在一个单一的目标函数的情况下，定义域映射对应的是实数线。
In the case of a single objective function, decision space is mapped to the real line.
证明了扩张实数空间是实数空间的加两点紧化空间，指出了存在着加更多点的紧化空间。
It proved that extended real topological space is compactification space of real topological space added to two points. It pointed out that there exists compactification space added more points.
在复数域内利用分离变量法，得到了这类方程的级数形式的解析解，而最后的解是实数形式。
By using variables separation in the complex number field, the real analytical solution in the form of Fourier series was obtained.
第二个参数严格匹配一个非字母和数字组成的字符串，该字符串后面依次为空格、整数、另一个空格，最后是一个实数。
The second argument strictly matches a non-alphanumeric string followed by a space followed by an integer followed by another space and finally a real number.
综上所述的结论是，希尔伯特旅馆容纳不下所有的实数。
The conclusion is that the Hilbert Hotel can't accommodate all the real Numbers.
他们的目标是在内部办公室建立“一个真实数据来源”，而巩固后端系统是必要的第一步。
Their objective is to establish "one source of truth" in their back office, and consolidating back-end systems is a necessary first step.
根据真实数据统计，在当今社会用四个月才能换来一小时的面试是很正常的。
Four months of searching to get a one-hour job interview is a realistic statistic in these times.
某些西方观察家甚至怀疑，真正的答案是零：撒了几十年的谎使得克里姆林宫自己也到了不知真实数字的地步。
"Some Western observers speculated that the real answer was zero-perhaps the decades of deception had led to a point where not even the Kremlin knew the true figure."
本例中的不同之处是先自动进行过滤，然后设计人员在报表中添加事实数据。
The difference in this case is that the filtering is done automatically for the author until they add fact data to the report.
模拟是按照采样方法分类的，因为输入是根据代表真实数据总体的概率分布而随机生成的。
The simulation is categorized as a sampling method because the inputs are randomly generated from a probability distribution that stands in for a real data population.
取而代之的是统计各方面的平均发行量，包括购买量和被证实数量。
In its place is a summary number for total average circulation, both paid and "verified."
事实数据是全面的。
一家俱乐部的球迷是否最棒是个主观性命题，很难用现实数据来说明。
Whether a club has the best fans in the world is a subjective opinion difficult to back up with facts.
这看起来可能有些怪，但是想想实数的数量是无限的。
This may seem odd, but recall that there are an infinite number of distinct real values.
我们不可能获得关于犯罪行为的切实数据，部分原因是不断增长的伊拉克监狱系统却没有中心数据库。
Verifiable statistics about recidivism are impossible to come by, in part because the growing Iraqi prison system has no central database.
添加的这段代码的结果是页面显示时有了真实数据，而不是 1012这个假值。
The result of this addition is that the page will be shown with live data, rather than the dummy value of 1012.
UBL 2.0是OASIS为电子商务开发的标准，能够相当全面地满足真实数据的需要。
UBL 2.0 is a standard for electronic commerce developed by OASIS and is quite comprehensive as real-life data usually is.
这里是真实数据。
在第2部分中，我主要关注这样一些函数，它们的目的是操作浮点数，而不是抽象实数。
Here in Part 2, I focus on the functions that make sense only when you realize that they're designed for operating on floating-point Numbers instead of abstract real Numbers.
问题是我们没有得到发生真实数字的充分资料。
The problem is that we haven't really got enough data to be able to put numbers on it.
这里的逻辑是parse将在输入流中首先查找一个字符串，然后查找整数，最后查找一个实数。
The logic is that parse will look first for a string, then for an integer, and finally for a real, in that order, in the input stream.
“这些是你们的真实数据，”他们报告说，“现在，你们要怎么改？”
"These are your actual Numbers," they reported. "Now, what would you like them to be?"
页面中的数据是真实数据(基于项目的规范)，结构也准备好了，可以转入Tapestry应用程序了。
The data in the page is realistic (based on the project's specifications), and the structure is ready to be rolled into your Tapestry application.
因此银行存款的真实数字是1.48万亿美元。
Jeff提供了来自该领域一些真实数据，这可证明对于那些将在2008年开始SOA项目的公司是有益的。
Jeff provides some real Numbers from the field which could prove helpful for companies starting their SOA initiatives in 2008.
开启该功能时，变更会先写入Journaling日志，定期集中提交(目前是每100ms提交一次)，然后在真实数据上进行这些变更。
When enabled, changes are written to the journal logs first. Periodic group commits (currently every 100ms) then handle playing these changes back on the real data.
指数函数是一个很好的例子，它表明处理有限精度浮点数(而不是无限精度实数)时是需要非常小心的。
The exponential function serves as a good example of how careful you have to be when dealing with limited-precision floating-point Numbers instead of infinitely precise real numbers. ex (Math.exp ).
我们有规律地下载最新的数据库备份并在本地恢复它们(我们总是针对真实数据进行开发)，从而我们知道我们的备份是有效的。
We regularly download the latest database backups and restore them locally (we develop against live data all the time), so we know our backups work.
我们有规律地下载最新的数据库备份并在本地恢复它们(我们总是针对真实数据进行开发)，从而我们知道我们的备份是有效的。
We regularly download the latest database backups and restore them locally (we develop against live data all the time), so we know our backups work.
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