微分的

Moreover, multivariate splines are closely related with some topics in pure mathematics, such as, abstract algebraic, algebraic geometry and combinatorics.

另一方面，多元样条与基础数学的一些领域，如：抽象代数、代数几何、微分方程及组合数学等，亦有着密切关联。

The adjoint variable method for design sensitivity analysis of multibody system dynamics based on ordinary differential equations is presented.

基于常微分方程数学模型建立了多体系统动力学设计灵敏度分析的伴随变量方法。

Was systematicly introduced to the field of image processing, and formed a relatively integrated theory system combined with other mathematic tools such as mathematic morphology and affine geometry. The level set methods proposed by S.

但直到九十年代才比较系统地将偏微分方程引入图像处理领域，结合其他一些数学工具如数学形态学和仿射几何等，形成了比较完整的理论体系。

A differential equation for calculating squeeze-film air damping in slotted plates is developed by modifying the Reynolds equation.

推导出了一个适用于槽板结构压膜空气阻尼的微分方程。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Compared with the traditionalroot-locus method, the root-locus method proposed in this dissertation has thefollowing characters:1 The poles location is expressed by polar coordinates.2 The poles location is computed directly.3 The object includes the closed-loop systems and controllers.4 The influence of the parameters on the polar radius and angle can be studied mainly by differential operation.5 The relationship between the polar radius and angle can be studied mainly by differential operation.

与传统的根轨迹法相比，本论文中所采用的根轨迹法具有以下的特点：1 使用极坐标表示极点的位置2 直接计算闭环极点的分布3 研究对象包括闭环系统与控制器4 以微分运算为主要手段，研究了参量的变化对极点的极径和辐角的影响5 以微分运算为主要手段，研究了极点的极径与辐角间的关系本论文从研究Dahlin 控制器振铃现象的成因及消除方法出发，主要进行了以下方面的研究：运用根轨迹法对Dahlin 控制器进行了动态性能分析。

This thesis first proposes the idea of EM in view of the drawbacks existing in traditional modeling methods. The main approaches and the general procedure of EM are described and the recent work of GP is surveyed using a taxonomy. Secondly, in terms of model types, the EM problem of complex functions, the EM problem of system of ordinary differential equations and the EM problem of higher-order ordinary differential equations are studied in detail. Finally, some advantages and disadvantages of the EM method are summarized at the end of this thesis.

本文首先针对传统建模方法的不足，提出了演化建模的思想，阐述了演化建模采用的主要方法和一般步骤，并分类概括了遗传程序设计目前的研究内容；然后，按照所建模型的类型不同，分三章详细研究了复杂函数的演化建模问题、常微分方程组的演化建模问题以及高阶常微分方程的演化建模问题；最后，本文对演化建模的主要特点和目前存在的主要问题作了概括和总结。

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。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。