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2015美国大学生数学建模竞赛D题


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To Create a More Sustainable Future for Our Children
Summary
Sustainable development is affected in all aspects of social, economic, educational, scientific, political, and so on. The purpose of this paper is to analyze of the factors affecting sustainability, and put forward a more scientific and rational program. First of all, through the principal component analysis and cluster analysis provides a measure on the basis of nationa l and policy basis of degree of sustainable development. It determines whether a country is sustainable development. Then, establish a sustainable development plan of Nepal over the next 20 years by regression analysis prediction method. Finally, evaluated the program at a number of factors to be effective though Analytical Hierarachy Proces and Regression. And identified those projects and policies of the country's sustainable development measures have the greatest effect. At the same time, some suggestions on the sustainable development of a country in the future was put forward. Model 1 In order to measure the sustainability of a country, choose 20 representative countries from the global to form a small world. Taking into account various factors, selected 17 indicators of sustainable development as an evaluation index, the data are normalized, then by means clustering, the clustering of indicators to determine the weight of each category and principal component analysis, to calculate the national sustainable development index and rank. You get the d egree of sustainable development in the country and whether it is sustainable development. Model 2 Nepal selectedas a representative from the LDC list, it will inhibit sustainable development indicators were developed with reference to the replacement index, the data regression, considering the problems of the country's existence, re-forecast the country in the next 20 years according to our forecast of the development trend of the development trend for the next 20 years in Nepal to create a sustainable development plan. So that the country toward a more sustainable future. Model 3 Based on the sustainable development measures effectiveness evaluation of the problem,by constructing judgment matrix to reflect the plan between the relative importance of sustainable development indicators. Consistency of judgment matrix calculated ratio of 0.024 is less than 0.10, verify the consistency of the matrix. The plan describes a sustainable future for Nepal is valid. Consider the factors of war and natural disasters, with regression method to predict the country in the next 20 years of sustainable development index changes. By calculating the weight of each index weight, you can analyze what factors and policies for sustainable development of the country would come to have the greatest impact. These reforms were negative capital investments and policies that achieve maximum sustainable results. Finally, the model using the method of scientific analysis, and discusses the advantages and disadvantages of the model, taking into account the practical application of the direction of improvement and make some optimization strategies.

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1 Introduction
1.1 Background
Sustainable development is one of today's hottest topics exist, the biggest challenge we face is how to deal with problems between development and the limited resources, how do we distinguish whether it is sustainable development? What to do for the future of sustainable development planning, changing unsustainable development, promoting sustainable modes of production and consumption patterns, the state institutions and policies to promote sustainable development aspects of the reform, that we and our children have a I hope in the future.

1.2 Our work
?

?

?

?

We tackle four main sub problems: Factors affecting the evaluation of sustainable development of a country are analyzed based on the theory of sustainable development. Develop a model for the sustainability of a country. This model should provide a measure to distinguish more sustainable countries and policies from less sustainable ones. Choose from forty-eight poorest countries LDC country, according to the model of a task1 has been established for the selected countries to create a more sustainable development plan in the next 20 years in the development process, so that the country toward a more sustainable future. Evaluate the effect our 20-year sustainability plan has on our country’s sustainability measure created in Task 1. And predicted under the evaluation system to implement our plan will happen the change over the next 20 years. According to the selected country, we should consider the environmental factors, Climate change, development aid, foreign investment, natural disasters, and the instability of the regime, etc. We determine which project or policy for the sustainable development measures of the state will have the greatest effect. Write a report to explain the established model, including sustainable development, sustainable development plans, according to the model and the national environmental situation, analysis the effect of the plan. For the ICM provides a sustainable development of intervention strategy about investment in LDC countries.

2 Basic Assumptions
? ? ? Suppose that we are looking to the data that is real and effective. Suppose we selected 20 countries to represent the world. Suppose that in the second model we selective country no major natural disasters and major contagious diseases, political stability over the next 20 years.

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3 Symbol Descriptions
In the section, we use some symbols for constructing the model as follows. Symbol Description The i evaluation object of the j indicator is aij Every date of

aij
aij
xi
xi
yi
rij
A

aij ’s normalized indicator

The i country Standardized index variables The principal component of i The correlation coefficient of the i and j ’s indicator Judgment matrix The largest eigenvector eigenvector consistency ratio

?max
W CR

P.s: Other symbols instructions will be given in text.

4 Solutions
4.1 Task 1 4.11 The model
The principal component analysis can determine a few principal components from the connected factors and evaluate the all-around sustainable development. According to the related literature, find the influence factors for the sustainable development of country. We selected the 17 of these important factors as indicators. The condition of national sustainable development and the geographical position of nodes were fully considered. We selected the 20 typical countries.(The United States、Japan、The British、China、The French、Russia、 The Swedish、 Netherlands、 South Korea、 Ukraine、 Brazil、 South Africa、 Mexico、 Indonesia、 Canada、Thailand、The Norwegian、Nepal、 Spain、Jamaica)With these representatives worldwide.

