(1) The assumptions in the paper should be expressed in strict and exact mathematical language, so that readers will not misinterpret them.

(2) The assumptions put forward are indeed necessary for establishing a mathematical model, and the assumptions unrelated to establishing the model will only disturb the reader's thinking.

(3) Assumptions need to be verified. The rationality of assumptions can be obtained from the process of analyzing problems, such as making common-sense assumptions from the nature of problems; Or by observing the image of the given data, the functional form of the variable can be obtained; You can also refer to other materials and draw an analogy. For the latter, the relevant contents of references should be pointed out.

2, the establishment of the model

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After making assumptions, we can introduce variables and their symbols into the paper, express the relationship between them abstractly and accurately, and finally successfully establish equations or summarize them into other forms of mathematical problems through certain mathematical methods. Here, we must use the method of analysis and demonstration, that is, the method of reasoning, so that readers can clearly understand the process of getting the model. It is forbidden to jump too much in the process of logical reasoning between contexts, which affects the persuasiveness of the paper. Where reasoning is needed, there must be deduction. When quoting a ready-made theorem, we must first verify the conditions that satisfy the theorem. All kinds of mathematical symbols used in this paper must be explained when they first appear. In short, the process of getting the mathematical model should be clearly expressed, so that readers can get a basis for judging the scientific nature of the model.

3. Calculation and analysis of the model

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After the actual problem comes down to a mathematical problem, it needs to be solved or analyzed. In numerical solution, the calculation method should be explained, and the name of the software or calculation program used should be given (usually in the form of appendix). You can also use computer software to draw curves and surfaces, and vividly express the numerical calculation results. According to the calculation results, some conclusions helpful to practice are obtained by analytical method.

Some models (such as nonlinear differential equations) need stability or other qualitative analysis. At this time, it is necessary to point out the mathematical theory on which it is based and draw a clear conclusion on the basis of reasoning or calculation.

In the process of model establishment and analysis, conclusions with universal significance can be expressed in the form of clear theorems or propositions. Conclusion the problems that should be paid attention to in use can be listed in the form of mnemonics. Theorems and propositions must clearly state the conditions for the conclusion to be established.

4. Discussion of the model

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This mathematical model can be discussed from many aspects. For example, we can explore how the model will change for different scenarios. Or according to the actual situation, we can change some assumptions made at the beginning of the article and point out the changes in the mathematical model. Different numerical methods can also be used to calculate and compare the results. Sometimes we should broaden our thinking and consider the changes brought about by different modeling methods.