查询词典 derived equation

Nonlinear Schrdinger equation of optical field in logarithmically saturable nonlinear media is derived firstly from scalar Helmholtz equation.

0引言近年来，光学孤子由于其独特的物理特性和广阔的应用前景，在光学领域引起了极大的关注[1~3]。

Based on the theory of nonequilibrium statistics and density operator equation, the generalized master characteristic function for the nonextensive reaction-diffusion systems affected by pressure is derived by equation satisfied by calculating the time variation of probability distribution function, where the pressure of the nonextensive systems is given in the framework of Tsallis statistics.

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出。与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性。

Considering that thermodynarmic irreversibility and hydrodynamic equations can not be derived rigorously and unifiedly from the Liouville equations, the anomalous Langevin equation in the Liouville space is proposed as a fundamental equation of statistical physics.

考虑到热力学不可逆性和流体力学方程不能严格统一地从刘维方程推导出，本文提出了刘维空间的反常朗之万方程作为统计物理的基本方程。

In the couping solution, based on the characteristics of the models in this dissertation, each of loading step is finished in unit time. Thus the volumetric strains on the current increment step as analysis parameters are inserted into the equation of continuity and a physical equation for pore water pressure is presented. The fundamental solutions of two kinds of classic problems (axial symmetry and plane strain) are derived. By use of the fundamental solutions of pore water pressure combined with finite element method of soil mechanics, a semi-analytical and semi-numerical method for nonlinear consolidation equations is presented.

在耦合分析中，根据本文模型的特点，将每一荷载增量步看作单位时间完成，对应当前增量步的体变分量作为分析参数代入连续方程，建立了基于数值模型的孔压变化方程，根据工程中最常见的两类问题推导出基本解，结合土骨架的控制方程建立了此类液-固耦合问题的半解析半数值解答体系，编制了有限元程序，从而实现了从建立本构关系到模拟固结问题的全数值方法。

The revolution bellows is idealized as a series of conical frusta, joined at nodal circles. The linear finite element analysis equation and the geometrical nonlinear finite element analysis equation in Total Lagrangian Formulation for the revolution bellows are derived using stationary total potential principle.

考虑到油罐刚度比波纹管刚度大的多，将油罐看作为刚体，将波纹管部分和管道部分分别用空间梁单元离散化，通过分析得到波纹管与油罐连接接合面、波纹管与管道连接接合面不同单元之间的位移协调约束方程，并用罚函数法进行处理。

From the three-level rate equation,the analytical expressions of the output power and the combining efficiency of the spectral combining system were derived based on the simplified model and propagation equation of the light in fiber lasers.

在简化模型的基础上，从三能级粒子速率方程出发，结合光纤激光器的光束传输方程，推导出光纤激光器谱合成系统的输出功率和合成效率的解析表达式。

The contact angle-time equation and the equation of border line of liquid bridge were derived.

实验结果表明，重力对Ag-Cu-Sn合金与Fe基片之间的润湿性有很大影响。

Through the description of the principles of estabeishing the regress-ion analysis model,carrying out the terts of significance and choosing theoptimal regression equation ,the correlative equation between human biolo-gical age and phybiological parameters has been derived and proved in thispaper.

通过建立回归分析模型、进行显著性检验、选择最优回归方程等过程的原理，找出并论证了人的生理年龄同血压和各种脉图之间的相互联系。

Beginning with forming mechanics of seal medium, the character of magnetic fluid has been researched and magnetic fluid, which fits the demand, is made out. Then from the point of fluid mechanics, the kinematics equation and Bernoulii equation of magnetic fluid are derived. Based on the production practic of sinterer, straight seal theory is given. Last of all, the accuracy of deriving of theory is proved by experiment.

作者首先从密封介质的形成机理入手，分析了磁性流体的性质，配制出符合要求的磁性流体，又从流体力学的角度推导出磁性流体的运动学方程和磁性流体的贝努力方程，根据烧结机生产的实际，进一步推导出应用于烧结机上的直线密封理论，最后通过试验验证了理论推导的正确性。

An equation is derived by theoretical analysis, to establish a relationship between suspended sediment concentrations and ADCP echo intensity output. For the survey at the entrance to Jiaozhou Bay, an ADCP is mounted on a moving vessel; the calibration coefficient in the equation is determined by in situ measurement. Then, a semi-empirical formula is obtained and used to calculate suspended sediment concentration profiles along several crosssections.

理论分析获得了海水中悬沙浓度与ADCP输出的回声强度之间的函数关系式；在胶州湾口门进行走航式测量，同步采水样进行现场校正来率定相应的ADCP声学信号，获得了计算悬沙浓度的半经验公式；进而得到走航断面准同步的悬沙浓度剖面。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。