数学论文常用语句 经典句式
【转载请注明出处】http://www.cnblogs.com/mashiqi
2018/07/15
常数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.
由于epsilon取值的任意性，我们可以得出结论...
- since epsilon is taken arbitrarily, we can conlude...
我们暂时混用一些符号
- with (a slight)/some/an abuse of notation
- with slight ambiguity
我们假设\(f\)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(有依据的)假设：
- under a reasonable assumption on...
取消假设：
- drop the assumption
主要是理论上的重要性：
- is primarily of theoretical interest
它本身也是个有意思的主题：
- It is of interest in its own right.
想法/灵感来自于：
- The idea of this work/This derivation is motivated by
抽出一个子列：
- after passing to a subsequence
类似前面的方法：
- by arguments similar to the ones used in xxx, we have xxx.
为了保持行文流畅
- To keep the context flowing
这随后的内容中，就会清楚。
- 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.
随时可以询问获取
- available upon request
按照如下的方式
- as follows / in the following manner
不失一般性：
- 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.
为了这样的目的：
- to this end
于是乎：
- it follows that
问题的解，方程的解
- solutions to the problem / solutions of the equation
与......紧密相关：
- is closely connected/related to
从现在开始，...将会被默认已知并不被再次强调：
- from now on, ... will be understood and not mentioned.
- In the following analysis, ... will be omitted but implied.
但是本文只考虑一般的(简单的)情形
- But we choose not to complicate our lives by considering overly general cases in this paper.
数值仿真清晰地显示出
- our numerical simulations show clearly that
根据数据来选择合适的参数
- The constants/parameters are chosen to fit the data.
如何写abstract：要用一般现在时态
1. 第一句话概括全文，说清楚做了哪个方面的研究。In this paper, we are concerned with the [二级学科] problem associated with/of...
2. 第二句话概括本文得到了那些结果。We establish / prove ...
3. 第三句话，如果第二句话把本文的工作概括的太笼统了，可以在第三句话中稍微再展开一点，详细一点。但不要太详细，尽量少出现数学符号。
4. 第四句话写本文的亮点与新颖之处。The major novelty of this/our study/paper is/are...
