查询词典 simultaneous differential equations

At the chapters of theory analysis,constitutive equation of dusty is deduced from the results of the experiment and related theories about oblique shock wave.after that relationship of parameters reflecting flow-field characteristic are deduced from theories of shock wave polar .The paper set up conservation equations depicting gas and solid flow-field by double fluid model,thus equations and constitutive equation of granular phase form closed equations.then the paper uses AUSNT vector splitting method to numerically calculate the equations.

理论部分主要包括：利用实验测试结果以及斜激波理论测试出该堆积粉尘的本构方程，然后利用和激波极曲线理论得到反映流场特征参数的变化曲线；本文还利用双流体模型，建立了描述气—固两相流动的守恒型方程组，与本构方程一起构成封闭方程组。

The calculation of the rotordynamic coefficients of a multistepped annular seal in hydraulic turbines is discussed in this paper. Based on the Hirs' turbulence lubrication theory and the bulk flow model, the governing equations for the flow in the seal are developed by using the Moody's friction equations. The governing equations are perturbed when the rotor and the stator are coaxial. The Runge Kutta integration method and the Newton Raphson iteration method are used to solve the perturbation equations....

本文首先在Hirs紊流润滑理论的基础上，采用体积流动模型及Moody摩擦方程建立起阶梯口环水封中流体流动的控制方程，将各个方程在转子与定子同心处进行摄动，采用Runge－Kuta积分法及迭代过程求解摄动方程，建立起水轮机阶梯式口环水封的转子动力特性系数的计算方法，为水轮发电机组轴系的动力学分析提供了必要的理论基础。

The viscoelastic modeling in 2-D SEG/EAGE salt dome model is carried out by using the simplified viscoelastic equations. A comparison of the viscoelastic single-shot records derived from acoustic equations, Carcione's equations and the simplified viscoelastic equations is made.

并利用该简化方程对SEG/EAGE二维盐丘模型进行了正演数值模拟，将模拟得到的单炮记录和声波、Carcione黏弹性波方程模拟得到的单炮记录进行了对比分析。

For obtaining the numeral solutions of round elastic plates in axisymmetrical deformation with varying-thickness in nonlinear deformation in the unsteady electromagnetic field and mechanical field,by establishing the equations of motion,the equations of distortion,the equations of Lorentz force,the equations of electronic dynamic mechenical,and adopting iterative method,we gained the nonlinear magneto-elastic calculation method and outcome of current-carrying shell,and gained the influencing degree toward mechanical parameter of varying thickness round ferreous plates in the electromagnetic field and mechanical field.

为了获得内边界固定的环形导电薄板在均布力与横向磁场作用下的变形问题的数值解，通过建立运动方程、变形方程、电动力学方程和洛仑兹力方程，运用迭代法得出了载流板壳的非线性磁弹性的计算方法和结果，以及机械场、电磁场对铁质变厚度圆板各力学参量的影响程度。

The results calculated by the Elovich rate equation showed that K release rates from 1 mol.L-1 HNO3 extraction ＞those from 2 mol.L-1 HNO3 extraction ＞those from H-resin extraction. Elovich equations combining with the data of H-resin and 2 mol.L-1 HNO3 successive extraction could well described the release characteristics of soil K. The correlation coefficients of the equations reached most significant levels (r＝0.956**—0.999**), and standard errors of specific K release capacities between the vaules calculated by the equations and those measured by both successive extractions were smaller(s=1.61 and 3.52). The specific release rates of soil K calculated by the Elovich rate equations were significantly correlated with the indices of soil K availability (the amounts of easily available K, nonexchangeable K, total available K in soils and K absorbed by ryegrass).

研究结果表明：1 mol.L-1 HNO3提取法的释K速率＞2 mol.L-1 HNO3提取法的释K速率＞氢饱和交换树脂提取法的释K速率；氢质交换树脂和2 mol.L-1 HNO3提取法结合Elovich模型较理想地描述了土壤K素的释放特性，拟合方程的相关系数均达极显著水平(r＝0.956**-0.999**)，土壤特征累积释K量的计算值与实测值的标准差较小(s=1.61和3.52)，且通过速率方程计算的土壤特征释K速率与K素有效性指标(速效K、缓效 K、有效K及黑麦草总吸K量)的相关性也较为密切。

The main creating aspects are finding and clarify such a fundamental physical process that the grain boundaries emit vacancies under compressive stress to induce solute non-equilibrium grain boundary dilution and absorb vacancies under tensile stress to induce non-equilibrium grain boundary segregation, formulizing the structural equations and the composition equations in force equilibrium in grain bounary region to describe this physical processes and the kinetic equations for non-equilibrium grain boundary segregation under tensile stress, calculating the modulus in grain boundary region from the expermental data of grain bounday segregation using the structure and coposition equations and calculating the diffusion coefficients of vacancy-solute atom complexes using the kinetic equation simulating the experimental results of grain boundary segregation.

本项目的主要创新点是，发现并阐明了弹性应力场作用下空位与晶界交互作用的基本物理过程：在张应力作用下，晶界会吸收空位，引起溶质非平衡晶界偏聚；压应力作用下，晶界会发射空位，引起非平衡晶界贫化。建立了描述此物理过程的晶界区力学平衡的结构方程和成分方程；？建立了张应力引起的非平衡晶界偏聚动力学方程？；用晶界区力学平衡的结构方程和成分方程？，首次通过实验测量计算出多晶材料晶界区的弹性模量；通过建立的动力学方程模拟实验结果，首次获得溶质原子－空位形成的复合体的扩散系数。

Then he combined the evolution equations with the Euler equations, and finally got the model equations based on the quasi-conservative equations.

Shyue将该计算方法推广到基于一般刚性气体状态方程的γ模型和体积分数模型的准守恒型Euler方程组。

The article presents a simultaneous determination method for three kinds of water-soluble dyes: acid red, acid brown and acid black by solving simultaneous equations using a UV-VIS spectrophotometer.

介绍了利用解联立方程组的方法，在紫外可见分光光度计上实现了对酸性红、酸性棕和酸性黑的混合染料中三种成分浓度的同时测定。

It can be extended to solve partial differential equations with higher order such as KdV equations and biharmonic equations.

该方法可以推广到更高阶的方程，如Korteweg-de Vries方程、重调和方程等。

Derive the equations of continuity by using the method of infinitesimal based on the mass balance equations and the differential equations of gas and oil phase fluid flow.

再根据物质平衡原理，利用微元法分析凝析油气渗流规律，建立连续性方程，从而导出凝析油气渗流微分方程。

Aquatic or marsh-growing fern allies; known to have existed since the Cenozoic; sometimes included in Lycopodiales.

生活于水中或湿地的蕨类；从新生代生存至今；有时归于石松目之中。

The engine was uprated from a 90hp Franklin to a 125hp Lycoming.

改良过的引擎是从90hp到125hp莱康明富兰克林。