对应问题

In this paper, we construct the differential equation to solve the unconstrained optimization problem. Such methods solving the ill-conditioned problems are very effective. It indicates that the asymptotically stable region of explicit the Euler method to solve the differential equation equals to the descent region of the gradient method to solve the original unconstrained optimization problem.

我们发现，在用Euler方法求解二次优化问题的等价动力系统的方程时，由方法的步长确定的稳定区域对应于这些方法所得到的迭代公式的步长满足单调下降算法的条件确定的单调下降区域，因此我们可以利用这个性质构造解无约束优化问题的数值方法而不采用标准的常微分方程的数值求解公式。

These results can help us to deeply understand the first and second-order expansion of f on the U -space.

UV-分解理论可应用到数学规划中：对于有限个约束的非线性规划问题，可以对这一问题所对应的精确罚函数作UV-空间分解。

Though the load analysis on the tunnel roof wall-rock in the fault footwall tunnel, this paper solves the problem of the tunnel support of tunneling through the great fault; and though the load analysis on the corresponding wedge of the lower abandoned tunnel, solves the problem of the influence of the lower abandoned tunnel on the upper tunnel floor.

通过对断层下盘巷道顶板围岩的受力分析，解决了煤巷掘进过大断层的巷道支护问题；通过对下部废巷道对应的楔形体的受力分析，解决了下部废弃巷道对上部巷道底板的影响问题。

Fourier analysis consists of Fourier series which can solve limited one-dimensional space Heat-conduction question and Fourier integral which can solve infinite one-dimensional space Heat-conduction question. This is more systematic compared with the other methods, and embodies corresponding beauty of Mathematics to Physics.

傅里叶分析包括傅里叶级数和傅里叶积分，用傅里叶级数法解决有界细杆的热传导问题，用含参数的傅里叶变换法解决无界细杆的热传导问题，比其它方法更系统，体现出一种数学与物理对应的美感。

By using a gauge transformation between thetwo eigenvalue problems, we obtain a correspondence between the hie -rarchy of nonlinear evolution equations associated with the Kaup-Newelleigenvalue problem and the hie rarchy of nonlinear evolution equationsassociated with the AKNS eigenvalue problem.

利用规范变换，我们得到了与Kaup-Newell特征值问题相联系的一族非线性演化方程和与AKNS特征值问题相联系的一族非线性演化方程之间的一个对应关系，并给出了Kaup-Newell系统的Darboux变换及其证明。

Further, with the help of Riccati equations, an infinite number of conservation laws for the solton hierarchy are deduced. For the sake of simplicity, taking the general TD hierarchy as an illustrative example, we prove that its 2×2 Lenard pair of operators forms a Hamiltonian pair. Thus the isospectral evolution TD hierarchy is the general Hamiltonian system and possesses the Bi-Hamiltonian structures and Multi-Hamiltonian structures. By using the method of derivation of functional under some constraint condition, a complete one-to-one correspondence between the Hamiltonian functions of the hierarchy and its conservation density functions can be built. These results can also be applied to the isospectral evolution soliton hierarchy of this paper. Finally, there's a gauge transformation between the spectral problem of this paper and the AKNS system. Moreover, the potentials in these spectral problems satisfy the general Miura transformation, the corresponding relationship between the two soliton hierarchies is also given.

进一步本文还通过特征函数的组合关系所满足的Riccati方程，得到了该等谱方程族的无穷多个守恒律；为简便起见，本文以广义TD族为例，由它的2×2 Lenard算子对的性质证明了此算子对为Hamilton算子对，这说明广义TD族是广义Hamilton系统且具有Bi-Hamilton结构和Multi-Hamilton结构；进而利用它的依赖于谱参数的一般守恒密度的积分在约束条件下求泛函导数的方法，得到了广义TD族的Hamilton函数与守恒密度之间的对应关系，这些性质对于由本文提出的2×2谱问题所导出的等谱孤子族仍成立；另外此谱问题与AKNS系统存在着规范变换，位势之间有广义Miura变换，而孤子方程之间也满足一定的等价关系。

In order to avoid the repetition, we find a group of coefficients that are generated with field and its gradient data. To establish explicit linear relation between structural index based on the linear relation, depth is calculated when calculated parameters are given without touching the field data. Accordingly, it can avoid the repetition of Euler's equation calculation and greatly reduce the works load as well as enhance efficiency.

为了避免这种重复，这里找到了一组系数，该系数与场值及其梯度值有关，并直接建立起场源位置与构造指数N简单的对应关系，从而把解欧拉方程的最小二乘问题转化成了解线性方程的问题，避免了解欧拉方程组时的重复计算，大大地减少了计算工作量，有效地提高了工作效率。

For some special class of motions of incompressible bodies it is possible to reduce the problem of motion to a corresponding problem of equilibrium.

对于不可压缩物体的某一类特殊运动有可能把运动问题简化成一个对应的平衡问题。

Establish integrated invertibility theory over it: By R〓R〓 transformation method, we solve the problem of deciding weakly invertibility and finding weak inverse, By founding the bijections between all quadratic form automata and input memory linear finite automata, we find a algorithm to produce all weak inverse quadratic form finite automata.

本文着眼于这些最基本问题，将有限域上的二次型和置换多项式理论引入有限自动机可逆性的研究，构造了一类由二次型构成的非线性有限自动机（3.6定义），称之为二次型有限自动机，我们在其上面建立了与线性有限自动机可逆性理论相对应的完整的可逆性理论：采用线性R〓R〓变换方法，解决了此类有限自动机的弱可逆性判定、求弱逆问题（3.10、3.12定理）、通过建立全体二次型有限自动机与全体输入存储线性有限自动机之间的保持弱逆性的一一对应，给出了产生全部可逆二次型有限自动机的方法。

Furthermore,under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some c...

进一步地，在对全局解的一定假设下，还提供了原约束问题的全局最优解与增广Lagrange函数，在原问题变量空间的一个紧子集上的全局最优解之间的一些对应关系。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。