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Table 1: 17 affected countries for sustainable development indicators Social Development
Urban population (% of total) ,Population, total ,Health expenditure, total (% of GDP),Military expenditure (% of GDP) Food safety index , Trade in services (% of GDP)

Financial

The sustainable development

Education Economy

Tertiary education (% ) CO2 emissions (metric tons per capita) Combustible renewables and waste (% of total energy), Forest area (% of land area),Arable land (% of land area), Electric power consumption (kWh per capita) Fossil fuel energy consumption (% of total),Alternative and nuclear energy (% of total energ High-technology exports (% of manufactured exports) ,Research and development expenditure (% of GDP)

Environment

Science & Technology

Step 1 is raw data was collected to carry out the standardized treatment.
Assumption the i evaluation object of the j indicator is aij 。Converting indicators aij into normalized indicator a ij ,

a ij ?

aij ? u j sj

,

? i ? 1, 2,

, 20; j ? 1, 2,

,17 ?

1 20 Where u j ? ? aij , 20 i ?1

2 1 20 sj ? aij ? u j ? , ? ? 20 i ?1

? j ? 1, 2,

17 ?

We have u j , s j shows the j index of the sample mean and standard deviation. Then

xi ?

xi ? ui , si

? i ? 1, 2,

,17 ?

is standardized index variables.

Step 2 is computing the correlation coefficient matrix R .

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Through correlation coefficient matrix R ? ? rij ?17?17

rij ?

?a
k ?1

17

ki

? a kj

n ?1

,

? i, j ? 1, 2,

,17 ?

Where rii ? 1, rij ? rji , rij is the correlation coefficient of the i indictor and the j indictor.

Step 3 is calculating eigenvalues and eigenvectors.
Calculate the correlation coefficient matrix eigenvalues ?1 ? ?2 ? corresponding eigenvectors u1, u2 , eigenvector m new target variable
? ?17 ? 0 , and the

, u17 ,in this u j ? u1 j , u2 j ,

?

, u17, j

?

T

, Consist of

? y1 ? u11 x1 ? u21 x 2 ? ? u17,1 x17 ? ? y2 ? u12 x1 ? u22 x 2 ? ? u17,2 x17 ? ? ? y ? u x1 ? u x 2 ? ? u x17 1,17 2,17 17,17 ? 17
In the equations, y1 is the 1th principal component , y2 is the 2th principal component , ?, y17 is the 17th principal component.

Step 4 is it choose p ? p ? 17 ? principal components and calculating comprehensively evaluated values.
By calculation the contribution rate of information and the accumulative contribution rate that eigenvalues ? j ? j ? 1, 2,

,17? .

bj ?

?j

??
k ?1

17

? j ? 1, 2,

,17 ?

k

is the contribution rate of information that the principal component y j .

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ap ?

??
k ?1

p

k

??
k ?1

17

k

is the accumulative contribution rate of the principal component y1, y2 , close to 1 ?? p ? 0.85, 0.90, 0.95? ,select the previous p variables y1 , y2 ,

, yp

.

When ? p

, y p as p

principal component, substitute original m variables. To comprehensive analysis of p principal components. On the base of this, calculate the comprehensive score.

Z ? ? bj y j
j ?1

p

Where b j represent the j the contribution rate of information that principal component.

4.12 Solutions
This section discusses the necessity of constructing an index system of national sustainable development and basic principles while constructing the system. We can get has strong correlation between indicators. For example, the proportion of urban population to total population and the per capita share of health care spending. Renewable will only make up the percent of total energy and the per capita share of energy use. By conventional methods, using these indicators to evaluate sustainable development mode, it is very difficult to complete. Inevitably cause repeated information and affect the objectivity of the judgment result. So we using clustering analysis the indicators. We used MATLAB software to calculate the correlation coefficient and correlation coefficient matrix between 17 indicators. ( See attached table 1) These data suggest that there is a strong correlation between some indicators. A variable analysis was made for 20 out of 17 characters, except 11 characters was not significant, 6 characters were analyzed through classification. Then the representative indicators are selected from each class. For each of the variables (indicators) of the data are standardized. The result is shown in figure 1.

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6 5.5 5 4.5 4 3.5 3 2.5 2 1.5

4

9

1

15

3

11

13

16

5

7

10

6

12

17

2

8

14

Figure 1: The cluster analysis tree diagram of indictors The Fig.1 shown the 17 indexes can be divided into six classes. The first kind :[1,3,4,9, 11,13,15,16], the second kind:[5,7,10], the third kind:[6], the fourth kind:[12, 17], the fifth kind:[2], the sixth kind:[8,14]. Number represents the value shown in table 1.So we from the 17 indexes selected representative six indicators for analysis: x1 : Health expenditure, total (% of GDP), x2 : Tertiary education (% ), x3 : Forest area (% of land area),

x4 : Fossil fuel energy consumption (% of total), x5 :Growth rate of population every year,
x6 :Combustible renewable and waste (% of total energy).
We used the principal component analysis method and MATLAB to solve the problem. Table 2: Eigen value, Contribution rate and accumulative contribution rate eigenvalue Contribution rate Accumulative (%) contribution rate (%)

x1 x2 x3

2.541425 1.331968 1.139823

42.35709 22.19947 18.99705

42.35709 64.55656 83.55361

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x4

0.677815 0.18589 0.123078

11.29691 3.098174 2.051303

94.85052 97.9487 100

x5
x6

The table shown the principal component analysis of the effect is very good. Select top 5 below principal component comprehensive evaluation, first 5 eigenvalue corresponds to the eigenvector is shown in table 3. Table 3: We can see that the cumulative contribution rate of judgment index of top 5
The first eigenvector The second eigenvector The thirdly eigenvector The fourthly eigenvector The fifth eigenvector

