2016美模赛题B翻译_太空垃圾
2016美赛B题翻译
2016 MCMProblem BSpace Junk太空垃圾The amount of small debris in orbit around earth has been a growing concern. It is estimated that more than 500,000 pieces of space debris, also called orbital debris, are currently being tracked as potential hazards to space craft. The issue itself became more widely discussed in the news media when the Russian satellite Kosmos-2251 and the USA satellite Iridium-33 collided on 10 February, 2009. A number of methods to remove the debris have been proposed. These methods include small, space-based water jets and high energy lasers used to target specific pieces of debris and large satellites designed to sweep up the debris, among others. The debris ranges in size and mass from paint flakes to abandoned satellites. The debri s’ high velocity orbits make capture difficult.在地球轨道上的小碎片越来越受到世界的关注。
2016年数学建模美赛A题题面及翻译
2016 MCM Problem AA Hot BathA person fills a bathtub with hot water from a single faucet and settles into the bathtub to cleanse and relax.一个人用一个水龙头让浴缸装满了热水，（然后？）睡进去来清洗和放松。
//那就先放到一定的程度，泡进去，然后边加水这样。
Unfortunately, the bathtub is not a spa-style tub with a secondary heating system and circulating jets, but rather a simple water containment vessel.不幸的是，这个浴缸没有温泉热水模式，就是没有另外的加热系统和循环的喷嘴，而是个简单的水密闭容器。
After a while, the bath gets noticeably cooler, so the person adds a constant trickle of hot water from the faucet to reheat the bathing water.不一会儿，这个水池明显的变冷了，所以这个人打开水龙头，加入了持续的细细的水，来加热这个浴缸里面的水。
The bathtub is designed in such a way that when the tub reaches its capacity, excess water escapes through an overflow drain.这个浴缸设计成一种形式，当这个池子到达了它的容量，多余的水会通过一个溢出排水系统排出。
Develop a model of the temperature of the bathtub water in space and time to determine the best strategy the person in the bathtub can adopt to keep the temperature even throughout the bathtub and as close as possible to the initial temperature without wasting too much water.设计一个浴缸里面的水温度关于空间和时间上的模型，去决定最好的策略，让这个人在浴缸里能够在不浪费太多的水的前提下，去尽量的靠近初始的温度。
2016年美国大学生数学建模E题英文版论文
In this paper, a model is established to provide a measure of the ability of a region to provide clean water to meet the needs of its population, and find out the reason for the lack of water resources.Specific tasks are as follows:For Task 1: We establish a model. In the model,we think the supply of clean water depends on the amount of surface water, underground water and sewage purification. The water requirements are decided by the amount of life water, agricultural water and industrial water in the region. In water supply, surface water is affected by the annual average temperature, annual average precipitation and forest coverage rate. The groundwater is impacted by the annual average temperature, annual average precipitation. The agricultural water is affected by the population of the region and annual average precipitation. The GDP of the region influences the industrial water consumption. We use the principle of multivariate nonlinear regression to find out the regression coefficient. And then make sure its function. The ratio of water supply and water requirements is used as a measure of the ability of a region to provide clean water. We find that the ability of a region to provide clean water is good or not by comparing the ratio with 1.For Task 2: The model selects the Shandong Province of China as the testing region.We analyse the data of China's Shandong area between 2005 and 2014, and then crystallize the model through the thought of the function fitting and multivariate nonlinear regression. By the model,we think Shandong province's ability to provide clean water is weak.And then from two aspects which physical shortage and shortage of economic,this paper analyses the causes of water shortage in Shandong Province,and thus test the applicability of the model.For Task 3: We select several factors affecting water supply and water demand badly,which is annual precipitation, annual average temperature, the forest coverage rate and population forecast. We analyse the data of China's Shandong area between 2005 and 2014, according which to predict the changes of those factors in 15 years.After that this paper uses the model to analyse the situation of Shandong’s water in 15 years.For Task 4: According to the model in Task 1 and the analysis of the Task 2. We find the main factors influencing the ability to provide clean water in China's Shandong province. By these factors we make the intervention program.In view of the low average annual rainfall, increase the average annual rainfall by artificial rainfall.In view of the forest coverage rate, forest plantation and protect vegetation is came up with. For sewage purification capacity, putting forward to improve sewage treatment technology and improve the sewage conversion rate and increases daily sewage quantity. In view of the total population, we put forward the policy of family planning for water consumption per capita, putting forward to set the daily water consumption per person. And puttingforward the industrial wastewater must reach the indexes of the rules, developing seawater desalination technology to increase the supply of clean water.Water has always