可以解的

We prove the L~1-stability of weak solutions for arbitrarily large data on multi-dimensional bounded or periodic domain or whole space.

作为研究的出发点，在第三章里，我们首先考虑弱解的L~1稳定性，通过得到关于密度梯度的新熵估计和精细的能量估计，我们可以证明逼近解的收敛性。

PSO is a population-based optimization algorithm, which mimics the social behavior of animals in a flock. It makes use of individual and group memory to update each particle position allowing global and local search optimization. The objective function considered was the total weight of the structure subjected to stresses, displacements and forces constraints. The effects of the parameters were investigated as well and such combination of tuning parameters promote a better global search behavior avoiding premature convergence while rapidly converging to the optimal solution. Results showed the effectiveness of the proposed method by comparing with ANSYS Design Optimization Tool (zero-order method). The PSO with the tuning parameters makes it an ideal method for offshore wind turbines foundations optimization tasks.(2) A reliability analysis method for pile foundation bearing axial loads based PSOThe performance function of pile foundation's axially bearing capacity sometimes is nonlinear and complex, on the basis of geometric meaning of structural reliability index, an optimum model with PSO for structural reliability analysis under arbitrary random variables was established, The PSO algorithm is very efficient to solve global optimization problemsIts use in structural reliability field presents not only the advantage of its facility of implementation, but also the possibility to obtain the design point and the failure probability with a good accuracy. In addition, PSO is a zero order algorithm, for no derivative is necessary for its implementation.

本文的研究针对桩式海上风机基础结构的特点，在国内外有关研究成果的基础上对海上风机基础结构优化设计理论和可靠度方法一些相关问题进行了较为深入的研究，具体做了以下几个方面的工作：(1)基于粒子群优化的桩式海上风机基础确定性优化设计方法桩式海上风机基础的优化设计是一个复杂的、非线性约束的优化问题，针对传统的基于梯度信息的优化方法在处理非线性问题中易陷入局部最优解的问题，本文将一种耦合惩罚函数的PSO算法引入到海上风机基础结构概念设计中，PSO算法是从群体动物聚集觅食这一活动中受到启发而发展的，该算法利用个体和群体的信息共享不断改进自身的位置从而进行局部和全局最优搜索，本文中以桩和三脚架连接段直径及壁厚为设计变量，以基础总重量作为优化的目标函数，在给定的约束条件下建立了三脚架基础优化数学模型，另外本文还研究了PSO参数变化对结果的影响，协调的参数组合可以避免陷入早熟收敛而能够快速的获得全局的最优解，通过与ANSYS优化模块的计算结果比较验证了该方法的有效性，本方法为海上风机基础的确定性设计提供了一条有效的途径。

Users can decompress the contents of a self-extracting chaos-files simply by running it like any other program.

用户可以解压缩的内容，一个自我解压缩的混沌的档案，只要运行它像任何其他程序。

It is helpful for us to construct difference approximation schemes for HJ equation with aids of schemes for conservation laws.

众所周知，即使在初值条件0是充分光滑的情况下，一般来说，虽可以得到式(1 )的连续解，但其解的导数却是间断的。

Because the analytical solutions can be obtained in computations of elastodynamics problems, the considered problems become considerably simple and possess an evident generality, hence the deduction of self-similar solutions in other form has significance.

由于在弹性动力学问题的计算中可以获得解析解，使得考虑的问题相应地简化，并具有一定的普遍性，因此对自相似形式的解的推导具有重要的意义。

Using the method of blow up lower and upper solutions, the existence and boundary behavior of positive boundary blow up solutions for some elliptic systems of competitive type with singular weight functions are obtained, here the singular weight functions are permitted to be bounded in some parts of the boundary, and to go to infinity or even oscillate in other parts.

利用爆破上、下解方法，本文建立了带奇异权函数的竞争型椭圆方程组正的边界爆破解的存在性和边界行为，这里奇异权函数可以在边界的某一部分有界，而在其他的部分趋于无穷或者震荡。

For the homoclinics taking on values in the unbounded domain, in order to apply the usual "Mountain Pass " theorem, A compact embedding theorem is proved.

为克服同宿解取值于无界域而缺乏自然紧性，证明了一个紧嵌入定理，从而可以利用通常的山路引理与对称山路引理获得同宿解的存在性与多重性条件。

This method can approach local extreme value available, but it is not the optimal solution or optimal resolution.

用这种方法可以有效逼近解的局部极小点，但不一定能得到最佳解或最佳的分辨率。

With the present m ethod both the stability of the peri odic solutions and the asymptotic e xpressions for the periodic solutions ca n be obtained easily.

采用本文所提出的方法，无论是周期解的稳定性，还是渐近解都可以较容易地获得。

0 In the set of rational numbers can be worked out with , how can we solve the problem about the equation x 2＋1 = 0 without solution in the set of real numbers?

类比引进就可以解决方程 x 2－2=0在有理数集中无解的问题，怎么解决方程 x 2＋1=0在实数集中无解的问题？

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。