x1
x2
x3

-0.409030 0.263702 0.021681 0.496779 0.450205 -0.559650

0.291174 0.727037 0.082609 0.384383 -0.472440 0.094112

-0.388060 -0.201880 0.834113 0.162299 -0.237270 0.174001

0.605947 0.112647 0.536904 -0.297220 0.324865 -0.371480

0.455624 -0.582040 -0.060380 0.639642 -0.134990 -0.150400

x4
x5

x6

By calculation we obtain

? y ? ?0.409030 x1 ? 0.263702 x 2 ? ? 0.559650 x 6 ? 1 ? y2 ? 0.291174 x1 ? 0.727037 x 2 ? ? 0.094112 x 6 ? ? ? y ? 0.455624 x ? 0.582040 x ? ? 0.150400 x 1 2 6 ? 5
Symbol means

y1 CO2 emissions (metric tons per capita), Urban population (% of total), Health
expenditure, Electric power consumption (kWh per capita), High-technology exports (% of manufactured exports), Combustible renewables and waste (% of total energy) , Fossil fuel energy consumption (% of total)

y2 Military expenditure (% of GDP), Arable land (% of land area), Tertiary education
(% )

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y3 Forest area (% of land area)
y4 Fossil fuel energy consumption (% of total), Trade in services (% of GDP) y5 Growth rate of population every year
So we arrive at the conclusion that based on the principal component analysis constructs the appraisal model:

Z ? 0.4236 y1 ? 0.2220 y2 ? 0.1900 y3 ? 0.1130 y4 ? 0.0310 y5
Though this model we have compared the level of sustainable development in a selection of 20 countries. The rank is shown in the table below. Table 4:Comprehensive evaluation of ranking
Country Z rank Country Z rank Country Z rank Japan 0.9805 1 Netherlands 0.3488 8 Mexico -0.4731 15 The United States 0.9779 2 Canada 0.2789 9 Jamaica -0.5109 16 South Korea 0.9467 3 Ukraine 0.1375 10 Brazil -0.5560 17 Spain 0.5809 4 The French 0.1004 11 Indonesia -0.5809 18 Russia 0.5242 5 The British -0.0325 12 South Africa -1.1826 19 The Swedish 0.4898 6 Thailand -0.2338 13 Nepal -2.0270 20 The Norwegian 0.4652 7 China -0.2340 14

Table 3 shows it can be seen in Japan, the United States and South Korea sustainability index is high, Japan's total forest area accounted for 86.6%, college enrollment rate was 61%, the av erage annual healthcare spending of $4752; American per capita health expenditures and coll ege enrollment rate relative to other countries in the forefront, 83.6% of the total energy cons umption of fossil fuels, South Korea's forest area percentage of the total land area of 63.8%, 8 2.8% of the percentage of the total energy consumption of fossil fuels. At the same time also can clearly see that Brazil, Indonesia, South Africa, Nepal sustainable comprehensive index o f the four countries are low. Brazil in fossil fuel energy consumption accounts for 54.6%, perc entage of the total of Indonesia's health spending $108 per capita, population growth rate was 1.2%, the South African population growth rate of 1.3%, the per capita health spending $145, enrollment in colleges and universities by 4.17% 1.2% population growth, Nepal in colleges and universities enrollment rate of 14%, fossil fuel energy consumption accounts for 12.5% p ercentage of the total. Set up by our model and find the data synthetically analysis judgment more factors of sustain

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able development. More sustainable development of the country's forest cover has a very larg e area, medical and health spending, college enrollment rate is high, the slow population gro wth, science and technology developed. Less sustainable development state of these aspects h ave different degrees of problems, by improving these aspects can make the country more sus tainable development.

4.13 Analysis of the Model Strengths
Principal component analysis of various indicators can be converted to a small number of integrated indicators several unrelated, principal component analysis is based on all the main components of variance followed by the size of the order, and in the analysis of the problem, you can give up part of the main ingredient, just take the front several larger variance to represent the original variables principal component, thereby reducing the computational effort.

Weaknesses
Explain the meaning of the principal component with ambiguity, unlike the original meaning of the variables so clear, precise. Next, some of the main ingredients are extracted must be able to give a realistic explanation of the background and significance, otherwise the main ingredient will actually had plenty of information without meaning.

4.2 Task 2
4.21 Establish a sustainable development model of Nepal over the next 20 years
From task 1 we can see Nepal ranked dead last in the sustainable development of the countries. A comparison of Nepal with the viable country of the top 4.We found that Nepal’s sustainable development the main component indicators very low. Learn about Nepal children are often deprived of access to schools and the majority of the population of the country have little access to higher education. It the human population had increased so rapidly, the need and demand of medical service was both lower than the mean national value, and the little forest area, fossil energy consumption is low. In accordance with the above analysis, we are trying to create a plan that will allow Nepal to sustainable development of over the next 20 years. The ability of country sustainable development of Nepal during 2005-2013 is evaluated in this paper. At the same time, there are some problems need to improve which are found in the national development. In task 1 has calculated Nepal’s comprehen sive index of sustainable development of Z. Establishing models using regression forecast method, and solving the models though methematica software. We look for the date of Nepal’s five principal component index during 2005-2013.For linear regression prediction equation after index changes. On the basis of the data from the tests, linear regression was conducted and the related regression equation was formed.

