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In this study, we try to provide the examples of the application of mathematics to music; the application of golden ratio to musical structure; the calculation and derivation of Pythagoras scale、pure scale and twelve-tone equal temperament scale; the application and analysis of mathematics in fifth-degree co-generation method; and the two-dimension research of the interval and scale. These discussions apparently show the strong correlation of mathematics and music.

本文藉由数学与音乐的多元对话，探讨音乐领域中数学的应用范例；黄金比例在乐曲结构之应用；运用数学推演和计算毕氏音阶、纯律音阶和十二平均律音阶的组成；探讨五度相生律的应用范例与数学的密切关系；归纳和分析音程和音调的数学二元图表，在在都显示出数学与音乐密不可分的关系。

In fact, back in early 2004, Netcom general manager and deputy general manager Tian Zhang Chunjiang with PCCW Chairman Richard Li Tzar begun discussions on the matter of cooperation, the two sides after a number of high-level in Shenzhen and Tokyo round of negotiations.

事实上，早在2004年初，网通集团总经理张春江和副总经理田溯宁就与电盈主席李泽楷开始商讨合作之事，之后双方高层在深圳及东京进行多轮谈判。

These discussions have led to a remarkable unanimity.

这些讨论导致引人注目的一致意见。

I locked the door in order to continue our discussions undisturbed.

我把门锁上了，以便我们可以继续讨论而不受打扰。

But as the club of rich nations struggles to be taken seriously (many argue the G-20 more accurately reflects the distribution of economic power in the world today), unkept promises to Africa will matter ─ especially since the recession has fueled discussions and doubts about whether big aid programs are really worth their high cost.

但是正当富国俱乐部力争赢得他国对其重视（许多国家认为 G20能更加准确地反映出当今世界经济实力的分布），尤其是由于经济衰退更加剧了对大援助项目是否真正值得他们付出高昂代价的讨论和怀疑，此时履行对非洲的承诺显得尤为重要。

But as the club of rich nations struggles to be taken seriously (many argue the G-20 more accurately reflects the distribution of economic power in the world today), unkept promises to Africa will matter — especially since the recession has fueled discussions and doubts about whether big aid programs are really worth their high cost.

但是由于富国俱乐力图认真考虑（很多国家认为G20能更加准确地反映出当今世界经济实力的分布），未履行的对非洲的承诺将是个大问题。特别是由于经济衰退，使得针对大援助项目是否真的值得他们付出高昂代价的讨论和怀疑被火上浇油。

But this does not rule out unofficial discussions.

但这并不排除进行非正式的讨论。

Eg. But this does not rule out unofficial discussions.

但这并不排除进行非正式的讨论。

There had been discussions among part-time teachers about the unfairness and the unreasonableness of the situation.

兼职教师中常有抱怨，觉得这种待遇不公平也不合理。

This uncertainty makes it difficult for us to determine its scope exactly.But we can find in the scholars'discussions that public interest is the'interests of unspecific persons and its content is uncertain.

国内外学者对如何界定公共利益的讨论，揭示了公共利益是不特定多数人的利益这一基本含义和内容的不确定性这一基本特征，并为合理界定公共利益指明了方向。

The X-ray diffract was used to analyze the crystal structure of the composite. Results show that after the talc was treated with blend coupling agent, the crystal structure of talc changed, and effect Intercalation phenomenon.

通过X射线衍射分析可知，用混合偶联剂对滑石粉进行预处理后，滑石粉晶体结构发生改变，产生了插层现象，使PP／滑石粉复合材料为纳米复合材料。

An authentic Maui wedding might require the services of a 'kahu', which is a Hawaiian minister.

毛伊可能需要一个真实婚礼服务'kahu'，这是夏威夷部长。