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The problem is NP-hard, so we want to find approximate algorithms to solve the problem.

由于这个问题是NP-hard的,因而我们转为寻找问题的近似算法。

From the view of mathematics, it is a NP-hard combinational optimization problem with constraints and it is difficult to find the global optimal solution in theory.

从数学上讲,机组投入问题是一个多约束的NP-hard组合优化问题,很难得到理论上的最优解。

Owing to the strong condition of equivalence relation, there exist some limits, and It has been proved to be NP-Hard to find all reductions and a minimal reduction.

由于等价关系条件较强,有一定的局限性,已经证明求所有约简和最小约简是NP-Hard问题。

Compared to my previous exhibition Prayer Beads and Brushwork, his work are even less painting, less feeling from brushworks, and hard to enjoy. It is hard to find a single painting in traditional meaning.

与前几年我做的《念珠与笔触》中的作品相比较,关奉东的作品更没有绘画性,更不具有笔触意味,更难有观赏性,几乎不产生任何一件传统意义上的,耐人寻味的,被称为作品的独幅画。

His works,sculpt,color and process are so nonotone, even simply repeating the briefness. Compared to my previous exhibition Prayer Beads and Brushwork, his work are even less painting, less feeling from brushworks, and hard to enjoy. It is hard to find a single painting in traditional meaning.

与前几年我做的《念珠与笔触》中的作品相比较,关奉东的作品更没有绘画性,更不具有笔触意味,更难有观赏性,几乎不产生任何一件传统意义上的,耐人寻味的,被称为作品的独幅画。

We introduce convex,and in particular semidefinite,optimization methods,duality and complexity theory to shed new light to this relation for the single stock problem, given moments of the prices of the underlying assets,we show that we can find best possible bounds on option prices with general payoff funcations efficiently,either algorithmically(solving a semidefinite optimization problem)or in closed form, conversely,given observable option prices,we provide best possible bounds on moments of the prices of the underlying assets,as well as on the prices of the other options on the same asset by sovling linear optimization problems for options that are affected by multiple stocks either directly(the payoff of the option depends on multiple stocks)or indirectly(we have information on correlations between stock prices),we find on-optimal bounds using convex optimization methods,however,we show that it is NP-hard to find best possible bounds in multiple dimensions,we extend our results to incorporate transactions costs,this paper,in theory and practice can provide a reference to researchers and designers about Chinese financial derivative products,the full text is divided into six chapters as follows: ChapterⅠ:Papers on the background and significance of the subjects on a number of option pricing models as well as their advantages and shortcomings of the model and describes the status of research and writing papers and the main contents of the basic idea.

相应地,给定期权价格,也能够出标的资产瞬时价格的最有可能的最好的界。还有通过解决一个线性最优化问题,根据同一标的资产的其他期权的价格来找到这个期权的界值,对于期权受到多种股票价格直接影响(期权的收益依赖于多种股票)或者间接影响(我们有股票之间联系的有用信息),如果使用凸规划方法我们就会发现没有最优的界,也能够证明对于多维情形确实是很难找到最优的最有可能的界值,最后将这一结论推广到考虑交易成本的情况。本文在理论和实践上给我国金融衍生产品研究者和设计者提供一定的参考。全文共分为六章,具体安排如下:第一章:阐述论文的选题背景和意义,介绍期权定价的一些模型以及这些模型的优点与缺点,并介绍国内外研究的现状以及论文的写作基本思路与主要内容。

In doing back-up data, we followed the work to be done is to switch to a system running DOS, and DOS command line in the implementation of "fdisk / mbr" command string to try to repair the hard disk of soft failure occurred ; if such a repair method to try is invalid, then we can go online to download and install the hard drive Bad Track professional testing tool to double-check the local hard disk in the phenomenon of the existence of Bad Track, Bad Track If you can not find the hard disk, it can not detect hard drive through the phenomenon is likely to be caused by the logic of failure, when the only thing we can use the way is hard to find the logic of the corresponding brand Bad Track Repair Repair Tool to re-click the hard disk, I believe that case the hard disk will be able to detect the phenomenon can not be resolved the.

在做好数据的备份工作后,我们接下来要做的工作就是将系统切换到 DOS 运行状态,并在 DOS 命令行中执行" fdisk /mbr "字符串命令,来尝试修复硬盘中发生的软故障;要是这种修复方法尝试无效的话,我们可以到网上下载安装一些专业的硬盘坏道检测工具,来仔细检查本地硬盘中是否存在坏道现象,如果找不到硬盘坏道的话,那硬盘检测无法通过的现象很可能是逻辑故障引起的,此时我们唯一可以使用的办法就是找到对应品牌硬盘的逻辑坏道修复工具来重新修复一下硬盘,相信这么一来硬盘检测无法通过现象就能被解决了。

However, it took me awhile to find what MOKI means, and it is also hard to find out how to adopt the MOKI.

谢谢莎拉。不过,我花了一段时间找到什么moki手段,它也很难找出如何采取moki 。

You'd be hard pressed to find a more beautiful city than Guilin.

你要找到一个比桂林更漂亮的城市实在是不容易。hard pressed to 不容易。

Eighty-two percent of the Usage Panel accepts the sentence I find it hard to identify with any of his characters; whereas only 63 percent now accepts this same usage when the reflexive pronoun is used, as in I find it hard to identify myself with any of his characters.

用法专题小组中82%的成员认为我觉得很难认同于他小说中的人物一句是正确的;而现在只有63%的成员接受使用反身代词来表达同一意思的句子,即I find it hard to identify myself with any of his characters。

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