The flow was assumed as quasi-steady state and we applied the Multiple Reference Frame to calculate flow field. Rotational frame was use to calculate flow of impeller swept region, and flow surrounding it; stationary frame was use to calculate flow of the rest region that neat the baffle or the wall. The turbulent model used was High Reynolds k-ε model; wall function is used to calculate the flow near the wall. Because of the axial symmetric of the stirred tank, the computational domain was only half of the tank and periodic boundary was used.
假设流场为拟似稳态，应用多重参考座标系，以旋转座标系计算叶片旋转区域及其附近之流场，以静止座标系计算其余靠近壁面及挡板之流场；紊流模式使用高雷诺数之模式，对靠近壁面的流场使用壁函数来处理，由於搅拌槽具备轴对称的特性，故本模拟只取一半的搅拌槽作为计算范围以减少计算量。
Three dynamic behaviors are stationary asymmetric segregated state、periodic one and stationary homogeneous one. The effect of granular parameters such as mass radios of two kinds of granulars、diameter ratios、granular number、restitution coeffictients and the length of compartment on oscillation regime and clustering amplitude are investigated in detailed. The rules of dynamic characteristics of system associated with these parameters are presented. The clustering amplitude varies with the increase of applied intensity in Boltzmann function, which is found firstly.
在数值模拟方面，采用事件驱动法模拟两室、三室和四室盒装化系统中颗粒气体的演化过程，重现了颗粒混合物的三种动力学形态----非对称聚集态、振荡聚集态和对称均匀态，详细讨论了两种颗粒的质量比、直径比、颗粒个数比、恢复系数和盒子宽度等参数对振荡区间范围和聚集幅值的影响，给出了盒装化系统动力学演化特征随这些参数变化的一般规律，第一次指出系统的聚集幅值随激振强度的增加按照玻尔兹曼函数关系变化。
The long-term seepage control effects of the surrounding rocks of the underground powerhouse are performed by a stationary seepage analysis method combining the variational inequality formulation of Signorini's type with an adaptive penalty Heaviside function to guarantee the numerical stability and convergence. Meanwhile, the difficulty in finite element mesh generation is reduced and the calculation time and modeling accuracy are balanced with a global model of equivalent modeling and a submodel of accurate modeling for drainage hole array.
为确保数值计算的稳定性和收敛性，采用Signorini型变分不等式和自适应罚函数相结合的稳定渗流分析方法，对厂房围岩的长期渗控效应进行计算分析；同时，采用基于等效模拟的整体模型分析和基于精细模拟的子模型分析相结合的方法，以减小有限元建模难度并协调计算量和计算精度之间的矛盾。
The stationary control system which core function is interlock logic control is a significant part of the train operation control system. The switch, route and train control are disposed and the train operating safe are protected by the interlocking system.
地面运行控制系统是中低速磁浮列车运行控制系统的重要组成部分，联锁是地面控制运行系统的核心功能，实现对管辖区域内进路、道岔、列车的逻辑控制，保障列车的安全运行。
Theorem of projection is more important in the study of prediction of stationary discrete-time sequence and function approximating.
投影定理在平稳时间序列的预报及函数退近研究中起着重要的作用。
On the basis of analyzing TCU structure and function, a stationary test method is studied.
但目前TCU均依靠进口，国内尚无配套的测试系统。
One must not think that anything is fixed or stationary in this universe. Everybody moves certainly the poles move and they have already started their function of shifting their respective positions.
吾人不应认为这宇宙中一切事物是固定不动的，每样东西都在移动，当然两极也在移动，它们已经开始移动彼此位置。
When the plane wave returns and crosses the molecule, it produces an interference pattern with the stationary part of the electron wave function, like two trains of water waves crossing and forming a checkerboard disturbance.
一旦平面波折返并横越过分子，它便会与待在轨道上的电子波产生干涉图样，就像是两道水波相遇所形成的西洋棋盘般明暗交错的扰动。
First of all, original signals are decomposed into a finite number of stationary Intrinsic Mode Functions, and then a number of IMF containing main flow regime information is selected for the further analysis.
