创建一个可以“增强”普通数值函数的decorator并不困难。
It is not hard to create a decorator that "enhances" a regular numerical function.
其中，差分演化算法在数值函数优化方面的性能要优于其它的优化算法。
The performance of DE algorithm is superior to other algorithm in numerical function optimization.
经典的粒子群优化算法是一个在连续的定义域内搜索数值函数极值的很有效的方法。
The classical Particle swarm optimization (PSO) algorithm is a powerful method to find the minimum of a numerical function, on a continuous definition domain.
如果Python应用程序碰到数值函数方面的明显瓶颈，为这些函数创建一个Pyrex版本就非常有意义。
If a Python application encounters a significant bottleneck in numeric functions, creating Pyrex versions of those functions is very sensible.
基于模糊数空间的一种新的序关系，给出了可微的凸模糊数值函数、拟凸模糊数值函数的刻划定理，并讨论了它们的关系。
Based on a new concept of ordering, the characterizations of differential convex fuzzy-valued function, quasi-convex fuzzy-valued function are given and their relation is discussed.
然而，在使用Pyrex编写特殊的数值函数时，另外一个需要考虑的选项是是否可以使用NumericalPython作为工具。
Another option to think about, however, in writing specialized numeric functions using Pyrex is whether Numerical Python might be a suitable tool for your work.
如果使用双字节数据类型作为输入，它就会给出双倍的length函数值。
It gives double the LENGTH function value if double-byte data type is used as input.
也就是在什么方向上，函数值不变化呢？
这些函数将处理或返回数值。
至于定义嘛，实际上，就是把区域分割成许多小区域，再把一点的函数值乘以那个小区域的面积，然后对乘积求和。
And the definition, actually, is we split the region into lots of tiny little pieces, we multiply the value of a function at the point times the area of a little piece and we sum that everywhere.
每条线都被一个数标出，每个值都代表了一个函数值。
And, each of them has a number next to it which tells us the value of a function there.
也就是，如果我给你一个单位向量，试问，我沿着这个方向移动，我的函数值会变化得多快呢？
OK, so if I give you a unit vector, you can ask yourself, if I move in the direction, how quickly will my function change?
它应指向函数值较大的一边。
这里没有数值型的函数能够告诉您这类信息。
"There's no numerical function that could give you this type of information."
一些函数的输入是数值，比如字符串函数的起始、长度和偏移量参数。
For some functions, a numeric value is input, for example start, length, and offset parameters of string functions.
把它们加起来就得到了函数值。
Add them together and that would give me the value of my function.
如果想知道是极大值还是极小值，那就只需用常识，或者直接比较各点的函数值？
So, if you want to know if something is a maximum or a minimum, you just have to use common sense or compare the values of a function at the various points you found. Yes?
现在我可以告诉你，它总是，指向更大的函数值的方向，可能半个小时后就会知道为何了。
But let me just tell you immediately to the side, which side it's pointing to it's always pointing towards higher values of a function OK, and we'll see in that maybe about half an hour.
就二重积分来讲,它是对区域里函数值求总和。
The way we actually think of the double integral is really as summing the values of a function all around this region.
这将导致关键字记录为0(但仍然返回匹配的结果)，并且函数值将是记录的唯一组成部分。
This will cause the keyword score to be zero (but the matching documents will still be returned) and the function value to be the sole component of the score.
iso - quanta是由具有相同目标函数值的点所构成的空间中的一条线。
An iso-quanta is a line in space formed by points with the same objective function value.
这意味着如果x变化,函数值不会发生一阶变化。
That means when I vary x the first order the function doesn't change.
换而言之，当约束使用新的(x 1,x2)对时，x2的变化不会引起目标函数值的变化。
In other words, a change in x2 won't change the objective function's value, given that the constraint holds for the new (x1, x2) pair.
我们说过简单的竖直区域是x在a与b之间，而y在x的函数值两个值之间。
So, we said vertically simple egion looks like x goes between a and b, and y goes between two values that are given by functions of x.
对每个x和，在高度为函数值的地方描点。
y So, for each x and y, I plot a point at height given with the value of the a function.
实际上是相同的，函数值为0的点在哪里？
x y It's really the same thing. So, x, y, let's see, where is this function equal to zero?
与其使用内置的XPath函数true()，不如输入数值1。
Rather than using the built in XPath function true(), it is more efficient to simply enter the numeric value 1.
函数查询——评分受到索引域的的数值取值或次序的函数影响。
Function Query - influence the score by a function of a field's numeric value or ordinal.
这种方法允许您将数据作为参数值传递给构造函数调用，如清单3 所示。
This approach lets you pass data as argument values to the call, as Listing 3 shows.
到目前为止，该系列文章一直关注单个标量函数(数值、字符串和布尔值)的使用。
So far in this series of articles, we've been restricted to the use of single scalar values (Numbers, strings, and booleans).
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