ANSYS is used to carry out analyzing and studying the dynamic characteristics for the exponential torsional vibrating horn, some important characteristic parameters are obtained, such as natural frequency, vibration mode, vibration node, magnifying factor, response situation to exterior force and so on, and the conclusion is in line with the traditional method in theory.
运用AN SY S有限元软件分析了指数型扭振变幅杆的振动特性，所反映的固有频率、振型、位移节点、放大系数等一些重要参数以及它对外部激振力的响应与传统理论方法的结果相当吻合。
The average fitness is considered to be a constant in traditional schema theory. But in practice, the average fitness will grow while the best schema grows, so the best schema will not be exponential growth exactly.
传统的模式定理认为种群平均适应度保持不变，但在实际运算中随着最优模式的增长，平均适应度也随之增长，因而最优模式是不完全按照指数级增长方式增长的。
The continuation theorem of coincidence degree theory and analysis techniques are applied to study the existence and global exponential stability of periodic solutions of BAM neural networks with distributed delays.
利用迭合度理论的延拓定理和分析技巧，得到了周期解的存在性和全局稳定性的充分条件，对设计这种类型的神经网络具有重要意义。
Exponential growth is observed in a protein-assisted RNA world *Dedicated to Manfred Eigen, the pioneer of molec- ular evolution and intellectual father of quasispe- cies theory, on the occasion of his 80th birthday.
另外关于病毒是如何起源的，病毒进化如何适应生物圈进化等历史观的内容得到保留并适当扩展，如增加了原始RNA世界和准种动力学的最新进展等。
Based on Lyapunov stability theory, an exponential synchronization controller and adaptive laws of parameters are designed.
利用Lyapunov稳定理论设计了指数同步控制器和参数自道应律，基于线性矩阵不等式技术给出了其指数同步的充分条件。
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。
Then, we may calculate actual figures of storage life for the product. This article shows five data analysis methods, which are simple linear regression, exponential regression, weighted exponential regression, polynomial regression (method of least squares) and grey theory.
本文采用一元线性回归、指数回归、加权指数回归、多项式回归（最小二乘法）和灰色理论等五种分析方法分别对五种试验数据进行了拟合与预测。
In this paper, the exponential sum approximation is studied by utilizing Pad é approximation theory and Laplace transformation theory. A simple solution of exponential sum approximation is obtained and illustrating examples of numerical values are given.
文章利用Padé逼近理论和拉普拉斯变换理论研究了指数和逼近这一非线性逼近的问题，得出了指数和逼近的一种简易求法，并给出了数值例子。
Result shows that the model established agrees with the assumptive exponential model based on the nerve network theory and the feasibility of the method is prove.
结果证明：根据试验数据建立的模型与假设的指数神经网络模型很吻合，证明了方法的可行性。
GM (1, 2) model of the grey system theory is improved by using the experience of the exponential relationship between producing cost and cumulative output. Original data is used to set up model and will not be accumulated.
该文根据生产费用和累计产量呈近似指数关系的经验，对灰色系统理论的GM（1,2）模型进行了改进，原始数据不再进行累加运算，直接建立模型。
By analyzing normal PID controller's shortage and combining the theory of intelligent control with the prime of non-linear control, a PID algorithm based on exponential function compensation and a PID algorithm based on function switch compensation are created.
通过分析常规PID控制算法的不足，结合智能控制的思想和非线性控制的精华，提出了两种非线性补偿PID算法：基于指数函数补偿的PID和基于函数切换补偿的PID。
By means of functional analysis, particularly, the linear operator theory on Banach space, the existence of the strictly dominant eigenvalue is proved, showing the asymptotic stability, the linear stability and the exponential stability of the solution.
使用泛函分析方法，特别是Banach空间上的线性算子理论，证明了严格占优本征值的存在性，以及系统解的渐近稳定性，线性稳定性和指数稳定性。
Exponential distribution is applied widely in the areas of queuing theory and reliability theory.
指数分布在排队论和可靠性理论等领域应用广泛。
In this thesis. Bayesian and empirical Bayesian theory are used to estimate the scale parameter of the double exponential distribution and the loss function and risk function of the Weibull distribution.
本文将贝叶斯，经验贝叶斯理论应用于双指数分布族的刻度参数估计和Weibull分布的损失函数和风险函数的估计。
Under the Lyapunov theory and the existing results of the robust stability of discrete time control system, the result of exponential like uncertainty structure in the sampled data control system is employed, and a sufficient condition for the robust stability of sampled data control system is proposed.
利用Lyapunov理论和已有的对离散系统鲁棒稳定性的研究成果，并应用采样控制系统中矩阵指数形不确定性结构的结果，可以给出采样控制系统鲁棒稳定界的一个充分条件。
By virtue of nonlinear semigroup theory, energy-perturbed approach and exponential multiplier method, we show that the vibration of the beam under the proposed control action decays exponentially or in negative power of time t as t →∞.
首先利用非线性半群理论和能量摄动方法，证明了文中所给出的非线性耗散边界反馈控制可以镇定闭环系统的能量，并导出了闭环系统的能量的衰减速度。
The problem of exponential stabilization for a class of uncertain systems with sector nonlinear input is discussed. Under the matching condition, a kind of continuous robust controller is presented based on Lyapunov stability theory, which guarantees exponential stability of the closed loop systems.
研究一类输入为扇区非线性的不确定动力系统的指数镇定问题，在假设系统不确定性满足匹配条件的情况下，基于Lyapunov稳定性理论给出了一种连续型的鲁棒指数镇定控制器方案。
Theorem 3 In the theory of Boolean algebra without atomic elements to decide a sentence with length n the Turing time and space spent in the procedure is in the exponential degree of 22 cn.
定理3无原子布氏代数的一个长度为n的语句的判断过程所消耗的Turing时间和空间都是属于22cn指数级。
Based on the theory of the electromechanical analogy and the special wave equation, the equivalent circuit of the exponential acoustic waveguide was derived, the formula of its impedance transformation was obtained.
基于机电类比原理，从特殊形式波动方程出发，推导出了指数形变截面声波导管的等效电路，从等效电路推导出了声波导管的阻抗转移公式。
The amount of similarity theorems is expanded from 3 to 11, and the concepts of similarity criterion numbers, similarity exponential equation, fundamental physical quantities, and functional physical quantities are advanced, so that the system of similarity theory is strengthened.
将相似定理的数量由原来的3个扩充至11个，并提出了相似准数、相似指数方程、基础物理量以及函数物理量等概念，从而增强了相似理论的系统性。