变分方程

Physical parameter substitutes for phase-changing latent heat, then critical temperature of thermal conductivity welding is determined, so finite difference equation can be solved by MATLAB software.

改变热物性参数替代相变潜热确定了热传导焊接的临界温度值，利用自编的MATLAB程序对有限差分方程进行求解，数值模拟了焊件的温度场。

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。

The Galerkin method is used to transfer the partial differential equations to variation dynamic systems.

用Galerkin方法把偏微分方程转化为变分动力系统。

Finally, For the first time, the Ritz variational based mode matching method using new basis functions is proposed to deal with a discontinuity region. The general process to construct the linear equation group is developed, and the equation group's rank is only half of that of the cascading treatment. Thus the efficiency can be increased.

还首次采用新型基函数并利用里兹变分法和模式匹配法提出了构造处理一段不连续性问题的线性方程组的一般理论，方程阶数可比常规的级联处理方法降低一倍，可提高计算效率。

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

We introduce the iterative method of Jacobi type to solve the discrete problem of the quasivariational inequality system. A new proof for the monotone convergence of the iterative method is given under appropriate conditions.

我们首先介绍求解Hamilton-Jacobi-Bellman方程的近似拟变分不等式组离散问题的一类Jacobi型迭代算法，在一定假设条件下，对这类算法的单调收敛性给出了一个新的证明。

The rigid-flexible coupling dynamics of flexible multibody systems with free largeoverall motions is studied for the first time in chapter 6.The equations of the motion forthe flexible multibody system are obtained utilizing Jourdain's velocity variationalprinciple and forward recursive formulation.

第六章首次对大范围运动为自由的柔性多体系统的刚-柔耦合动力学问题进行研究，用Jourdain速度变分原理和单向递推组集建模方法建立了柔性多体系统的刚-柔耦合动力学方程。

Delay differential equations; variational structure; Minimax theory; Morse theory; multiple periodic solutions; subharmonic solutions; Z_p geometrical index

基础科学，数学，数学分析时滞微分方程；变分结构；极小极大理论； Morse理论；多重周期解；次调和解；广义Z_p几何指标

The Euler-Lagrange equations and corresponding natural boundary condition are derived by the variation of Ohmic energy dissipation under the constraint of magnetic helicity balance.

在磁螺旋平衡的约束条件下，对总的欧姆耗散取变分，得出了环位形下的Euler_Lagrange方程和自然边条件。

We cosider a class of semilinear elliptic systems with the Neumann boundary value condition by using variational methods, two existences theorem are proved for under critical exponents and critical exponents.

利用变分法讨论了一类带Neumann边界条件的半线性椭圆方程正解的存在性，并得到了在下临界指标时的两个存在性定理。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。