函数值

How to establish the adjoint medel is discussed by using the Gateaux differential of function and the concepts of the adjoint operators in Hibert space. At the same time it is verified that selecting proper finite difference scheme can ensure discrete form remaining the same adjoint r...

文中利用泛函的Gateaux微分和Hilbert空间上伴随算子的概念讨论了连续的伴随模型的建立，并通过选择适当的差分格式离散伴随模型，使其保持连续时的伴随关系，同时给出了水温初始场最优化过程及相应的同化试验数值结果。

Using level-set method, mathematical representation for contimuum structures is proposed by means of the vector of level-set, and the general structure topology optimization can be expressed by a constrained functional minimization problem of a set of level set functions.

其次利用水平集方法将一般拓扑优化问题描述为一组水平集函数的约束泛函极小化问题，应用敏度分析，给出了此泛函极小化数值迭代求解公式，即水平集演化方程。

Through establishing the functional of the source pulse which is based on the concept of "usable energy" in the received pulse and then extremizing the functional by means of the calculus of variations, the mathematical models of the optimized source pulse waveforms are shown to be associated with the eigenfunctions of a homogeneous Fredholm linear integral equation of the second kind. An efficient algorithm is developed for numerically solving the integral equation models.

论文研究了基于延迟反射脉冲序列无源标签的UWB RFID系统的基本工作原理并进行了详细的信号描述和分析，通过建立基于接收脉冲"有效能量"概念的源脉冲波形函数的泛函和使用变分计算泛函极值，得到了相关于第二类齐次Fredholm线性积分方程特征函数的源脉冲波形最优解数学公式模型，并开发了一套有效的数值求解算法。

Numerical simulations were done by ANSYS based on the finite element method,in which the functional is solved by Hamilton principle.

模拟软件采用ANSYS，数值计算基于有限元数值计算方法，并利用哈密顿原理求解泛函，在控制计算精度的基础上，得出了该电子光学系统的内部静电场分布和轴上电位分布，同时对静态条件下的电子轨迹进行了模拟计算。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

Based on modern optimization theory and optimal control theory, this dissertation studies some questions as follows:1. The optimization model of parameter identification of three-dimensional geologic history numerical simulation, algorithm and its applicationGeologic history numerical simulation is a basic content of basin numerical simulation, and the porosity is the major parameter in the evolution and development process of oil-bearing basin. According to the sedimentation and burial mechanism, the physical and chemical principles of oil geology, the mudstone porositys non-linear parabolic partial differential equation has been established.

本文应用现代最优化及最优控制理论，对如下一些问题进行了研究： 1、三维地史数值模拟的参数辨识优化模型、算法及应用地史模拟是盆地数值模拟的一个基础性的研究内容，地层孔隙度是含油气盆地地史演化发育过程中的重要参数，根据地层沉积埋藏机理和石油地质的物理化学原理，通过引入数学物理方程概念，建立了泥岩三维孔隙度场方程，根据问题的特点，给出了方程的定解条件，对方程的动边界也给出了处理方法，并且证明了解的存在性与惟一性，在此基础上建立了以当今实测数据为拟合准则的三维地史数值模拟的参数辨识优化模型，这是一个含有二阶偏微分方程约束的泛函极值问题。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

We take the nonlinear Klein-Gordonequation in an infinite strap and in a cylinder as examples to illustrate how to deal withnonlinear problems by using Jacobi pseudospectral methods.

Jacobi谱方法和拟谱方法数值分析理论的研究极大地丰富了现有谱方法的理论基础，同时将发展泛函分析、数值逼近论和偏微分方程数值解的相关理论。

A new method is proposed for estimating the PSF values of turbulence from turbulence-degraded images.

摘要提出了一种直接从湍流退化图像中估计湍流点扩展函数值的方法。

In the optimization iteration, the levelset function values of nodes are considered as design variables. To computedifferences normally, the Heaviside function is handled for smoothing, theregularized Heaviside function is selected to avoid the oscillation inhomogenizations method, and the results can converge smoothly.

在优化迭代过程中，节点上的Level Set函数值被看作是设计变量，并且为了便于微分计算能够正常进行，对Heaviside函数及其导函数做了光滑化处理，选取了一种正则化的Heaviside函数，避免了均匀化方法中出现的振荡现象，可以平稳地收敛到最终结果。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。