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z ? ?0 ? ?1 x ? ?
Where x1 on behalf of the independent variable, ?0 , ?1 z on behalf of dependent variable, on behalf of regression coefficient, ? on behalf relative error, x on behalf a particular year z on behalf of comprehensive index of sustainable development. Where

R ?
2

? (z? z) 1? ? (z? z)

2 2

The composite index of sustainable development over the past nine years to fit, find the effect is not very good fit. Our optimization the model, obtained nonlinear regression equation.

? ? ?0 ? ?1 x ? ?2 x2 ? ?3 x3
Calculate R 2 closer to 1, the better, F greater than the critical value of F, we can conclude that from 2005 to 2013 Composite Index fitting chart, according to the trend of the past few years to fit one of function of predicting the next two decades sustainability, in planning for the future development of Nepal based on sustainability indicators after the change. Through enrollment in higher education in Nepal, dollars, fossil fuel consumption, population growth, per capita health expenditure annual percentage index was improved, and then standardize the data to calculate the composite indicator Z sustainable development. Prediction method using regression model, the model was solved by methematica software, we find data ~ 2013 five main component indexes of Nepal 2005, make specification changes come after linear regression equation to predict.

z ? ?0 ? ?1 x
By calculation we obtain

z ? ?64.383644 ? 0.3213x
R2 ? 0.982 F ? 884.162 P ? 11.25389 ?10?8
We obtain Z after fitting is 98.2%, to make the fitting degree is higher and the prediction results more accurate. We will further optimize the model. The optimized regression equation is as follows.
z ? ?0 ? ?1 x ? ?2 x 2 ? ?3 x3 ? ?

Using existing data regression prediction, get fitting curve is as follows.

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0.30 0.25 0.20 0.15 0.10 0.05

2006

2008

2010

2012

Figure2:The fitting curve of comprehensive evaluation index in 2006~2013

R2 ? 0.994 F ? 993.63 P ? 6.7728 ?10?8
After the further optimization of the model degree of fitting reach99.4%, F more than the critical value of F , p

0.05 .So the model is feasible.

According to Fig.2 fitted curve ,we know the sustainability of the actual comprehensive index

z during 2005~2013.And we should predict the sustainability of comprehensive index.
z ? ? 0 ? ? 1 x ? ? 2 x 2 ? ? 3 x3

z ? ?1.29903x ? 0.00127734 x2 ? 3.13934 ?10?7 x3
The error between them is very small; we work out residual e ? z ? z , the relation of actual value and predicted value. As shown in Tab. 5.
Table 5: Residual, actual value and predicted value.
2005 2006 0.068 0.074 -0.006 2007 0.11 0.109 0.002 2008 0.14 0.143 -0.003 2009 0.18 0.1763 0.0037 2010 0.22 0.2078 0.0122 2011 0.23 0.238 0.008 2012 0.26 0.267 0.007 2013 0.30 0.295 0.005

actual value predicted value residual

0.042 0.038 0.004

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0.5 0.4 0.3 0.2 0.1

2010

2015

2020

2025

2030

Figure 3: The trend of sustainability during 2005-2032

Nepal's sustainable expansibility is in the growth the tendency. It will have Z=0.5864 in 2032. At that time will achieve a more sustainable development. To sum up, we to Nepal the sustainable development plan of the next 20 years. From the model indicates that the influence factors of sustainable development. Such as the per capita of medical care expenditure, the consumption of fossil fuels, population increase, the enrollment rate of higher education. Resources are the basis for the sustainable development of a country.

We have some plans:
1)First, local government roust enforce the supporting, including funds and policy. Make sick people have a place of treatment. 2) As fossil fuels are cheaper than carbon-free energy sources, developing countries argue that a premature shift to low-carbon energy may slow development. So does Nepal. But they should introduction of new technology conservation of natural resources by peaceful extraction of these fossil fuels. It improved their living standard through developing industry. We know that Green IT if done properly can go hand in hand with sustainable solutions and cost reductions. 3) It should attached great importance to the development of education. Education is the human reproduction and creating, and must pay attention to the development of individual subjective education 4) In my judgements, human beings may create a better and more peaceful future by controlling population growth and pollution. They should increased vegetation cover, and strictly control population growth, improve the quality of the population, reducing the population pressure on the environment. 5) There are abundant of grassland tourism resources in Nepal, but the utilization of it is very limited. Developing tourist industry through accelerate the development of cultural

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industry. We believe these strengths can help Nepal build great developments over the next two decades.

4.22 Analysis of the Model Strengths
Through the indicators of developed countries for reference to promote the sustainable development of Nepal replaces the index. Enable Nepal future the sustainable development to have a better tendency. Application of regression prediction method, Let the actual and predicted values of 2005 to 2013 the highly fit.让 So that the next 20 years to get a good predictor of sustainability.

Weaknesses
Changes to the index on behalf of subjectivity, Assuming the model does not represent the real situation, the country is difficult to predict some changes may occur in the future.

