exclusively专门 undobtedly毫无疑问的 notable 值得注意的 tremedous/significant极大的 notion概念
definition定义——define Interpret……as…… 理解……为 invoke(+模型援引，引用 equation方程式，等式
function因变量——提示符号的含义 matrix矩阵，模型
constant 常数，常量It requires I to be a constant for …to be true
algorithm演算方法——a general algorithm 通用算法 simplify the algorithm 简化算法 we have produced a general algrrithm to solve this tpye of problems. derivative微分，倒数 antiderivative 不定积分 optimal results 最优结果
invesgate the problem from different point of view调查问题——investgation调查 survey 调查
subproblem 子问题，次要问题——major problem 主要问题 metric 度量标准，指标 digit 数字 delete some digits element /component 元素
解题思路seek/explore——
explore different ideas探索不同的想法
we seek to device a new model for solving the problem by exploring the new direction suggested by their investigations.
解决方案design/device ——develop/establish/conduct
Based on our analysis, we design a model for the problem using integral linear programming(线性积分). We then devise a polynominal-time apprximation algorithm to produce near optimal results.using integral linear programming.We then device a polynominal-time approximation to
We conduct sensitivity analysis on…to find…xxx analysis is also performed.
解决结果tackle/solve
We tackle the problem using the new technique we developed in the previous section.While it is difficult to solve the problem completely, we are able to solve a major subproblem.
计划与打算 approach/propose
We approach the problem using the proposed method. We propose a new approach to tackling the problem. 词组
Basedon…以……为基础 According to根据
Devide …into…——subdivide into细分
…is applied to…使用了……模型来……——we apply our model into将我们的模型运用于
Modelproves to be efficient in other sports.模型被证明在其他方面有效 ….,which indicates that………反映了
…,which led to the change of…导致了……的变化 We…..only to find that..我们……只是发现了…… … doesn’tmatter……是无关的 Take…as example/as a case study举例
formulate and justify the assumptions 阐述并证明假说 design/establish a model设计模型
devise an algorithm 设计一个运算法/计算程序 carry out numerical simulations 进行数学模拟
for our problem a relationship exists that(… 我们的问题中存在一个关系式，使…… we will assume/suppose that…我们假设……
compare with different approaches 与不同的措施相比较
There are at least two notions of where the sweet spot should be—an impact location on the bat that either · minimizesthe discomforttothehands, or · maximizes the outgoing velocity Of the ball.
We focus exclusively on the second definition我们专注于第二种定义
We interpret the error of +2 as a normal distribution,.一with standard deviation of 1。 Toillustrate the upon two points,we choose the following two norms.为了说明上述两个观点，我们选择了下面两种标准
What follows in the chapter will hammer at…本章节接下来会集中…… …system works by………系统通过……工作 类比手法 as for…..,similarly there are… 对比 a ….while b…
连缀词 first,…second,…,after that…,at last…
Summary
1Restatement of the problem（introduction） Problem background,previous study,our work 2Assumptions
（symbols,definitions and assumptions） 3Justification ofOur Approach 4The Model
4．1 Dissatisfaction of a passenger needing a connection 4．2 Dissatisfaction of a passenger not needing a connection 4．3 Total dissatisfaction on an aircraft 5Testing the Model 6Results
7Strengths and Meaknesses References 标题：
how to please most of the people most of the time locating a drug runner:miami vice style
centroids,clusters,and crime:anchoring the geographic profiles of serial criminals(固定轮廓 loading two railroad cars
taking the mystery out of sudoku difficulty:an oracular model 计算
The total wins a could be calculated as follows:
a = ???????? (3.1)
-Where ???????? denotes wins for the ????????? year. The total loses b could be calculated as follows:
Let r denotes …,then it can be calculated as follows:
Symbols for ………的符号（后接表格） symbol——definition summary
·赛题重述与阐明：用自己的语言描述将要解决的问题。
·解释假设条件及其合理性：强调建模所用的假设，而且清楚地列出建模所需的所有变
量。
·模型设计及合理性论证：指出所用模型的类型或构造新的模型。 ·描述模型的测试情况及灵敏度分析：包括误差分析等检测项目。 ·优缺点讨论：包括模型及解题方法的优点与不足。 长度稍超过半页即可。
In the last few years，the 9-by-9 puzzle grid known as Sudoku has gone from being a popular Japanese puzzle to a global craze.用吸引人的语言激发读者兴趣 不包含太多的细节
简明扼要地将解题方法描述清楚，包括全部要点及主要思路，并阐明所得出的结论。 如果有数值运算，还应该给出重要的计算结果 最好不要在摘要中使用数学公式。
We study the sweet spot on a baseball bat. We begin by establishing a model of a bat hitting a ball by analyzing a video of a professional hitter.Using this model, we determine that hitting a ball with a bat can be seen as an imperfect collision of two balls,where the bat is replaced by a hitting ball.
In order to….,we…
To evaluate the accuracy of the two models,…is defined.It is supposed to…为了评价两个模型的准确性
Introduction—— 1重述赛题
2明确解题目标（可以用列表形式） 3澄清原题中的模糊概念
4对现有文献在相似问题的研究进行综述和评论 5简要描述参赛小组的解题方法和主要结果