查询词典 derived equation

In chapter three,we have derived a generalized dual London equation for the Abelian "electric" field A_μfrom the effective dual Abelian-Higgs model.The approximative result and the numerical simulation result as well as their figs were shown via solving the dual Abelian-Higgs model with different methods.Hereby the vortex solution of the chromo-electric field and the vortex energy density were also discussed.Finally,we have studied the dual Abelian-Higgs model with additional vacuum constant,and have unpuzzled the vacuum constant corresponding to the bag model.When the quark sources is introduced, the vacuum constant in the MIT bag model is proportional to the quartic of the monopole mass.

利用不同方法求解该方程，给出了该方程的近似结果和数值模拟结果，并分别对两种情形画出图像作了比较，据此还讨论了色电场的涡旋解及能量密度，最后讨论了含有附加真空常数的对偶阿贝尔-黑格斯模型并对应口袋模型给出了附加真空常数的物理解释，引入夸克源之后还预言麻省口袋模型中的真空常数正比于单极质量的四次方。

Then the relationship which unknown coefficient satisfies from additional condition is derived. We deduce the existence and uniqueness of solution of the pseudoparabolic equation at last.

首先在假定系数已知的条件下，求出方程的形式解，然后再利用附加条件得到未知系数满足的关系式，最终给出了此类反问题解的存在唯一性。

First, a simple criterion on the delay-independent asymptotic stability has been derived in the form of the algebraic Riccati inequality and algebraic Riccati equation for the linear systems with time-varying multi-state delays.

4针对工业生产中广泛存在的不确定时滞过程，研究了时滞系统的渐近稳定性的判定方法和镇定方法。

A generalized mathematical model was developed to describe the distribution of over-potential.Dimensionless variables μ and ω that characterize the polarization and influence of side electrode reaction in the system,were derived from modeling.Adomian's decomposition methodADM）was used to solve the nonlinear differential equation of the model to obtain an approximate analytical solution,which was in the form of algebraic expressions of infinite power series.By the solution,the relationship between over-potential distribution and average selectivity could be easily calculated without solving the nonlinear model time and again.

建立了描述超电势分布的普遍化数学模型，归纳出表征电极极化和副反应影响的量纲1数μ和ω，并用ADM（Adomian's decomposition method）对该非线性微分方程模型求解；所获得的逼近解代数表达式，可方便地计算不同参数下超电势分布对平均选择性的影响，而毋需反复求解模型微分方程。

According to Lagrange equation in analytic dynamics, the dynamic equations of the Double-Axis Gyro Stabilized Platform of a certain airborne SAR antenna are derived, its linear model and the transfer functions of other main parts in the DAGSP are given and at last the block diagram of DAGSP is given.

6利用分析力学原理，推导了某机载天线双轴陀螺稳定平台的动力学方程和线性化模型；给出了天线双轴陀螺稳定平台中各主要环节的传递函数及数学模型。

The characteristic equation of the beam is derived, as well as an analytic expression of its eigenfunction.

推导了此梁弯曲振动的频率方程及振型函数的解析表达式。

An analytical coupled water-energy balance equation at arbitrary time acale was derived by dimension analysis and mathematical derivation.

本文通过量纲分析和数学推导得到能用于任意时间尺度上的水热耦合平衡方程，该方程含有唯一参数。

The mutual coherence and angular correlation function of scattered wave from two dimensional rough surfaces is derived with Integral Equation Model and then calculated for perfectly conducting rough surfaces, then the scattering of incident pulse wave with different shape is calculated and the shape of scattered pulse is presented.

采用积分方程法推导出了二维粗糙面的双频互相关和角相关函数，数值计算了具有不同粗糙度的良导体粗糙面的双频互相关函数，在此基础上分别计算了二维粗糙面对δ脉冲、Gaussian脉冲和矩形脉冲的散射，并给出了散射脉冲的波形。

With reductive perturbation technique, we derived a Korteweg de Vries equation (ut - 6uux + uxxx = 0) of the nonlinear vibrating string equation, which is easier to solve than the original form.

本论文运用约化摄动法分别研究了非线性弦振动、等离子体物理、血液流动和非线性电路传输线等领域中的孤波现象。

In this paper, the control factors of anaerobic digestion are discussed based on the summarization of present research literatures. The mechanism of the effect of pH and Eh on anaerobic digestion is analyzed with microbiology and biochemistry theory. The equation describing the effect of pH variation on Gibbs free energy variationΔGis derived using Nernst equation, and the specific control conditions in engineering are summed up according to the present research achievements.

在总结已有文献的基础上，讨论厌氧消化过程的控制因素，并利用微生物学和生物化学理论分析了pH值和Eh对厌氧消化过程影响的机理；利用Nernst方程推导出了描述pH值变化对吉布斯自由能变化ΔG的影响的方程式；并结合已有的研究成果，总结了实际工程中的具体控制条件。

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。