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In this paper, a semilinear elliptic equation with critical Sobolev-Hardy exponents is studied, the existence of nontrival solutions for which is proved by the linking theorem in variational calculus.

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程，运用变分理论中的环绕定理证明了方程非平凡解的存在性。

The metric variational energy momentum tensor and the Belinfante tensor is equivalent and gauge invariant.

如果经典的作用量在度规的表达变换下不变，那么能动张量的迹为零， g^{ab}T_{ab}=0

It also researches the application of variational method to solve the perturbation function in the energy principle.

本文还探讨了变分方法在求解能量原理中的扰动函数的应用。

For one-dimensional ocean temperature model, we optimally determined the initial and boundary conditions and related model parameters through variational assimilation method along with inverse problem techniques using incomplete and complete observational data,so as to determine the variation of position of epilimnion which has influences on SST.

由于温跃层的变化对海表温度的影响，我们以简单的海温模式为例，采用变分同化技术及反问题的技巧，在局部和整体观测资料下，对初、边值条件和模式参数等进行最优估计，确定温跃层的位置及其变化规律。4。

Then we derive first-order necessary optimality conditions for optimization problems with affine variational inequality, which joint upper-level feasible region Z includes a linear inequality constraint and a linear equality constraint.

其次，我们研究Luo的带仿射变分不等式约束优化问题，其中上水平约束Z不仅含有线性不等式约束，而且含有等式约束情形时的一阶最优性条件，同时还给出了Z的切线锥的表达式。

The solution of the linear variational inequality problem is transmuted to an equilibrium point of neural networks.

线性变分不等式问题的解被转化为神经网络的平衡点。

In the paper, we use the same idea to solve the variational equation,which equivalent to the Fredholm integral equation of the first kind with constraint.

这个积分方程的解只能确定到相差一个与边界的法向量成比例的向量，且在边界上的积分必须为零。

Variational regularity of the normalized equivalent radius( r norm= r/Λ) with normalized frequency is found out for different photonic crystal fiber parameters.

该分析和结果可为利用有效折射率法分析光子晶体光纤时等效芯半径的选取提供一定的理论依据。

In the paper, Existence theorem for generalized variational inequalities is established in locally FC-spaces space and its applications are presented.

文章提供关于局部FC-空间上的广义变分不等式的存在性定理，并给出它的一些应用。

Finally, the perturbation problems for the mixed variational-like inequalities problems are discussed, and the existence and uniqueness theorem of the solutions for the perturbation problems is also proved.

最后，讨论了混合似变分不等式问题的扰动问题，并证明了扰动问题的解的存在唯一性定理。

The changes of the HAF after liver injury may be related to the volume of blood loss, the intraabdominal pressure and the pneumoperitoneum duration.

肝撞击伤伴失血后肝动脉血流量的变化与失血量、气腹压力以及气腹持续时间等有密切联系。

Reneging on our commitments to the world's poor cannot be an austerity measure, she said.

放弃我们给世界上的穷国的承诺不能成为一种紧缩措施。