been the hot spot in the world.The future is also not exceptional. Only finding out the problem, we can suit the remedy to the case.The model measure the ability of a region to provide clean water by analysing the cases which influence the supply and remand of water. Based on this,make a good intervention program. Offering helps to solve global water issues.1 Introduction (4)1.1 Problem Statement (4)1.2Problem Analysis (4)1.2.1Task 1 Analysis (4)1.2.2Task 2 Analysis (4)1.2.3Task 3 Analysis (5)1.2.4Task 4 Analysis (5)1.2.5Task 4 and 5 Analysis (5)2 Assumptions and Notations (5)2.1 Assumptions (5)2.2 Notations (6)3 Model Establishment and Solution (7)3.1 The effect of single factor on the water supply in a certain area (7)3.1.1Effects of annual average temperature, annual average precipitation and forest coverageon surface water resources in a certain area (7)3.1.2 Effects of annual average temperature and annual precipitation on groundwaterresources in a certain area (7)3.1.3 Influence of total population and per capita water consumption on daily waterconsumption in a certain area (8)3.1.4 The influence of average annual rainfall and total population on agricultural waterconsumption in a certain area (8)3.1.5 Effect of average annual rainfall and population in an area of agricultural water use (9)3.2 Function Arrangement (9)3.2.1 Water supply function (9)3.2.2 Water demand function (9)3.2.3 The ability of a region to provide clean water (10)3.3 In order to test the accuracy and usability of the model, this model is selected as a test area inShandong Province, China. (10)3.3.1 Total surface water resources (10)3.3.2 Total groundwater resources (13)3.3.3 Total industrial water consumption function (15)3.3.4 Total agricultural water consumption function (16)3.3.5 Assessment of water supply capacity (18)3.4.2 Remediation Measures (19)3.5 Forecast for the next 15 years (19)3.5.1 Forecast of average annual rainfall (20)3.5.2 Prediction of annual temperature (21)3.5.3 Prediction of forest cover (21)3.5.4 Prediction of population (22)3.6 Intervention Program (23)3.6.1 Present ofthe Intervention Program (23)3.6.2 Implement ofthe Intervention Program (24)4 Advantages and Shortcoming of the model (25)4.1Advantages： (25)4.2 Shortcoming (25)5 Improvement of model (26)6 Reference (26)7 Appendices (27)7.1 Data used in task 2 (27)7.2 Matlab Source Code (29)1 Introduction1.1 Problem StatementOn the earth, the water that human beings can use the water directly or indirectly, is an important part of natural resources. At present, the total amount of the earth's water is about billion cubic meters, of which the ocean water is billion cubic meters, accounting for about 96.5% of the total global water. In the remaining water, the surface water accounts for 1.78%, 1.69% of the groundwater. The fresh water that human mainly use of is about billion cubic meters, accounting for only 2.53% in the global total water storage. Few of them is distributed in lakes, rivers, soil and underground water, and most of them are stored in the form of glaciers, permafrost and permafrost, The glacier water storage of about billion cubic meters, accounting for 69% of the world's total water, mostly stored in the Antarctic and Greenland, the available clean water in the dwindlingwith time going by.In order to assess the ability to provide clean water of an area, we set up an assessment model.1.2Problem Analysis1.2.1Task 1 AnalysisTask 1 requires establishing a model to measure the ability of a region to provide clean water. At the same time,we also need to provide a measure standard.This paper make the ratio of water supply and water requirements of a region as the measure standard, by which to measure the ability of a region to provide clean water.A region's main source of water is groundwater, surface water and sewage purification.The model assumes the volume of groundwater in a region is mainly affected by average annual temperature, annual precipitation;Thevolume of surface water is mainly affected by the average annual temperature, annual precipitation, the forest coverage rate.These factors decide water supply of an area.The waterdemand of an area mainly includes living water, agriculture water and industrial water. We assume living water is affected by the population and per capita consumption decision;Agricultural waterdepends an annual precipitation and population decision;Industrial water is mainly decided by a gross regional product.The above factors decide the water demand in a certain area.1.2.2Task 2 AnalysisAccording to the information provided in the map, in Asia, China's Shandong Province is the region meeting the requirements.Through the data collection of Shandong Province, we can find the annual temperature, annual precipitation, the forest coverage rate, groundwater, surface water, sewage treatment capacity, water,agricultural water, industrial water, population,per capita consumption and GDP data.And then according to the model of Task 1,we analyze the ratio by using multivariate nonlinear regression to make sure that Shandong province is a water-deficient area.After proving that Shandon province is