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The explicit solution expressed by elementary function of equations of heat and mass transfer in spray air washer is solved.

利用常微分方程研究喷水室热质交换方程组的解，得到了各断面空气的干球温度和含湿量及水温之间的关系式，得出了喷水室热质交换方程组用初等函数表示的显式解，给出了各种状态参数情形下解的表达式。

In order to prove the reliability, test studies have been primarily carried out in the indoor soil bin. The data of the vehicle driving state parameters under the same or different terrain are analyzed. The process curves are compared by different control schemes. The theoretical model of the optimum driving state is reliable and fuzzy control scheme is feasible. The disturbances and unknown factors of control system are analyzed. Test results prove that the half-tracked air-cushion vehicle can drive steadily under control of the computer. At the same time the sensors used to measure soil mechanics characteristics on line need to be developed. And it is the important problem to be solved in the future study. The necessary regulation and correction are put up. So the studies in this paper provide some instruction for the further research work.

为了验证本文提出的最佳工作状态及最佳垫压理论，并分析控制系统的可靠性和稳定性，本文在半履带式气垫车的模型车上，在室内土槽中进行了初步的实车性能和理论验证试验，考察了在同种和不同土壤条件下气垫车的行驶状态参数的测量数据，比较了采用不同控制方法下的过程曲线，验证了最佳工作状态的理论模型和模糊控制系统方案的可行性与可靠性，从而保证了采用自整定模糊PID控制器能够使半履带式气垫车在稳定行驶最佳工作状态下；同时通过试验研究，分析了系统中各干扰与未知因素，对控制方案进行了相应的调整和修正，为今后进一步的研究工作提供了一定的指导。

The traditional smoke theory considers that the smoke particles will sedimentate due to gravity after forming of smoke screen, and then the particles reach a final sedimentation velocity thanks to the effect of air-resistance and buoyancy, and the equation can be solved by the Stokes pellet resistance theory and often used to analyze the performance of smoke.

传统烟幕理论认为，在烟幕形成后，烟幕微粒受到重力的作用开始沉降，同时受到空气阻力和浮力的作用，最后使烟幕微粒达到终端沉降速度，这个速度方程可以通过Stokes圆球阻力理论求得，并被用来分析烟幕的性能。

To be successful, a crucial selectivity problem in the conversion of aldehyde 4 to aldol 3 had to be understood and solved.

要取得成功，关键选择性问题转化为乙醛醛34已被理解和解决。

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。

Cardano's Ars Magna is a landmark in the history of mathematics. It started the theoretical research on algebraic equations, solved the polynomial equations of third-degree and forth-degree in a general and systematical way, and studied the imaginary number as well as its operations for the first time.

卡尔达诺的《大术》在数学史上具有重要的地位，它开创了代数方程的理论研究，首次系统地给出了三、四次多项式方程的一般解法，并且最早讨论了虚数及其运算。

Secondly, by applying inverse Fourier integral transform to the displacement, and uniting the constitutive and geometrical equations, the analytical expression of stress in Laplace domain were derived. Thirdly, by defining dislocation density functions, the Cauchy singular integral equations were obtained according to the boundary condition and interface connection conditions, and the problem was reduced to algebraic equations by Chebyshev orthogonal polynomial. Based the these, the unknown coefficient of the algebraic equations can be solved by Schmidt method. Finally, the time response of dynamic stress intensity factor and energy release rate are obtained by inverse Laplace transform.

首先，利用积分变换方法，推导出粘弹性层的控制方程组；其次，引入位错密度函数，并结合边界条件和界面连接条件，导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组，然后，应用Chebyshev正交多项式化奇异积分方程组为代数方程组，并采用Schmidt方法对其数值求解，最后，经过Laplace逆变换，求得动态应力强度因子和能量释放率的时间响应。

The system of differential equations for a geodesic line on an algebraic surface was discredited into a nonlinear system. Then it was solved numerically based on iterative methods.

在算法中，把决定代数曲面测地线的微分方程组离散为一个非线性方程组，然后采用迭代数值方法求解。

ODE and algebraic system of equations may be solved using the methodology in this demo.

常微分方程和代数方程的系统可能会解决，使用的方法在本演示。

The proposed algorithm use the related deduction of division with reminder of polynomials and the key equation is solved by column transformation of matrix. Then the formula of quotient and reminder can be got quickly which can reduce the times of iterative operation.

该算法利用多项式带余除法的相关推论，通过矩阵的列变换来求解关键方程，这样可以快速地得到商式和余式，从而可以减少迭代运算的次数。

Now he worked in ajoint venture.

现在他在一家合资企业工作。

More troops in Afghanistan won't change any of the foregoing.

更多的在阿富汗的军队也不会改变之前的状况。