参数积分

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polynomials with the complex argument for the constitutive parameter.

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polyno...

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

Pole-placement and Inner model tuning methods are discussed finally;(2) For the linear derivative action, several different tracker-differentiators are presented to improve the quality of the derivative signals;(3) A neural network tuning method is given for the nonlinear PID controller which includes the above tracker-differentiator;(4) For the linear integral action, a nonlinear pre-phase integrator is studied in order to decrease the phase delay problem; Simulation results show that the nonlinear PID controller including the pre-phase integrator posseses better performance in both fast and stable property, and strong ability of anti-disturbance;(5) A simple optimal criteria is introduced to optimize the parameters of the nonlinear PID controller based on the pre-phase integrator.

仿真研究表明，由此形成的非线性复合积分PID控制系统，具有快速而平稳的过渡过程和超强的干扰抑制能力；(5)采用物理意义简单明确的目标函数的优化设计方法，对上述非线性PID控制器进行参数整定，达到了满意控制典型工业过程的目的。通过对直线电机伺服系统的仿真研究，表明该种非线性控制器具有同时跟踪多个目标的优越性能。

Based on a graphical stability criterion in parameter space, the range of proportional-gain is given. For both stable and unstable open-loop plants, the stabilizing region in integral derivative space is plotted and determined directly, not to be calculated mathematically.

基于参数空间的图解稳定性准则，在已知比例增益范围的前提下，针对稳定和不稳定开环对象，直接在积分－微分参数空间绘制和确定稳定区域，避免了复杂的数学计算。

Then, it studies the supply chain management system as a complex system to confirm the state existing during operating of the system. After that, it conducts a probability analysis on the state which the system located by applying supplement variable method, and establishes the model of distributed parameter system in a form of partial differential equations. Combining C0 ? semigroup theory in the functional analysis, it conducts a dynamic analysis on the established mathematical model. Using this method, it obtains the mathematical expression of the dynamic solution and the steady state solution, and proves the uniqueness, non-negativity and the asymptotic stability of the system solution. This dissertation applies the Matlab tool and uses two-step, three-step Simpson integral equation to imitate the condition of system solution. Then, it adds possible mode of failure and the optimization adjustment state to the system, based on which it has established the distributed parameter system model which is described by partial differential system of equations. Combining the functional analysis C0 ? semigroup theory, it studies the established mathematical model, and obtains the mathematical expression of the dynamic solution system and the steady state solution. It has proven the existing of uniqueness of the system solution, the asymptotic stability of system solution and the system solution. In addition, it has lying the theory rationale for further analysis and the research on the optimization of system.

本文首先简要综述了供应链理论、可靠性研究、鲁棒性研究以及供应链鲁棒性研究的现状；然后，将供应链系统作为一个复杂系统来分析，确定了系统运行过程中所经历的状态，通过引入补充变量的方法，建立了用偏微分方程组描述的分布参数系统模型，用泛函分析中的C_0 -半群理论得到了系统动态解和稳态解的数学表达式，证明了系统解存在的唯一性、非负性和指数阶渐近稳定性；并借助Matlab工具，利用二阶、三阶辛普森积分方程模拟系统解的性态，并给出系统动态解的仿真图；本文又对上述系统增加了系统可能失效状态和优化调整状态，并在此基础上建立了用偏微分方程组描述的分布参数系统模型，同样用泛函分析中的C_0 -半群理论对所建立的数学模型进行了研究，得到系统动态解和稳态解的数学表达式，证明了系统动态解存在的唯一性、非负性及渐近稳定性，为进一步分析和研究供应链优化奠定了理论基础。

Based on Born approximationmethod and the local principles of wave function in inhomogeneous medium and theray theory and the integral equation theory,this dissertation researches the theory andsimulation of the inversion method of large perturbational medium parameters andbreaks through the approximation condition of the small perturbational parametersand the weak scattering in traditional inversion method.

本文在Born近似方法的基础之上，基于非均匀介质中波函数局部理论和射线理论及积分方程等理论方法，对大扰动参数反演方法的理论和数值模拟进行了研究，突破了传统反演方法要求的参数小扰动和弱散射条件。

For the first time we parametrize such a flow with two physical constants, namely the specific angular momentum accreted by the black hole j and the energy quantity K.

我们首次应用两个物理常量，即角动量积分常数j和能量参数K给出了含激波的吸积流解对应的参数空间。

It adopts the single chip computer control calculation meritorious service capacity, and parameters such as real power, reactive power, meritorious service rate element, tension fundamental harmonic virtual value and tension harmonious wave virtual value and so on these are separation to the calculation branch to the measurement that on the basis of the scattered integration formula in immediate future scattered Fourier transformation, the exchange basseted on to power system parameter sampling idea was achieved to adjust all the journey moreover the frequency alternating current frequency and the tension virtual value as well as the electric current virtual value in the way of software .

它采用单片机的控制运算功能，根据离散积分公式即离散傅立叶变换，基于对电力系统参数进行采样的思想，实现同时对一路工频交流电的频率、电压有效值、电流有效值的测量，用软件计算分析出有功功率、无功功率、功率因素、电压基波有效值、电压谐波有效值等参数。

It adopts the single chip computer control calculation meritorious service capacity, and parameters such as real power, reactive power, meritorious service rate element, tension fundamental harmonic virtual value and tension harmonious wave virtual value and so on these are separation to the calculation branch to the measurement that on the basis of the scattered integration formula in immediate future scattered Fourier transformation, the exchange basseted on to power system parameter sampling idea was achieved to adjust all the journey moreover the workmans frequency alternating current frequency and the tension virtual value as well as the electric current virtual value in the way of software .

它采用单片机的控制运算功能，根据离散积分公式即离散傅立叶变换，基于对电力系统参数进行交流采样的思想，实现同时对一路工频交流电的频率、电压有效值、电流有效值的测量，用软件计算分析出有功功率、无功功率、功率因素、电压基波有效值、电压谐波有效值等参数。

Moreover, the SALS images were digitally analyzed by means of Debye-Bueche and Mie scattering theory to obtain corresponding structure parameters describing the morphology, e.g., correlation distance ac, integral constant Q and fractal dimension Dc as well as the relationship between these parameters with blend composition, blending time and content of the compatibilizer.

根据Debye-Bueche和Mie散射理论，利用光散射处理软件对光散射在线采集数据进行了分析并得出表征合金体系相结构的参数：相关距离ac、积分不变量Q、分形维数Dc等并分析了各结构参数与体系组成、共混时间及相容剂含量的关系。

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。