查询词典 exponential function

Malthus argued that natural populations grow at an exponential rate, whereas the increase in food supply is linear.

在书中，马尔萨斯认为自然界中人口是以指数方式增长的，而食物的增长却是线性的。

The second section: Under the conditions of nonlinear boundary controbility, we consider the initial boundary value problem of Camassa—Holm equations with dissipative. By using the contractive mapping fixed point theorem and a priori estimates, the existence of global smooth solution, global attractor in H〓, time periodic solution or almost-periodic solution and the global exponential stability are proved.

第二部分：在非线性控制边界条件之下，对于带耗散项的Camassa—Holm方程的初边值问题，用压缩映射不动点原理及先验估计方法，证明了整体光滑解的存在性、整体解的指数稳定性、H〓空间中整体吸引子的存在性以及时间周期解和殆时间周期解的存在性。

Discussions mainly on the solution and its simple applications of the equation of interest rate and amount of circulating fund are given. The discussions also involve the proof of tending to the equilibrium state of network of stock market based on the time discrete form of the equation by using Banach theorem of contraction mapping, and the influence of amount of circulating fund with exponential attenuation due to the decreasing of banking interest rate.

文中着重讨论利率_流通量方程的解及其简单应用，包括时间离散化时股市网络用Banach收缩映射定理证明最终趋向平衡状态，以及银行减息引起资金流动按指数型式衰减等。

Note that due to the exponential holding time,such a process is still a Markov process,but it is irreversible.

注意到由于指数逗留时间的无记忆性，这样的过程仍然是马氏过程，但不可逆。

Empirical Bayes estimates of steady-state availability in exponential distribution model;2. Using vector Markov process theory and Laplace transform method,we obtain the Laplace transform of the reliability,the mean time to first failure,the steady-state availability and the steady-state failure frequency and so.

利用向量Markov过程理论和Laplace变换的方法，求出了系统可靠度的Laplace变换，系统首次故障前平均时间的表达式，系统的稳态可用度和稳态故障频度等可靠性指标；此外，还通过数值比较考察了系统参数对系统稳态可用度的影响，并对系统进行了效益分析。

Using the characteristic found,the maximum likelihood estimators and the moment estimator s of parameters of the multivariate exponential distribution of Freund are obtained.

利用分布密度分拆的思想，导出了二元及多元Freund型指数分布的一个特征，利用该特征，获得了二元及多元Freund型指数分布参数的最大似然估计及矩估计，还给出了强度服从二元Fre-und型指数分布时并联结构系统的可靠度估计及模拟。

Exponential distribution ; estimation of parameters ; strong convergence rate ; mean square convergence rate ; indicators of reliability ; Monte-Carlo simulation

指数分布；参数估计；强收敛速度；均方收敛速度；可靠性指标；蒙特卡罗模拟

In the chapter 3,we base on the existence of periodic solution ,using the method of linearization and applying the mean value theorem and the variation-of-constants formula, we get the sufficient condition of the exponential stability of periodic solution of a class of nonlinear functional differential system .

在第三章中，建立在系统周期解存在的基础上，利用线性化的方法，根据微分中值定理和常量变差公式，得到了一类非线性泛函微分系统周期解指数稳定的充分条件。

Risk model ; claims ; mixed exponential distribution ; bankruptcy probability

风险模型；理赔额；混合指数分布；破产概率

The main work is to give some sufficient conditions for the existence and global exponential stability of periodic solutions for PDNNs model, without assuming the smoothness, monotonicity and boundedness of the activation functions.

这里采用的主要方法仍然是Mawhin的重合度理论和Liapunov泛函的应用，并借助于一些重要的不等式和矩阵代数技术，得到更为一般并且具有很少限制的一些新的充分条件。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。