short of water through the model, we analyze the reasons for lack of water from two aspects: physical shortage and economic shortage.1.2.3Task 3 AnalysisBecause we already have the relevant data, we can function to fit the relationship between the variables and the year.Thus it is possible to predict in Shandong Province’s data in the 15 years, then input the data into the model to achieve the purpose of prediction.In addition, it can be combined with the actual situation and the selected areas of the corresponding policy to analysis which factors will have a great change in the 15 years.We still can analyze from two aspects of society and the environment.Social aspects includes the promotion of water conservation, population growth;Environmental aspects includes policy changes to the environment, sewage purification capacity enhancement and so on.1.2.4Task 4 AnalysisFormulating plans for intervention mainly start from the perspective of the main model. According to the content of the model, we can still divide all of factors into two types: the social and environmental factors. The intervention programs can be developed based on two types of factors that affect the supply of water, reducing as much as possible the negative impact of the factors that control factors and intensifying the development of a positive impact. In addition, because Shandong Province is beside the sea, desalination and other measures can be developed to increase clean water supply sources.1.2.5Task 4 and 5 AnalysisTask 4 intervention programs indirectly impact the water supply and demand water through a direct impact on GDP model of forest cover, annual precipitation, annual temperature, water emissions, sewage treatment capacity, population growth and the region.2 Assumptions and Notations2.1 Assumptions●The water resources in a region are derived from the purification of surface water,groundwater and sewage, and the demand of water resources comes from domestic water, industrial water and agricultural water.●The surface water supply in a certain area is affected only by the average annual temperature,annual precipitation and forest coverage. The groundwater supply is affected by the annual average temperature and annual precipitation.●The region's water consumption of a certain region depends on the population and per capitawater consumption; Agricultural water consumption is affected by the average annual precipitation and the numberof people. Industrial water is mainly determined by a regional GDP.● A certain region will not suddenly increase or decrease the population largely.●There will not be a serious natural disasters in a region in the next period of time.2.2 Notations3 Model Establishment and SolutionThe model established here is a use of a region's water supply and water demand ratio to determine whether the water shortage in the region, the main variables involved.3.1 The effect of single factor on the water supply in a certain area3.1.1Effects of annual average temperature, annual average precipitation and forest coverage on surface water resources in a certain areaDue to the average annual temperature, annual precipitation, the forest coverage rate and surface water of linear or nonlinear relationship exists, so first in order to determine the average annual temperature, annual precipitation, the forest coverage rate and surface water, and then the nonlinear multiple regression analysis method to determine the functional relationship between the three factors and surface water.The surface water content is 1y , Average annual precipitation, annual average temperature and forest coverage rate are 1x ,2x ,3x , Using nonlinear regression statistical methods, the use ofMATLAB fitting toolbox were identified1x ,2x ,3x of the highest regression power(MATLAB fitting toolbox of the highest fitting function is the 9 power, greater than the 9 power function is too complex, not much research value), According to the decision coefficient R 2 of the regression equation, the corresponding probability value of the statistic P , the regression coefficients β,0β,1n β,2n β, get the regression equation:35612412312345699999910123123111 (1)n n n n n n n n n n n n n n n y x x x x x x βββββ====++++∑∑∑∑∑∑3.1.2 Effects of annual average temperature and annual precipitation on groundwater resources in a certain areaThere is a linear or nonlinear relationship between the average annual temperature, average annual rainfall and the supply of groundwater, according to the idea of 5.1.1, the relationship between the average annual amount of groundwater supply, the average annual precipitation and the supply of groundwater is calculated. And the regression coefficient is determined, and the function relationship between the average annual temperature, average annual precipitation and the supply of groundwater isbased on the regression coefficient:Design of underground water for2y , with an average annual precipitation, annual average air temperature respectively 1x ,2x , using nonlinear regression statistical methods, according to the regression equation with coefficient of determination R2, F statistic corresponds to the probability