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Thirdly, by applying Frenchet derivative analysis, the iteration formula is derived to solve the constrained functional minimization problem, essentially the formula is a level set equation, in which the motion velocity of the level set is the shape sensitivity of material interfaces.

为了有效处理违反约束，这里还提出了在违反约束水平集的负法凸锥内构造水平集的法向修正速度的返回映射算法，它可以方便地处理多材料、多约束和含有非设计域的结构设计问题，使初值给定容易。

By applying Frenchet derivative analysis, the iteration formula is derived to solve the constrained functional minimization problem, essentially the formula is a level set equation, in which the motion velocity of the level set is the shape sensitivity of material interfaces.

这样就把材料界面表示为一组高维函数的水平集，使拓扑优化问题转化为材料界面追踪问题，这时材料界面的形状敏度就(来源：9aABb5C论文网www.abclunwen.com)是水平集的运动速度。

Firstly, the approach formulates a cost functional to turn the inverse problem into a constrained minimization problem according to least squares criterion, then the resulting constrained minimization problem is transformed into an unconstrained minimization problem by using a penalty function technique, and then the closed Fr chet derivatives of the Lagrange function with respect to the properties are derived based on the calculus of variations, finally, one can solve the resulting problem by using any gradient-based algorithm and the finite-difference time-domain method.

该方法首先以最小二乘准则构造目标函数，将逆问题表示为约束最小化问题；接着应用罚函数法转化为无约束最小化问题；然后基于变分计算导出闭式的拉格朗日函数关于特征参数的Fr chet导数；最后借助梯度算法和时域有限差分法迭代反演德拜模型参数。

We focus on a particular class of subsets in the above topological space which is named support-bounded constructible subset as an analogue of constructible subsets in module variety and is invariant under derived equivalence.

我们研究了复形拓扑空间的一类特殊的子集合，称为支撑有界可构集，它是普通模簇上可构集在导出范畴上的类比并且是导出不变的。

The fundamental principles underlying the concept of electronic beam steering are derived from electromagnetic radiation theory employing constructive and destructive interference.

电子波束控制的基本原理来自于电磁场理论的相干作用。

There is no requirement that the compiler lay out the base and derived parts of an object contiguously. Hence, Figure 15.1 is a conceptual, not physical, representation of how classes work.

C++ 语言不要求编译器将对象的基类部分和派生部分和派生部分连续排列，因此，图 15.1 是关于类如何工作的概念表示而不是物理表示。

In this thesis, a semi-classical model of the force on an atom is used to describe the motion of a two-level atom interacting with a standing wave laser field. The velocity dependent force and momentum diffusion are derived through optical Bloch equations by using the matrix form of the continued fraction technique. By investigating the dynamic properties of atoms in laser field, we can control and manipulate the mechanical motion of an atom.

本文利用半经典理论，从二能级原子在激光驻波场中所满足的运动方程出发，推导出密度矩阵元所满足的递推关系，利用矩阵连分数方法求解出密度矩阵元，从而求出依赖于原子运动速度的光压力与动量扩散系数，通过讨论原子在激光场中的动力学行为，为原子在激光场中被囚禁、形成原子列阵以及可控制的量子态，从而为量子信息处理提供理论基础。

Firstly, general mechanical displacement and a dispersion equation are derived by solving elastic field equations with continuity boundary condition.

本文推导了双层声波导结构乐甫波传感器的频散方程和质量敏感度。

This relationship will eventually be substituted into the equation of continuity for moisture, which is now derived.

这个关系式最终要代到下面要推导的水连续性方程中去。

From continuity equation and Navier-Stokes equation, non-dimensionalized stream function-vorticity equations is derived.

这是能否用有限元方法正确描述流场的关键。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。