數學論文經常使用語句 經典句式

【轉載請註明出處】http://www.cnblogs.com/mashiqi 2018/07/15
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常數C：

• the specific value of C is not required but should be clear from the surrounding context.
• C may denote different constants in what follows.
• Note the the value of the constants C will change during the proof.
• We denote by C the generic constant which is independent of... but may change line by line.
• We may use C and its variations, such as C_j, C_j^i, etc., to represent some generic smooth function(s) within... whose particular definition may change/(be changed) line by line.

因爲epsilon取值的任意性，咱們能夠得出結論...

• since epsilon is taken arbitrarily, we can conlude...

咱們暫時混用一些符號

• with (a slight)/some/an abuse of notation
• with slight ambiguity

咱們假設$f$充分光滑：

• We assume that $f$ is sufficiently smooth, so that we can take x-derivatives necessary times.
• XXX is the smallest possible extension in which differentiation is always possible.

合理的(有依據的)假設：

• under a reasonable assumption on...

取消假設：

• drop the assumption

主要是理論上的重要性：

• is primarily of theoretical interest

它自己也是個有意思的主題：

• It is of interest in its own right.

想法/靈感來自於：

• The idea of this work/This derivation is motivated by

抽出一個子列：

• after passing to a subsequence

相似前面的方法：

• by arguments similar to the ones used in xxx, we have xxx.

爲了保持行文流暢

• To keep the context flowing

這隨後的內容中，就會清楚。

• This will be clear later in this chapter.
• We denote... as... [for short / for notational convenience] if it is clear in the context.
• We shall somewhat incorrectly denote xxx by xxx.

隨時能夠詢問獲取

• available upon request

按照以下的方式

• as follows / in the following manner

不失通常性：

• without loss of generality
• It suffices to show that ... since .... E.x. It suffices to show that such connection exists in each coordinate chart since the uniqueness guarantees that connections agree if the charts overlap.

爲了這樣的目的：

• to this end

因而乎：

• it follows that

問題的解，方程的解

• solutions to the problem / solutions of the equation

與......緊密相關：

• is closely connected/related to

從如今開始，...將會被默認已知並不被再次強調：

• from now on, ... will be understood and not mentioned.
• In the following analysis, ... will be omitted but implied.

可是本文只考慮通常的(簡單的)情形

• But we choose not to complicate our lives by considering overly general cases in this paper.

數值仿真清晰地顯示出

• our numerical simulations show clearly that

根據數據來選擇合適的參數

• The constants/parameters are chosen to fit the data.

如何寫abstract：要用通常如今時態

1. 第一句話歸納全文，說清楚作了哪一個方面的研究。In this paper, we are concerned with the [二級學科] problem associated with/of...
2. 第二句話歸納本文獲得了那些結果。We establish / prove ...
3. 第三句話，若是第二句話把本文的工做歸納的太籠統了，能夠在第三句話中稍微再展開一點，詳細一點。但不要太詳細，儘可能少出現數學符號。
4. 第四句話寫本文的亮點與新穎之處。The major novelty of this/our study/paper is/are...