4.3 Task 3
4.31The model
Establish a model of evaluation on the basis of analytic hierarchy Analytic hierarchy evaluation method (APEH) First, let sustainable level of development as the overall goal of layer in this paper. Based on the growth rate of population every year, health expenditure, total (% of GDP), forest area (% of land area), Tertiary education (% ) and Combustible renewable and waste (% of total energy) as the secondary rule levels. Let Nepal as an object layer. Establish the hierarchical model analysis to determine the impact of each index for sustainability. As shown below :

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Figure 4 Analytic Hierarchy Chart

Secondly, establish the judgment matrix. Judgment matrix is the starting point of the APEH, indicate the relative importance of the target layer between layers for guidelines. Then, guidelines seek single layer weights. This is among the indicators of the relative importance of the criteria layer target layer, while it is calculated for each criterion level indicators relative to the degree of sustainability of development rights on the basis of weight. Table 4 is constructed to determine the successful bidder of the matrix, and then by calculating the judgment matrix orthogonal eigenvectors and corresponding maximum characteristic root, the index criteria layer draw the guidelines for the right weight.
Table 4 :

valuation 1 3 5 7

importance degree Compared to two indicators of equal importance Compared to two indicators, one of slightly more important than the other Compared to two indicators, one of obvious important than another Compared to two indicators, one of strong important than another

i and j index ratio was bij , the index j and i ratio
reciprocal was b ji ? 1/ bij

Need to check out structure (positive reciprocal) to determine whether a matrix A is a serious Without Uniform. In order to determine whether to accept the maximum positive reciprocal matrix characteristic root must be positive real numbers, Which all the components of eigenvectors corresponding to the real number. A feature vector of the remaining die are strictly less than max ? . A characteristic of the maximum value of 5, where 5 is the order of the matrix A, the remaining root characteristic A are zero. If the eigenvector corresponding to the largest

eigenvalue of A is W ? (w1 , w 2 ,..., w 5 ) ,let
T

bij ?

wi , i, j ? 1, 2,...,5 ,so wj

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? w1 ?w ? 1 ? w2 ?w ? 1 ? w3 ? ? w1 ? w4 ? ? w1 ? w5 ? ? w1

w1 w2 w2 w2 w3 w2 w4 w2 w5 w2

w1 w3 w2 w3 w3 w3 w4 w3 w5 w3

w1 w4 w2 w4 w3 w4 w4 w4 w5 w4

w1 ? w5 ? ? w2 ? w5 ? ? w3 ? ? w5 ? w4 ? ? w5 ? w5 ? ? w5 ?

So you can get a judgment order 5X5 matrix A = (bij) and the various indicators of weight W=( w1,w2,w3,w4,w5) 。 Finally, in order to test the consistency of judgment matrix, it is necessary to calculate the proportion of consistency CR. If CR <0.10, shows the calculation results of this sort have a satisfactory level of consistency.

4.32 Solutions
According to 20-year sustainability plan we have established .Using MATLAB software for solvin.

? ?1 ? ?5 ? A=( bij )= ? 1 ? ?7 ? ?3 ? ?

1 5 1 1 5 1 1 3

1 5 1 7 5

1 7 1 1 7 1 1 3

1? 3? ? 3? 1? ? 5? 3? ? 1? ? ?

Consistency Ratio,CR=0.0244<0.10, by consistency check,Show our sustainable development plan for 20 years in the country task one sustainable development measures is effective. We can get
W=(w1,w2,w3,w4,w5)=(0.0559,0.3437,0.0517,0.3858,0.1629 )

It is obvious that enrollment in institutions of higher learning is evident that the largest share, followed by the per capita health care spending, moreover fossil fuel consumption. Institutions of higher education enrollment rate is per capita health expenditure and consumption of fossil fuels to the national sustainable development initiatives will have the greatest effect. It is obvious Colleges and universities enrollment proportion is the largest ,the second is the per capita health spending, the third is the fossil fuel energy consumption. In other words, the enrollment in colleges and universities, per capita health expenditures and fossil fuel energy consumption in the national sustainable development measures will have the greatest effect.

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We have evaluated the effectiveness of sustainability measures, consider the future development of the country into two decades of natural disasters on this basis, the war might affect the sustainability of development in Nepal, so we have developed through the task II in a sustainable development plan for the next 20 years, we have come to the sustainable development of the regression equation composite Index We have evaluated the effectiveness of sustainability measures. In the next 20 years of development process, we consider the natural disaster and war may affect the sustainable development of Nepal. And through the tasks 2 set for the sustainable development plan in the next 20 years, we have come to the sustainable development of the regression equation composite Index.

z ? ?1.29903x ? 0.00127734x2 ? 3.13934 ?10?7 x3
Calculated from the above we can the sustainable development of the composite index from 2 013 to 2032, the following table Plan index, this is no natural disasters, war and ideally. But i n real life, we should consider the actual situation, so we made assumptions about the future, assuming that in natural disasters happened in 2018, the country makes sustainability index dr ops, we according to the change of the natural disasters caused by principal component index, using the method of task 2 is changed after the sustainable development of the comprehensiv e evaluation index, the war in 2023, made sustainable composite index has fallen dramaticall y, due to the effects of the war is very big, so in the next few years will be affected, sustainabi lity, it is difficult to restore to the previous, based on this, we according to the index of chang e from 2023 to 2032, the sustainable development of the comprehensive index is calculated, t he following table Plan index. From the above we can calculate the comprehensive index of sustainable development about 2013 ~ 2032, the following table Plan index. This is in the absence of natural disasters and conflict in an ideal world. But in real life, we should consider the actual situation. We make assumptions about the future. Supposing the country will happen natural disasters in 2018. Make sustainability index drops, we according to the change of the natural disasters caused by principal component index. Using task two ways to get a new comprehensive evaluation index of sustainable development, Conflict will occur in 2023, making sustainability index fell sharply. Due to the impact of the war, the development of the country will be affected in the next few years will be affected. Sustainability is difficult to restore to before. Based on the situation, according to the index of changes, calculated the comprehensive index of sustainable development from 2023 to 2032. The following table Plan index:
Table 5: The 2013 ~ 2032 sustainability index of plan index and may index Year Plan 2013 0.295 2014 0.321 2015 0.3469 2016 0.371 2017 0.394 2018 0.415 2019 0.436 2020 0.455 2021 0.473 2022 0.489

