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Main areas of focus are on overall delinquency levels, minimizing provision requirements and over charge-off/losses.

关键的领域包括：整体逾期水平、精简拨备要求以及销账/损失。

So before applying Mather's theorem of connecting orbits to concrete Hamiltonian system, we have to check whether the set W〓 is empty or not, and which cohomology classes are C-equivalent. In present paper, by investigating the topological structure of action minimizing sets near a co-dimensional one torus which is preserved under generic perturbations and becomes hyperbolic in nearly integrable Hamiltonian system.

与传统的Poincaré-Melnikov方法相比，我们方法明显优越之处在于，一方面我们的方法不仅可以得到双曲环面之间的异宿轨道，而且当该环面附近的其它环面破裂时，可以得到不同Mather集之间的连接轨道，另一方面，我们把异宿轨的存在性的证明转化为双曲环面极小同宿轨的某种弱孤立性的证明，所需条件比Poincaré-Melnikov方法弱得多。

All feature industry leading low energy consumption and a compact footprint that optimizes factory space while minimizing expense.

使用最低的成本，更低的能耗以及节约空间的设备将使您的工厂生产上更加游刃有余。

The damage of key-exposure has become the focus of the research. This problem may hardly be resolved complementally, what we can do is to minimizing the damage as we can.

密钥泄露对数字签名的危害越来越成为人们关注的焦点，该问题很难找到完全彻底的解决办法，只能尽可能减少其危害。

Great advances have been made in electronic and computer controls in recent times which permit complete automatic kettle operation independent of the compounder minimizing the possibility of human error.

电子及计算机控制在近代已取得重大进步，这可是整套自动化釜的操作不受混合物质的影响，极大地降低了人为出错的可能性。

Properties of efficient portfolios and the efficient frontier to the model are systematically analyzed. Our main results concerning the properties are: every efficient portfolio can be solved by minimizing portfolio risk under a given level of portfolio return or by maximizing portfolio return under a given level of portfolio risk; on the efficient frontier, the risk is a convex and strictly increasing function of the return and the return is a concave and strictly increasing function of the risk; the utility function on the efficient frontier can be expressed as a quasi-concave function of the risk or the return if the investor's utility function is quasi-concave.

从理论上系统地对该模型下的有效投资组合和有效前沿的性质进行了分析，结果表明：每一个有效投资组合可通过在给定期望收益水平的条件下最小化投资组合风险来获得，或者在给定风险水平的条件下最大化期望投资组合收益来获得；在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数；当投资者的效用函数是拟凹函数时，则有效前沿上的效用可表达成风险或收益的拟凹函数。

According to the criterion of minimizing the sum of the squares of the states posterior confidence region widths, we get the value of the updated Biscay distribution, then get the states interval estimation.

该方法结合了区间运算和Kalman滤波方法，分别根据状态和观测方程得到的预测值的Biscay分布，融合得到估计的Biscay分布值，进而得到状态的区间估计。

Most of the component structure connected by welding. Ensure welding intensity while minimizing the distortion of welding.

整个机构的大多数联接方式是焊接，应保证焊接强度，同时尽量减少焊接的变形量。

Chapter 5 is devoted the study of fuzzy optimization in fuzzy convex analysis structure given in chapter 4. We consider the problems of minimizing and maximizing a convex fuzzy mapping over a convex set and develop necessary and/or sufficient optimality conditions.

在第5章中，首先，在第4章所建立模糊凸分析的结构基础上，考虑了凸模糊映射的极值问题，得到了凸模糊映射取得极值的充分/必要条件。

We also construct an algorithm for minimizing its Moreau-Yosida regularization, because this is a smooth convex optimization problem.

极小化一个凸函数可以采用在UV-空间分解理论基础上提出的概念型超线性收敛算法，也可以采用极小化这一凸函数的Moreau-Yosida正则化函数的算法，因为这是一个凸规划的光滑最优化问题。

The French are not suggesting a new EU treaty, but they have plenty of other wheezes.

法国人并不是在建议签署一个新的欧盟条约，但他们有许多其他的阴谋。

This letter was written by my brother.

这封信是我弟弟写的。