任意地

This paper give an expression of budget set of no- arbitrage equilibrium by the stiefel manifold for the sake of orientation of equilibrium and construction of oriented index theorem.

对任意以2π为周期的连续函数f，本文构造了一个二重傅里叶级数，它在全平面上一致地收敛于f。

We can safely assume that the indiscriminate acts of our generation will have an adverse impact on future generations .

我们可以万无一失地想当然认为我们这一代人任意的行为将给未来的人造。。。

We can safely assume that the indiscriminate acts of our generation will have an adverse impact on future

我们可以万无一失地想当然认为我们这一代人任意的行为将给未来的人造成负面的影

We can safely assume that the indiscriminate acts of our generation will have an adverse impact on future generation s.

我们可以万无一失地想当然认为我们这一代人任意的行为将给未来的人造成负面的影响。

Day we flew to the highest offices, travel in the lowest point of any piece of land on the bank.

我们飞到天的最高处，游在地的最低点，行在任意一块土地上。

In this paper, we present an analysis of quotient image method from the view of image linear subspace, and point out its main deficien- cies: 1 inaccurate assumption of ideal class of object, 2 3-d subspace doesnt suffix to represent all images of an object under varying illuminations.

在本文中，我们从图像子空间的角度对商图像方法进行了分析，理论分析和实验表明，这种方法存在的主要缺点有：1不准确的理想类假设；2简单的三维点光源模型无法很好地近似任意光照情况。

In addition,3-d subspace in quotient image method doesn't suffice to represent all images of an object under varying illuminations.Therefore,an improved method based on image on 9-d linear subspace constructed using 9 images of object under the configuration is presented to overcome these deficiencies.And 9 images of another object under the configuration are generated.

此外，商图像方法中简单的三维点光源模型无法很好地近似任意光照情况，因此，提出一种基于九维线性子空间的改进的商图像方法，并利用改进后的商图像方法合成对象在统一配置光源方向下的9幅图像，克服了Lee所提方法的不足。

In the past managers simply restored ecosystems to match an arbitrary point in history.

过去，项目管理者只是简单地将生态系统恢复到任意一个时期的状况。

By use of the concept of domain of microcrack growth the damaged status of micocrack in rock can be described accurately and the problem about damage development of rock under any complicated loading pathes can be solved.

采用微裂纹扩展域的概念，准确地描述了岩石中微裂纹的损伤状态，解决了任意复杂加载路径下的岩石损伤演化问题。

Exive least-squares solutions, antire?exive least-squares solutions, bisymmetric least-squaressolutions, symmetric and antipersymmetric least-squares solutions, symmetric or-thogonal symmetric least-squares solutions, symmetric orthogonal antisymmetricleast-squares solutions and their optimal approximation to the linear matrix equa-tion AX = B, and solve them successfully. 2. For Problem II, we can convert it to another problem of finding the least-squares solutions with the least norm of a new consistent matrix equation. Onthe base of the solutions of Problem I we can apply the iterative method to get

本文所构造的迭代法的优点在于先利用法方程变换将求矩阵方程的最小二乘解转化为求一个相容矩阵方程的解的问题，再利用迭代法对于任意给定的初始矩阵进行迭代，均可在有限步内迭代出所求问题的一个解；可将问题II转化为求新方程的极小范数解的问题，同样用迭代法求解，从而系统且全面地解决了问题I、II在约束矩阵类如中心对称、中心反对称、自反矩阵、反自反矩阵、双对称、对称次反对称、对称正交对称、对称正交反对称矩阵中的最小二乘解及其最佳逼近问题。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。