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1、Theory Analysisn nMathematics Analysisn nModel Introductionn nEquation DescriptionMathematics Analysisn n1.Introduce theme and objective.1.Introduce theme and objective.n n2.Describe relative 2.Describe relative hypothesishypothesis,conditioncondition or or definitiondefinition.n n3.3.PresentPresent
2、 primary primary problemsproblems or basic or basic equationsequations.n n4.4.AnalyzeAnalyze and get some results.and get some results.n n5.5.DiscussDiscuss or or inferinfer according to above results.according to above results.n n3-5 may repeat.3-5 may repeat.n n1.Describe 1.Describe backgroundback
3、ground or theory basis of the or theory basis of the model.use referencesmodel.use referencesn n2.2.ListList and and analyzeanalyze some basic equations.some basic equations.n n3.3.DescribeDescribe the model in detail.the model in detail.n n4.4.ExplainExplain or or discussdiscuss the important the i
4、mportant characteristics of the model.characteristics of the model.n n5.5.DepictDepict how to apply the model in certain how to apply the model in certain situation with an example.situation with an example.n n2-5 repeat for each part,sub theme,or stage of 2-5 repeat for each part,sub theme,or stage
5、 of the model.the model.Model Introductionn nLayoutn nPunctuation Equation DescriptionNoticen nDescribe the definition of hypothesis or concepts before using them.n nPresent the problem before depicting the equations used.n nState each sub theme of the theory with summary at the end of each statemen
6、t.Express the relationship among sub themes if necessary.n nTense:Present tensePresent tense for facts.(most)for facts.(most)E.g.E.g.The solution can be obtained by solving Eq.(2).The solution can be obtained by solving Eq.(2).Future tenseFuture tense for new theme description in for new theme descr
7、iption in new paragraph.new paragraph.E.g.E.g.We will solve this problem in the context of the following We will solve this problem in the context of the following model.model.If X=0,then the process will If X=0,then the process will Past tensePast tense for for Past work or experiment results of th
8、e author of Past work or experiment results of the author of this paper.this paper.Hypothesis of Hypothesis of originaloriginal authors.authors.n nVoice:Passive voice.Passive voice.n nAvoid using:It is It is There is/are There is/are n n“We”as subject.n nSentences:It is supposed that It is supposed
9、that.We suppose that We suppose that (good)(good)Let us suppose that Let us suppose that Suppose that Suppose that (good)(good)After substituting this term for y in Equation(4),the After substituting this term for y in Equation(4),the equation can be rewritten as follows.equation can be rewritten as
10、 follows.After substituting this term for y in Equation(4),We After substituting this term for y in Equation(4),We can rewrite the equation as follows.(good)can rewrite the equation as follows.(good)If this term is substituted for y in Equation(4),the If this term is substituted for y in Equation(4)
11、,the equation can be rewritten as follows.(good)equation can be rewritten as follows.(good)Substituting this term for y in Equation(4)yields the Substituting this term for y in Equation(4)yields the following equation.(good)following equation.(good)The relationship between x and y is now The relatio
12、nship between x and y is now considered.considered.Now let us consider the relationship between Now let us consider the relationship between x and y.(good)x and y.(good)Consider the relationship between x and y.Consider the relationship between x and y.(good)(good)x and y are related in the followin
13、g way.x and y are related in the following way.(good)(good)n nSample sentences:Sample sentences:Consider the case in whichConsider the case in which Let us now consider the case Let us now consider the case Suppose that Suppose that Let d and V be scalings for the length and width.Let d and V be sca
14、lings for the length and width.We assume that We assume that under consideration here.under consideration here.If x=1,then we have the following equations:(equation)If x=1,then we have the following equations:(equation)Given that m=1.2,we obtain Given that m=1.2,we obtain (equation)(equation)The equ
15、ation for Ag/At becomesThe equation for Ag/At becomes(equation)(equation)The equation for Ag/At can be written/expressed asThe equation for Ag/At can be written/expressed as Substituting m into Equation 3,we obtain Substituting m into Equation 3,we obtain The relationship between m and n is as follo
16、ws.(equation)The relationship between m and n is as follows.(equation)A is inversely proportional to B,as shown below.A is inversely proportional to B,as shown below.Eq.5 takes the form.Eq.5 takes the form.From this equation,the relation between x and y can be From this equation,the relation between
17、 x and y can be expressed as expressed as If the same material is used,the above equation reduce to If the same material is used,the above equation reduce to We will now reduce Eq.3 to a simpler form.We will now reduce Eq.3 to a simpler form.On substituting this equation into Eq.16 and solving for x
18、2,On substituting this equation into Eq.16 and solving for x2,The The is defined as.is defined as.The The is given by is given by Upon performing the integration using Eq.19,substituting a+b Upon performing the integration using Eq.19,substituting a+b for x,let z=c/d,and simplifying,for x,let z=c/d,and simplifying,We will now integrate Equation 2 in order to derive the solution.We will now integrate Equation 2 in order to derive the solution.We can now derive the solution to Equation 2.We can now derive the solution to Equation 2.If Eq.16 is solved for X,If Eq.16 is solved for X,