nonlinear mathematical model was estabilished as well. Case study on Matlab/ Simulink was performed with binary logical variable used, the simulation result was consistent with the theoretical analysis which proveed the validitd and feasibility of the proposed model. The model could be used to assist Boost circuit design effectively and supplie a basis for parameter optimization.

为了辅助升压变换器在应用中的设计，分析了电流断续状态下Boost变换器的工作过程，建立了这种状态下的Boost变换器非线性数学模型，在结合二进制逻辑变量，建立了Simulink模块下的变换器仿真模型，研究表明仿真结果与理论分析结果一致，证实了模型的准确性和可行性，这种逻辑与模拟结合的简明通用的模型可以高效辅助Boost电路设计并为参数优选打下了基础。

Through constructing the function between the radius of a sphere and its auxiliary variables, the radius can be obtained if one of the coordinates of each spherical point is measurable and the other two are constant and unknown.

当球面点的坐标分量之一已知，而另外两个分量固定不变但未知时，通过建立球半径与辅助变量之间的关系，可达到测量球半径的目的。

the fast transposition algorithm to sparse matrix expressed by triple list is introduced.this algorithm needs to determine the position in the transposed matrix position of the first element which is not equal to zero in the original matrix each row,it uses two arrays as auxiliary space.in order to reduce the auxiliary space which the algorithm needed,an improvement is made through introducing two simple variables.the improved algorithm saves a half auxiliary space compared to the original algorithm at the same time complexity.

摘 要：介绍基于三元组表表示的稀疏矩阵的快速转置算法，此算法在转置前需要先确定原矩阵中各列第一个非零元在转置矩阵中的位置，在此使用2个数组作为辅助空间，为了减少算法所需的辅助空间，通过引入2个简单变量提出一种改进算法。该改进算法在时间复杂度保持不变的情况下，空间复杂度比原算法节省一半。

Mr Leamer's work on capital punishment demonstrated that the choice of controls matters hugely.

利默教授对于死刑的研究显示，对辅助变量的选择能够极大的影响分析结果。

Order determination is accomplished in two stages, i.e., the AR order is first determined by the minimum eigenvalue of overdetermined instrumental variable product moment and the MA order is then estimated by the minimum eigenvalues of a covariance matrix derived from the observed data.

该方法将ARMA模型的结构辨识分两步进行：首先利用超定辅助变量乘积矩(0IVPM)的最小特征值确定自回归部分的阶，然后利用协方差矩阵的特征值估计滑动平均部分的阶。

For signals that exhibit a weak or moderate long-term persistence,an OIVPM-MDL structure identification method is proposed based on overdetermined instrumental variable product moment and minimum description length criteria,and for signals with a strong long-term correlation between samples a combinative approach of inverse fractional filtering and the OIVPM-MDL method is also described.

本文研究了滤波分形差分高斯噪声过程的结构辨识问题，针对存在较弱和适中的长期间相关的信号，提出了一种基于超定辅助变量乘积矩和最小描述长度准则的OIVPM－MDL结构辨识方法；针对存在强长期间相关的过程，提出了分形反滤波与OIVPM－MDL的组合定阶方法。

In the training of HMM, referring to the auxiliary function in reference〓, and the method in reference〓 to get the estimations of the parameters of Markov chain, we define the likelihood function and auxiliary function for the maximum likelihood estimation of CDHMM, and then induce systematically the forward-backward algorithm and the re-estimation formulas for parameters of CDHMM.

在HMM的建模方面，本文借鉴文献〓中求多变量观测值马尔可夫链参数时辅助函数的选取方法，定义了CDHMM的似然函数和辅助函数；借鉴文献〓中求解马尔可夫链参数时的求偏导方法，并针对本文辅助函数加以简化和改进，系统地推导了HMM的前向—后向算法，以及CDHMM各参数的极大似然估计公式。

The algorithms for the reachability tree of marking variables and for S-invariants are implemented in this package.

设计和实现了SHLPN辅助分析软件，它包括了SHLPN标记变量可达图和S-不变量算法的实现。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了