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index May index Year Plan index May index 0.259 2023 0.505 0.296 0.321 2024 0.519 0.301 0.346 2025 0.532 0.324 0.371 2026 0.543 0.385 0.394 2027 0.554 0.391 0.401 2028 0.563 0.408 0.428 2029 0.571 0.425 0.455 2030 0.577 0.432 0.473 2031 0.582 0.455 0.489 2032 0.586 0.469

Through the data in the table, using MATLAB software comparison can be drawn this country over the next two decades, plans and taking into account the practical considerations of sustainable growth trend.
year&data

0.6

0.5

0.4

data

?plan index
0.3 may index ?

0.2

0.1

0

2014

2016

2018

2020

2022

2024 year

2026

2028

2030

2032

2034

From the graph we can see that the sustainable development of the plan change composite index trend slowly by changes in external factors assume after a downward trend, the development of change. However, does not affect the overall sustainability of the country over the next 20 years . In summary, through the task of solving the three, we tested the future of Nepal's 20-year plan to be effective, the implementation of the plan predicted in the next 20 years, sustainability is a growing trend, and that the level of the Assessment Act institutions of higher education enrollment rate countries the largest share, followed by the per capita health care spending, moreover fossil fuel consumption. So it can be carried out in the future development of these three areas of Nepal in capital investment and policy reform, and allow the country to a better, more sustainable development, but also allows investors to obtain the maximum benefit in this regard.

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5 Conclusions –– Future Work
Improved the model
Selection of more than two hundred countries around the world as the research object, Such data more complete and consider very comprehensive. Select the various sustainable development indicators, Such a more comprehensive evaluation and can reduce the error.

Popularization and application of the model
This model not only can be used for the evaluation and prediction of sustainable development, quality can also be used for the company development and future prospects, future rainfall, and the prediction of global sea level rise, and so on.

References [1] CHEN Jun-hui,XIE Ming-yong,Principal Component Analysis and Cluster Analysis of Inorganic Elements in Panax
Quinquefolium.L[J],Food Science of Ministry of Education,Nanchang University ,2006, 07

[2] LI Zuo-yong, WANG Jia-yang ,JOURNAL OF SICHUAN UNIVERSITY .[J],
24( 2)

2005

[3] Tang Hongyan, SUN Shenglong, YUNNAN ENVIRONMENTAL SCIENCE [J] 2005 24(2) [4] TingGang zhao,SuYun wang,JingYing Wei,”Mathematical modeling methods and mathematical
models”, Beijing,Science press,pp122~131,2010

[键入文字] Term# 39631 Page 1 of 19

The appendix
The appendix 1
1 The United States Japan The British China The French Russia The Swedis h Netherl ands South Korea Ukrain e 11. 5 6.6 -0. 2 69 0.4 82 11 0.3 89 573 7 170 3 293 2.9 2.6 1.2 10. 8 63. 8 16. 8 0.0 6 0.0 3 0.7 1 112 .6 102 .7 118 .5 709 9 101 62 366 2 80 98 77 2.1 6 4.0 4 0.7 4 91. 4 82. 8 79. 6 15. 6 19. 5 1.2 1.6 2 4.7 466 8 526 0 276 6 6 26 15 21. 9 16. 2 21. 8 12. 2 5.6 0.8 86 531 9 1.1 0.2 74 6.2 5.6 0.5 0.5 53 79 9.2 7.9 -0. 2 0.6 82 92 475 2 364 7 322 469 0 887 4.2 2.1 2.2 48. 4 29. 3 49. 4 69. 2 0.0 8 0.2 8 0.8 4 0.2 7 2.2 1 68. 6 12 0.0 3 0.1 101 .7 98. 2 126 .2 100 .1 113 .5 94. 2 184 8 547 2 329 8 729 2 648 6 140 30 70 76 58 27 62 61 3.3 9 1.7 2 1.9 8 2.2 6 1.1 2 3.4 1 31. 7 49 21. 5 94. 8 85. 1 88. 3 49. 1 91 46. 7 8.2 1 5.7 10. 8 3.8 7.9 3.6 2.9 2.3 353 9 302 0 202 9 383 2 511 3 513 4 13 21. 4 8 25 17. 3 9.5 26 22 17. 9 5.9 17 6.2 17. 6 2 0.7 3 81 4 889 0 5 3.8 6 33. 3 7 0.4 9 8 105 .9

The original data
9 132 46 10 94 11 2.7 9 12 83. 6 13 12 14 4.2 15 679 4 16 18 17 6.9