该方法首先对原始信号进行了经验模态分解，将其分解为多个平稳的固有模态函数trinsic mode function，IMF之和，再选取若干个包含主要流型信息的IMF分量进行进一步分析。
Track irregularities are actually complicated random processes, consisting of approximately stationary ergodic processes of general track irregularities in entire length and non-stationary processes reflecting geometric state of the local deflects in track. The thesis describes the characteristics of track irregularities in two ways, the characteristics of track local irregularity is expressed with peak, peak-peak, amplitude variety rate and wavelength, half-wavelength, cycle, etc, stationary and ergodic irregularities described by PSD and amplitude statistic parameters. Considering needs of vehicle-track dynamic model input, track local irregularities are described as mathematical functions, such as cosine, sinusoidal, exponent function, random track irregularity simulate from PSD by use of second filter method.
轨道不平顺实质上是一个与线路里程有关的复杂随机过程，它包含沿轨道全长的弱平稳随机过程和反映轨道局部特征的非平稳过程，本文从轨道不平顺局部特征和轨道不平顺统计特征两个方面对轨道不平顺的特征进行了描述，即用不平顺幅值、峰峰值、平均变化率和波长、半波长、1/4波长、谐波特性来描述轨道不平顺的局部特征，采用不平顺幅值的统计特性参数和不平顺功率谱密度函数来描述轨道不平顺统计特征，并基于时域分析的需要，将轨道局部不平顺表述为可用数学方式描述的函数，对随机轨道不平顺则采用随机过程的数值模拟方法由轨道不平顺功率谱构造时域内的轨道不平顺函数。
Subsequently, the stationary pressure principle proposed by Luke is extended, it is demonstrated that the preceding governing equations can be obtained from the variation of Lagrange function which equals the pressure in the case of container under horizontal excitation and rotation (pitching and/or yawing) excitation.
而后将Luke所提出的驻定压力原理推广，证明了贮箱受到平动和转动情形下，对其中液体的压力体积分形式的Lagrange函数的变分同样可以得到前述非线性偏微分方程组。
By the expansion of a function in terms of spherical harmonics, solutions in form of separation about the asymmetry disturbance were studied. At last, by the theory of stability of differential equations, under the no limitation or less than 1 to the symmetry stationary radius, the asymmetry stability of stable and unstable conditions were obtained.
然后利用球调和函数展开，研究了有关扰动的偏微分方程的变量分离形式的解，最后根据微分方程稳定性定理，在肿瘤静止半径没有限制或肿瘤静止半径小于1的情况下，得到了非对称扰动的稳定和不稳定的条件。
Stationary and nonstationary processes, including ARIMA processes. Estimation of process mean and autocovariance function. Fitting ARIMA models to data. Statistical tests for white noise. Forecasting. State space models and the Kalman filter. Robust time series analysis. Regression analysis with correlated errors. Statistical properties of long memory processes.
静态和非静态过程(包括 ARIMA 过程)，均值和时间序列分析：自协方差估计，用 ARIMA 模型拟和数据，白噪声序列的统计检验，预报，状态空间模型和 Kalman 过滤，时间序列分析的稳健性，残差具有相关性的回归分析。
In Chapter 2, I consider a queuing system in which there are two exponential servers, each having his own queue, and arriving customers will join the two queues separately, and analyze the two-dimensional Markov process representing the numbers of jobs in the two stations. A functional equation for the generating function of the stationary distribution of this two-dimensional process is derived and solved through the theory of Riemann-Hilbert boundary value problems. In Chapter 3, I consider the system with two parallel queues, in which arrivals join the shorter queue. I describe the problem of coupling and show that the generating function Fcan be continued as a meromorphic function to the whole complex plane.
