We completely solve the divisibility problem of class Numbers a class of imaginary quadratic fields.
完整地解决了一类虚二次域类数的可除性问题。
We completely solve the divisibility problem of class Numbers for a class of imaginary quadratic fields.
完整地解决了一类虚二次域类数的可除性问题。
Abstract: Recently, the problem of Class-imbalance has become a hotspot in machine learning and data mining.
摘要：最近在机器学习和数据挖掘上，非平衡类问题成为了一个研究热点。
And this becomes more of a problem when colleges don't talk about the class advantages and disadvantages of different groups of students.
当大学不探讨不同学生群体的阶级优势和劣势，这就成了一个更大的问题。
This becomes more of a problem when colleges don't talk about the class advantages and disadvantages of different groups of students.
当大学不对不同学生群体的阶级优势和劣势进行探讨的时候，问题就更大了。
Most, if not all, problems relating to class loading can be tracked down to a problem occurring in one of these phases.
虽然不是所有的问题，但至少大多数与类装入有关的问题都可以追溯到在这三个阶段中发生的某个问题。
Therefore, if a code generation problem occurs, it is most likely that the code generator can not handle the serialization of the method parameters or return types in your service class.
因此，如果出现代码生成问题，那么最有可能的是代码生成器不能处理您的服务类中的方法参数或返回类型的序列化。
The problem with this approach is that each country has a different median income, so the definition of what is middle class shifts from place to place.
这种方法的问题在于每个国家的收入中间值不同，所以中产阶级的定义也就随着地域的不同而有所变化。
Many developers find constraint violations to be a difficult type of class loading problem to resolve.
许多开发人员发现约束违反是一种很难解决的类装入问题。
To solve this problem, another class of business processes, which are long-running, can be used.
为了解决这个问题，需要使用另一种长期运行的业务流程类别。
Patterns in the broadest sense can also be applied to a particular class of problem — when transforming an input to an output.
模式从广泛意义来讲也可以运用到问题的特殊类别——当转换一个输入为输出时。
Accessors reduce the risk of the fragile base class problem where changes in a superclass ripple throughout its subclasses.
读写方法减少了超类中的更改影响到其子类的这种脆弱的基类问题所带来的风险。
They easily solve the problem of not having to store references to every class.
单例模式确实能够轻而易举解决无须对每个类的引用都进行存储的问题。
The second problem occurs when the class you are trying to use is found, but one of the classes it imports is not found.
第二类问题发生在找到了您正试图使用的类，但没有找到它所导入的某个类时。
Another way of handling this problem would be to throw an exception whenever a run-time instantiation of the generic class does not include a needed constructor.
处理该问题的另一种方法是：只要泛型类的运行时实例化没有包括所需构造函数，就抛出异常。
Every month, I'll solve a programming problem or class of problems common in the "care and feeding" of servers.
每个月，我都将解决在服务器的“维护与支持”中遇到的一个编程问题或一类共同问题。
The easiest way to resolve this problem is to ensure that there is only one copy of a class in the system — that is, that the class only appears in the classpath of one loader.
解决这个问题的最简单方法是确保在系统中只有类的一个副本——也就是说，类只出现在一个类装入器的类路径中。
This problem is actually a special case of a much larger class of problems related to user input validation.
这个问题实际上是与用户输入验证相关的一类更大问题的一个特例。
Anyone who does commit the solecism of talking or writing about class in America is assailed at once by a problem of definition.
在美国历史上，任何在谈论或书写有关阶级的内容中犯了错的人曾经都因该定义受到了攻击。
As we saw in the previous section, a huge problem in class design that makes testing difficult is having to initialize all sorts of objects that aren't required for your test.
正如我们在前一节介绍的，造成测试困难的大量类设计问题都集中在初始化各种不需要测试的对象上。
Often this is a good thing because it allows you to isolate parts of the problem, but it also has downstream consequences when you make changes to the parent class.
这通常是一件好事，因为它充许您将问题分成几部分，但是当您对父类进行变更时，它会产生不好的影响。
Of course, the problem with Listing 1 is that, in order to change parsers, you have to change the implementation class.
当然，清单1中存在的问题是，为了更改语法分析器，必须更改实现类。
And we want to help you learn how to map a problem into a class of algorithms of some efficiency That's our goal.
学会如何将一个问题，映射到一类，提升效率的算法中去，这就是我们的目标。
So this is a question that I want to continue today, to consider what the trial of Socrates means and I want to begin by going back to a problem or a paradox that I ended the class with last time.
这就是我今天要继续的问题，考虑苏格拉底受审的意义，我想要先回到一个问题，一个悖论，也是我们上堂课所遗留的。
But now, it was definitely a problem! By the end of the day, it was the talk of the entire class.
但现在，这完全成了一个问题，整整一天，全班都在议论这件事。
Each result comprises a context (for example, the class that matches an anti-pattern), and a description of the problem.
每个结果由一个上下文(举例来说，匹配反模式的类)和一个问题描述组成。
If this was a class in which we were going to worry about the general problem of identity across time, this would be a problem we'd have to directly face.
如果我们要讨论的是，贯穿时间的，质的总的问题，我们就需要，直面这个问题。
The quick but incorrect way to remedy the problem would be to eliminate the Leaf class and represent Leaf nodes simply by putting null Pointers in the left and right fields of a Branch.
一种快速但不正确的解决这个问题的方法是除去Leaf类并通过简单地将空指针放在Branch的left和right字段中来表示leaf节点。
The classification problem is then to find a good predictor for the class y of any sample of the same distribution (not necessarily from the training set) given only an observation [6]:338.
所谓的分类问题就是指对于相同分布的样本x（可以是训练集以外的样本），都能预知其所属的类。
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