此外讨论了一个非自伴的问题，对它和它的伴随问题的特征值、特征函数进行了详细的讨论，得到了一特征展开定理。
Besides, by giving a Dirac eigenvalue problem example and studying the eigenvalue and eigenfunction of it and its adjoint problem, we can obtain an eigenfunction expansion theorem.
更糟糕的是，当亚裔美国人确实开始出现在教科书上的时候，往往会伴随着一些问题。
Worse, when Asian Americans do make an appearance in lesson books, it is often laced with problems.
但也有一个坏处，使用即时通讯框架时遇到的任何问题可能会伴随复杂的类型发生。
One disadvantage is that any problems you encounter while using frameworks for messaging are likely to occur with complex types.
伴随年轻人婚姻的一个潜在问题是，你们或许还不明确你们将来的目标是什么？
One potential problem with getting married young is that you might not know exactly what your future goals are.
伴随大量藏书而来的最大问题就在于我有时会忘记哪些书我已经有了。
The biggest problem with having a large collection of books is that I'll sometimes forget which books I already have.
不像失明和失聪那样相对于别人(不受此问题困扰的人)常常很明显，伴随年龄增长的嗅觉丧失常常意识不到，因为它的产生我渐进的。
But unlike vision or hearing loss, which is often apparent to others, if not to the afflicted person, a loss of smell sensitivity with age is often undetected because it occurs gradually.
对农民来说，伴随这一销售方法的问题在于贸易商对不同市场的流行价格和食品加工公司的报价具有更加全面的信息。
The problem with this approach for the farmers is that the traders have a far better idea about the prices prevailing in different markets and being offered by processing companies.
支气管的样本是由我们所知的上皮细胞组成，伴随着它们有一个问题产生：它们的繁殖数量该是多少。
The bronchial samples consisted mainly of what are known as epithelial cells, and with these it was just a question of multiplying their Numbers.
攻讦被定义为发表煽动性的、贬损或刺激的信息在公共论坛上，这个问题伴随着互联网的诞生就有了，尽管它的根基要追溯更远。
Trolling, defined as the act of posting inflammatory, derogatory or provocative messages in public forums, is a problem as old as the Internet itself, although its roots go much farther back.
露比·罗思写的《我们不吃动物的原因》就是一本针对4到10岁小孩的图本。书里面描述了食肉伴随的农业和环境问题。
That's Why We Don't eat Animals by Ruby Roth, is a picture book targeted at children age 4 to 10. It addresses factory farming and environmental problems associated with eating meat.
其他对于大堡礁及其生态系统的环境压力来自径流的水质问题，伴随着大规模珊瑚白化的气候变化以及棘冠海星的周期性爆发现象。
Other environmental pressures to the reef and its ecosystem include water quality from runoff, climate change accompanied by mass coral bleaching, and cyclic outbreaks of the crown-of-thorns starfish.
许多自闭症儿童还伴随有其他状况，比如癫痫、焦虑障碍以及肠道问题等。
Many children with autism also have other conditions, including epilepsy, anxiety disorders and gastrointestinal problems.
这样能够使您在第三方控件中找出问题，并伴随着来自恶意文件源中更多的问题。
This enables you to find issues in the third party components, along with issues from a malicious file input source and more.
在可预见的将来，此类压力也许会对发达经济体的增长起到足够大的遏制作用，此作用伴随着其它诸多问题将剑指经济复苏。
Those strains might exert a restraining effect on advanced economy growth for the forseeable future-enough, in the presence of other problems, to threaten recovery.
随着清理行动开始后，许多问题伴随着新奥尔良的重建而暴露出来。
As cleanup operations got underway, many questions arose about how New Orleans would be rebuilt.
震后的问题中可能还有伴随大震而来的无数余震。
Compounding the problems of the quake aftermath will likelybe the numerous aftershocks that accompany any major earthquake.
现在，伴随着另一个核问题和新一轮继承权导致的动荡，饥荒再一次登陆这个国家。
Now, with another nuclear stand-off and fresh uncertainties about succession, famine again stalks the country.
震后的问题中可能还有伴随大震而来的无数余震。
Compounding the problems of the quake aftermath will likely be the numerous aftershocks that accompany any major earthquake.
然而，自闭症常常伴随其它或轻微或严重的问题。
However, it is often associated with other problems, and can also appear in mild and severe forms.
健康问题始终伴随着他们，满布血丝的眼睛，强酸环境造成的牙齿腐蚀和脱落，哮喘，过敏，胃痛，还有膝关节劳损。
Health problems include bloodshot eyes, teeth eroded to stumps due to the acidic conditions, wheezing, allergies, sore stomachs, and damaged knees.
越来越多的，健康专家和普通公众理解和接受了原发性噩梦是是一种频繁发生的睡眠问题，伴随着对睡眠质量和心理健康的严重影响。
Increasingly, health specialists and the general public appreciate that idiopathic nightmares are a frequent sleep problem with important consequences for sleep quality and mental health.
另外，您应当理解了伴随Ajax方式的一些高级设计问题。
In addition, you should understand some of the high-level design issues that come with the Ajax approach.
伴随该类型框架的另一个问题源于实现指导的严重短缺。
The other problem with this type of framework stems from the serious shortage of implementation guidance.
伴随着不可避免的问题扩散而来，我们不得不逆向思考，比如，当人们反对使用无人机时怎么办？
With the inevitable proliferation issues, we have to also consider the inverse problem, which is, what happens when people consider using drones against us?
沮丧和焦虑通常伴随着这些肠道问题出现。
Anxiety and depression commonly occur alongside these bowel conditions.
网络延迟：对规则服务的远程调用伴随而来的是网络延迟问题。
Network latency: With remote invocation of the rule services comes the issue of network latency.
伴随着电脑软件销量下跌，整个电脑产业存在更多的问题。
The falling sales of PC software dovetailed with broader problems across the computer industry.
1996年中期，显然我们在如何应付针对国内外美国人进行的袭击上还没有完整的答案，在未来几年，这个问题还将伴随着我们。
In the middle of 1996, it was clear that we didn't have all the answers on how to deal with attacks on Americans in this country and overseas, and that the problem would be with us for years to come.
1996年中期，显然我们在如何应付针对国内外美国人进行的袭击上还没有完整的答案，在未来几年，这个问题还将伴随着我们。
In the middle of 1996, it was clear that we didn't have all the answers on how to deal with attacks on Americans in this country and overseas, and that the problem would be with us for years to come.
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