全文包括三大部分：第一章介绍了基本的背景、研究进展和文章主要采用的方法；第二章研究的是有两个服务员共享的简单的排队方式的模型，即每个服务员有各自的队列，两队队长互不相关，分析了代表两个队长的二维马尔柯夫过程，推导出了二维过程的平稳分布的母函数的方程，并运用Riemann—Hilbert边值问题理论解出了母函数的表达式；第三章研究的是JSQ-PS模型(the joining the shortest queue model with processor sharing)，模型是组合了加入最短队模型和处理器共享模型而成的有用排队模型。
Main results of animal experiments: For model rats of chronic immobilization stress, weigh-gaining slowed down and fodder intake was less; time staying in the central grid prolonged and times of grid-crossing were much fewer in open field test; times of wriggling were fewer in tail-suspending test; index of adrenal gland markedly increased and no visible change occurred in the index of thoracic gland; transformation function of spleen lymphocyte and phagocytosis of enterocoelia phagocyte were suppressed; content of serum IL-1〓 increased; contents of IL-2, IL-6 and IFN-γ decreased and the change of their contents was more visible over time; counts of positive cell and points of optical density of BDNF and NT〓 in cortex and hippocampus were lower and above-noted result of TrkB was markedly higher; expression of mRNA of enkaphalin and prodynorphin in hippocampus of rats increased; many other genes in hippocampus changed such as NO7, 41, 11, 18 with gene expression reinforcement (Rattus norvegicus similar to RIKEN cDNA 6720467C03 gene), 28 [Mus musculus similar to ATP-binding cassette, sub-family A (ABC1), member 3 (LOC328776)], 23 (Rattus norvegicus complete mitochondrial genome) and 8 with weak gene expression; behavior of model rats was able to be changed by all three recipes and stationary time in tail-suspending test shortened only in Xiaoyaosan group; all three recipes enhanced the transformation function of lymphocyte and phagocytosis of phagocyte induced by ConA and increased the content of serum IL-1〓 and Sijunzitang alone had no effect on the content of serum IL-2, IL-6 and IFN-γ; all three recipes were able to prevent counts of positive cell as well as points of optical density of BDNF as well as NT〓 from decrease and trkB from increase in the cortex and hippocampus to different extent; all three recipes were able to decrease the gene expression of pro-dynorphin mRNA and Xiaoyaosan as well as Sijunzitang were able to decrease the gene expression of enkaphalin mRNA and action of Xiaoyaosan was better on these two indices than Jinkuishenqiwan; Xiaoyaosan could decrease the gene expression of №: 7, 11, 26, 42 and reinforce expression of №: 8, 28, activated the expression of №: 12 in hippocampus. Main conclusions were as follows.
三个复方都能够改善大鼠的行为学，都能缩短中央格停留时间，增加穿格次数和挣扎次数，但是只有逍遥散能够缩短悬尾实验中大鼠的静止时间；三个复方都对胸腺指数没有明显的影响；三个复方都增强了ConA诱导的淋巴细胞转化功能和巨噬细胞吞噬功能，能降低血清IL-1〓的含量，逍遥散和金匮肾气丸能升高血清IL-2、IL-6和IFN-γ的含量；三个复方均能升高皮层BDNF的积分光密度和海马中BDNF的阳性细胞数；逍遥散能降低海马和皮层中的TrkB阳性细胞数和海马TrkB的积分光密度；四君子汤和金匮肾气丸能降低皮层TrkB的积分光密度；金匮肾气丸能降低皮层TrkB的阳性细胞数；逍遥散升高皮层和海马中BDNF的作用比四君子汤和金匮肾气丸强；三个复方均能升高皮层和海马NT〓的积分光密度和海马中NT〓的阳性细胞数，逍遥散能升高皮层NT〓的阳性细胞数；三个复方均能降低海马内前强啡肽mRNA的表达，逍遥散和四君子汤能降低Enk mRNA的表达，逍遥散对这两个指标的改善作用明显优于金匮肾气丸组；逍遥散能够降低海马内7号、11号、26号、41号基因的表达；增强8号、28号基因的表达，可以使12号基因表达。
Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.
首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。
In fact, in the case of the extremal stationary axisymmetric EMDA black hole, Jd = y M2 —|￡ is a function of the black hole mass and charge, but the horizon area is just the compound function of this function, which yields the intriguing feature of this black hole derived from string theory.
事实上，在极端稳态轴对称EMDA黑洞的情况下，J_=M~2-Q~2/(2ω~(1/2)是以黑洞质量和电荷为变量的函数，而视界面积刚好就是该函数的复合函数，因此导致这个从弦理论得到的黑洞具有这一奇特的特性。
Based on switching function, mathematical models of three-level CSI and the combinational multilevel CSI have been analyzed in abc stationary coordinate and dq rotated coordinate, which are the basis of control system design.
基于开关函数，建立了三电平电流型逆变器和组合式电流型多电平逆变器在三相静止坐标系和两相旋转坐标系的低频数学模型，为电流型多电平变流器的系统设计提供了理论基础。
The two-dimensional statistical model of terrain is described by planar non-stationary random process and function W-M in Topography. On the basis of the statistical model of terrain, the simulated digital maps are produced by computer.
对仿真中用到的二维随机过程和分形学中的W-M函数产生地形数学模型的方法做了讨论，采用二维随机过程的方法产生了数字仿真地图。
At last, the power spectral density function and the mean square value function of the random displacement response of a plate with stationary random current of white noise were calculated.
最后通过具体算例，对处于外加磁场中的导电薄板通以理想白噪声的平稳随机电流，对其位移响应的功率谱密度函数和均方值函数进行了计算。