[键入文字] Term# 39631 Brazil South Africa Mexico Indone sia Canad a Thaila nd The Norwe gian Nepal Spain Jamaic a 0.1 5.8 2.7 1.2 -0. 2 0.3 54 18 79 36 280 8 318 0.8 1.4 0.9 25. 4 37. 1 31 0.0 8 0.2 7 0.0 4 130 .8 90. 1 104 553 0 155 3 31 0.2 85 0.7 106 14 0.3 12. 5 75. 9 82. 1 18. 1 0.7 17. 2 2.7 84. 1 6 266 6 113 5 1 33 7 383 0 11. 2 17 11. 7 1.3 80 905 5 1.4 14. 7 4.4 0.3 48 1.2 81 574 1 215 1.5 1 3.8 1.8 1.2 1.2 79 52 618 108 0.6 0.9 33. 2 51. 4 34. 1 37. 2 28 1.3 2 0.2 5 0.1 6 2.2 9 0.9 1.3 85 64 105 6 645 1.2 1.4 61. 6 7.6 0.3 7 0.2 3 0.1 9 0.1 125 .8 120 .5 112 .5 133 .1 106 .4 125 .8 101 .8 164 73 231 6 231 74 74 51 65 243 8 460 6 209 2 680 32 4.1 7 29 18 1.2 1 0.7 6 0.4 3 0.8 1 1.7 3 0.7 5 1.6 5 54. 6 87. 2 90. 1 66. 4 73. 7 80. 4 57. 3 37. 3 22. 9 0.6 18. 3 6.4 8.2 25. 4 4.9 727 0 179 0 594 2 19 21 12 10. 5 29. 5 17. 9 5.5 15. 4 2.7 Page 1 of 19 28. 9 10. 3 4.4 137 1 274 0 158 8 857 7 6.7 16 4.1 5 8.7 10 5.6

The appendix 2

17 indexes of correlation coefficient matrix

1

-0. 06 81 8

0.5 54 04 -0. 22 83 8

0.6 84 77 5 0.0 95 92 7 0.5

0.5 04 90 3 -0. 29 39 4 0.0

-0. 09 10 8 -0. 14 27 2 0.2

0.4 52 53 3 0.0 38 27 2 0.1

-0. 40 96 4 0.3 21 80 5 -0.

0.7 20 29 2 0.1 95 02 4 0.5

0.5 171 17 -0. 63 40 7 0.4

0.5 26 65 2 -0. 18 27 9 0.5

-0. 03 95 1 -0. 38

0.1 25 18 5 0.1 26 73 3

-0. 60 60 4 0.3 88 89 5 -0.

0.9 10 98 6 0.0 04 93 3 0.6

0.2 89 53 3 -0. 05 59 0.3

-0. 14 18 8 -0. 37 68 7 -0.

-0. 06 81 8 0.5

1

-0.

1

-0.

0.4

[键入文字] Term# 39631 Page 1 of 19

54 04 0.6 84 77 5 0.5 04 90 3 -0. 09 10 8 0.4 52 53 3 -0. 40 96 4 0.7 20 29 2 0.5 171 17 0.5 26 65 2 -0. 03 95 1 0.1 25 18 5 -0.

22 83 8 0.0 95 92 7 -0. 29 39 4 -0. 14 27 2 0.0 38 27 2 0.3 21 80 5 0.1 95 02 4 -0. 63 40 7 -0. 18 27 9 -0. 38 0.5 86 25 7 -0. 02 58 4 0.1 26 73 3 0.3 0.4 05 84 7 -0. 0.5 95 77 5 0.0 89 36 3 0.2 01 66 8 0.1 88 28 6 -0. 66 49 1 0.5 40 83 4 0.4 811 68

95 77 5 1

89 36 3 0.1 03 76 1

01 66 8 -0. 04 90 2 -0. 01 03 5

88 28 6 0.1 49 60 3 0.3 35 80 3 -0. 05 39 6

66 49 1 -0. 601 15 -0. 00 58 9 -0. 07 01 8 -0. 03 15 9

40 83 4 0.8 61 43 6 0.1 27 46 7 0.0 90 31 0.3 14 29 4 -0. 57 17 4

811 68 0.2 981 16 0.4 911 67 0.1 64 37 0.2 96 33 1 -0. 51 28 8 0.2 28 66 4

86 25 7 0.5 56 02 8 0.2 47 99 5 0.4 96 52 6 -0. 09 69 1 -0. 47 14 8 0.5 51 911 0.5 27 09

02 58 4 -0. 20 38 4 0.2 79 78 2 -0. 25 81 8 0.2 99 30 1 0.1 34 03 2 -0. 12 83 9 0.2 27 02 3 -0. 18 16 7

05 84 7 0.5 16 76 9 0.0 48 14 5 0.1 81 36 0.2 26 61 3 -0. 52 32 4 0.6 22 98 2 0.1 68 98 7 0.3 85 52 2 0.0 77 911

73 69 -0. 32 76 2 -0. 26 28 6 0.0 17 55 1 -0. 22 79 0.5 01 63 3 -0. 36 83 -0. 47 37 8 -0. 35 23 8 -0. 15 75 1 -0. 14 68

24 74 2 0.7 94 28 7 0.3 98 67 7 0.0 58 73 5 0.5 031 16 -0. 55 53 2 0.8 81 74 7 0.5 43 50 9 0.6 33 84 5 -0. 07 10 2 0.4 71 60 3 -0.

