查询词典 consistent equations

Base on nonlinear electro-magneto-elastic soupled dynamic equations of the plate and the expression of electromagnetic forces, the vibration equations of the thin beam plate under uniform transverse magnetic field and mechanical loadings are obtained.

在给出薄板的非线性电磁弹性耦合运动基本方程及电磁力表达式的基础上，得到了横向稳恒磁场和机械载荷共同作用下梁式薄板的振动方程。

Based on the discrete-time difference equation of the plant,an explicit solution of Diophantine matrix polynomial equations in multivariable generalized predictive control is derived without appealing to Diophantine matrix polynomial equations recursions or iterations,which makes the applications of generalized predictive control much more convenient.

直接利用被控对象的离散差分方程推导出多变量广义预测控制中Diophantine矩阵多项式方程的显式解，从而避免了其递推求解或迭代求解，使广义预测控制的应用更加方便。

The invention comprises a free-form surface prism with three optical surfaces, and a micro-image display; the free-form surface prism is made of plastic glass materials with the refractive index greater than 1; the three free-form optical surfaces are concave surfaces, which meet one of the three surface-type equations, and the location relationship of each surface meets three condition equations; the incident angle formed between the widest-field upper edge rays emitted by an LCD and the second free-form surface meets the total reflection conditions; and an image source element is an LCD of 0.61 or 0.59 inches.

本发明包含一个具有三个光学表面的自由曲面棱镜和一个微型图像显示器，自由曲面棱镜采用折射率大于1的塑料玻璃材料，自由曲面棱镜的三个自由曲面光学表面均为凹形面，它们应满足三个面型方程之一，并且各表面的位置关系应满足三个条件方程，由LCD发出的最大视场上边缘光线在第二自由曲面上的入射角应满足全反射条件，像源元件为0.61或0.59英寸的LCD。

Starting from the basic governing equations of axisymmetric Biot's consolidation of saturated transversely isotropic soils, and taking Laplace transform with respect to time t and Hankel transform with respect to r, the first order ordinary differential equations in term of z are obtained.

从横观各向同性地基轴对称Biot固结的基本方程出发，通过关于t的Laplace变换和关于r的Hankel变换，得到关于z的一阶常微分方程组。

The author used to solve the linear matrix method to simulate the equations of quadratic regression equation work curve with only a few simple mathematical expressions for the second straight three coefficient regression equations, received the good effect.

作者用矩阵法求解线性方程组的方法来模拟工作曲线的二次回归方程，仅用几个简单的数学表达式就直接求得了二次回归方程的三系数，收到了很好的效果。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

The construction of the solution space for shallow-water equations on the equatorialβ?plane and the equations about the tropical circulation to heating are mainly studied. The solution method of exact solution in the analytic function class and the computational procedure to the series solution are expressed for the well-posed problem.

平面近似的浅水方程组和热源强迫的热带环流方程组，重点研究了它们的解空间构造，并给出了各种适定的定解问题在解析函数类空间中准确解的具体的求解方法，并编制程序去计算其级数解。

Based on the water environment spatial data mining and visualization method, the paper presents these main characteristics and innovations:①Measurement of contamination fluxes:A scene-based research strategy is proposed:measurement /water quality analysis→flow field simulation→contamination transformation rule→fluxes scene simulation→temporal-spatial rule analysis.②Serial numerical models of water environment in the Qiantang River:The controlled equations of the flow field model of the main river,united controlled equations of the main contamination fluxes and water quality prediction model at emergent time are set up.③GIS-based water quality and contamination fluxes decision-making assistance system:A water environment database has been set up;based on MapX and C#.net platform,a system has been developed to facilitate visual inquiry,decision-making and graphics export.

本文基于水环境空间数据挖掘与可视化的研究方法与体系，研究中的主要特色与创新点为：①河流污染物通量测算的技术与方法：提出了基于工况测量/水质分析→流场模拟→污染规律解析→通量情景模拟→时空规律分析的研究方案；②钱塘江水环境模拟系列数学模型：建立了钱塘江干流研究区域流场数学模型的控制方程、主要污染物通量模型的联合控制方程、突发污染事故水质预报模型的基本方程；③基于GIS的水质预报与污染物通量决策支持系统的研发：建立水环境时空数据库，基于MapX和C#。net平台进行系统的构建与开发，为研究的系列成果提供可视化的查询、决策与图形输出。

The currency-used equations for calculating the life of the main bearings on rotary table and swivel take no consideration of all the affecting elements. The author offers thereby new equations that take an overall consideration of the load, rotary speed, lubrication, assembling, working environment, material and surface hadness.

针对现有文献给出的转盘和水龙头主轴承寿命估算公式对多种影响因素考虑不充分，与实际工况有一定出入的问题，推导出全面考虑载荷、速度、润滑、装配、工作环境和材料及表面硬度等多种影响因素，估算转盘和水龙头主轴承寿命的新公式。

A dynamic simulation mathematic model consisted of conservation equations of mass, momentum, energy, superheat steam equation, pressure drop equation, two-phase flows equations and relations before and after oblique shock.

建立了由两相流体质量守恒方程、动量守恒方程、能量守恒方程，过热蒸汽关系式、压降关系式、激波前后关系式及其它两相流关系式组成的动态仿真数学模型，模型形式为非线性方程组。

"Second Life is remarkably easy to work with, and is very popular,"

"第二次生命是显着容易的工作，并且很受欢迎，"

For example, we usually assume that materials are homogeneous and isotropic and free of internal defects or flaws.

为了得到适合有限元分析的模型，我们必须经过如图2所示的简化步骤。