77 95 2 0.3 78 28 6 0.1 16 38 7 0.1 51 38 7 -0. 25 09 2 -0. 25 91 4 0.3 32 32 2 0.2 19 23 4 0.6 28 00 4 -0. 20 12 4 0.2 55 05 -0.

10 60 8 0.0 02 60 7 -0. 10 28 6 -0. 26 43 -0. 13 98 8 -0. 29 05 3 0.0 27 52 5 0.1 98 55 2 -0. 10 41 4 0.2 081 18 0.1 43 59 -0.

0.1 03 76 1 -0. 04 90 2 0.1 49 60 3 -0. 601 15 0.8 61 43 6 0.2 981 16 0.5 56 02 8 -0. 20 38 4 0.5 16 76 9 -0.

1

-0. 01 03 5 0.3 35 80 3 -0. 00 58 9 0.1 27 46 7 0.4 911 67 0.2 47 99 5 0.2 79 78 2 0.0 48 14 5 -0.

1

-0. 05 39 6 -0. 07 01 8 0.0 90 31 0.1 64 37 0.4 96 52 6 -0. 25 81 8 0.1 81 36 0.0

1

-0. 03 15 9 0.3 14 29 4 0.2 96 33 1 -0. 09 69 1 0.2 99 30 1 0.2 26 61 3 -0.

1

-0. 57 17 4 -0. 51 28 8 -0. 47 14 8 0.1 34 03 2 -0. 52 32 4 0.5

1

0.2 28 66 4 0.5 51 911 -0. 12 83 9 0.6 22 98 2 -0.

1

0.5 27 09 0.2 27 02 3 0.1 68 98 7 -0.

1

-0. 18 16 7 0.3 85 52 2 -0.

1

0.0 77 911 -0.

1

-0.

1

[键入文字] Term# 39631 Page 1 of 19

60 60 4 0.9 10 98 6 0.2 89 53 3 -0. 14 18 8

88 89 5 0.0 04 93 3 -0. 05 59 -0. 37 68 7

73 69 0.6 24 74 2 0.3 77 95 2 -0. 10 60 8

32 76 2 0.7 94 28 7 0.3 78 28 6 0.0 02 60 7

26 28 6 0.3 98 67 7 0.1 16 38 7 -0. 10 28 6

17 55 1 0.0 58 73 5 0.1 51 38 7 -0. 26 43

22 79 0.5 031 16 -0. 25 09 2 -0. 13 98 8

01 63 3 -0. 55 53 2 -0. 25 91 4 -0. 29 05 3

36 83 0.8 81 74 7 0.3 32 32 2 0.0 27 52 5

47 37 8 0.5 43 50 9 0.2 19 23 4 0.1 98 55 2

35 23 8 0.6 33 84 5 0.6 28 00 4 -0. 10 41 4

15 75 1 -0. 07 10 2 -0. 20 12 4 0.2 081 18

14 68 0.4 71 60 3 0.2 55 05 0.1 43 59 -0. 52 07 4 -0. 43 46 9 -0. 04 05 7

52 07 4 1

43 46 9 0.3 13 71 9

04 05 7 -0. 02 55 1 -0. 02 53 3

0.3 13 71 9 -0. 02 55 1

1

-0. 02 53 3

1

The appendix 3 Score x1 x2 x3 x4 x5 x6 x7 x8 x9 1.64075553 1.733136808 0.707326275 -0.15305095 0.020825868 1.272602313 -0.73634962 1.497287671 1.405691931

Five principal component scores for each country

1.776420097 -0.30886145 -0.14193963 -1.38887739 0.871794996 -0.83494769 1.995014053 0.272092928 0.027159081

-0.6336089 1.559939192 -1.34754947 0.365001281 -0.18974486 0.789448871 1.708113852 -1.28719793 1.440706759

0.137409833 0.472471469 -0.41185458 0.71247481 -0.53592552 0.062543047 0.27664047 -0.8090886 0.371461236

-0.21402725 -1.1228871 0.061790453 -0.34391627 -0.1733385 0.435209279 0.098428403 -0.31843054 0.956524432

[键入文字] Term# 39631 Page 1 of 19

x10 x11 x12 x13 x14 x15 x16 x17 x18 x19 x20

1.331189445 -1.87818041 -1.31180943 -0.52663222 -1.61654514 0.218198341 -0.06293823 0.203011979 -4.84407245 1.4481469 -0.34859461

-1.04788632 -0.20826665 -1.31038651 -1.01289714 -0.39698179 1.108137017 -1.02376292 2.44303035 0.690380576 -0.16591499 -1.34330661

-0.15642626 1.10481201 -2.1646037 -0.89843729 0.411536008 -0.81632607 0.351906385 -1.1431226 0.297496522 0.682040817 -0.07398462

-1.57791119 0.765329535 0.692197782 1.196456474 0.891548867 0.779405418 -0.4269397 0.480390595 -1.62891296 -1.10857118 -0.33912581

0.460954049 -0.33999038 -0.0996444 0.332910249 0.422576768 0.241839344 0.050078016 -0.00738244 -0.02920592 -0.00117569 -0.4103125


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