value p, to determine the regression coefficientsβ,0β,1n β,2n β, got the regression equation: 312412123499992012121111n n n n n n n n n n y x x x x ββββ=====+++∑∑∑∑（2）3.1.3 Influence of total population and per capita water consumption on daily water consumption in a certain areaThe total population of a region and the amount of water consumption per capita and the daily use of the product of the relationship between the amount of water = total amount*Water usage per person consumption.Set daily water consumption is 5y , the total population, per capita water consumption were 5x , Q , 5y ,Q ,5x , the function of the relationship between the:55y Qx =（3）3.1.4 The influence of average annual rainfall and total population on agricultural water consumption in a certain areaDue to the annual precipitation and the total population and the area of agriculture of area of a water there is a linear or nonlinear relationship, according to the thought of multivariate nonlinear regression can be calculated average annual precipitation and the total population and the area of agriculture with the function relationship between water and to determine the regression coefficient and regression coefficient write GDP and industrial functional relationship between Gross domestic product GDP and industrial water consumption.Let industrial water consumption of 3y , gross production set 4x , using statistical nonlinearregression, regression equation based on the coefficient of determination 2R , F statistical probabilityvalue p corresponding to the amount determined regression coefficients0β,1n β, the regressionequation:11193011n n n y x ββ==+∑（4）3.1.5 Effect of average annual rainfall and population in an area of agricultural water useAgricultural water consumption of 4y , design with an average annual rainfall of 1x , 5x ,using statistical nonlinear regression, regression equation based on the coefficient of determination 2R ,F statistical probability value p corresponding to the amount determined regression coefficients 0β,1n β, the regression equation:3124121234999940151511n n n n n n n n n n y x x x x ββββ===+++∑∑∑∑（5） 3.2 Function Arrangement3.2.1 Water supply functionThe model takes into account a region's water supply from three aspects: surface water resources, groundwater resources and the amount of sewage treatment. The function relation between surface water resources, groundwater resources, sewage treatment and water supply is the function, that is, the amount of water supply = surface water resources + groundwater resources.The amount of water supply is X , and the sewage treatment capacity is *Q , by(2) (1):*12X y y Q =++（6）3.2.2 Water demand functionThe model takes into account the need for a region from three aspects: daily water consumption, industrial water consumption and agricultural water consumption. Daily water consumption, industrial water and agricultural water consumption and water demand is a function of the relationship between the function and the function, that is: water demand = daily water consumption + industrial water + agricultural water consumption.A demand for Y , by (3) (4) (5) to:345Y y y y =++（7）3.2.3 The ability of a region to provide clean waterA region to provide clean water and the area of water supply and water demand about, if water supply is greater than demand, the region provide clean water ability strong; on the contrary, the region provide clean water ability is weak. This model provides that a region to provide clean water capacity by the area of water supply and water demand ratioλ determined by (6) (7) available: (1)1λ>: the region's ability to provide clean water; (2)1λ=: the area provides a warning of the ability to provide clean water; (3) 1λ<: the ability of the region to provide clean water is weak;3.3 In order to test the accuracy and usability of the model, this model is selected as a test area in Shandong Province, China.Provide the capacity of water resources in China's Shandong Province, we collected in 2005 to 2014 this decade, Shandong Province, the total water supply, surface water resources amount, quantity of groundwater resources, sewage treatment capacity, agricultural water consumption, industrial water, living water, sewage emissions, forest coverage, total population, per capita water use, annual precipitation, GDP (see Appendix for the specific data).3.3.1 Total surface water resourcesSurface water resources amount 1y , groundwater resources quantity is 2y , industrial water use 3y , agricultural water use for 4y , with an average annual precipitation 1x , with an average annual temperature 2x , the forest coverage rate 3x , GDP for 4x , with a total population of 5x .The factors1y that is affected by 1x , 2x , 3x , in order to determine the relationship between the 1y , and 1x , 2x , 3x ,first use the data in the appendix table to make 1y with 1x , 2x , 3x scatter plots, such as the figure:Figure 1 Surface water resources and average annual rainfallFigure 2 Surface water resources and annual temperatureFigure 3 Surface water resources and forest coverFigure 1 is obtained by MATLAB fitting curve, the fitting found that1x and 1y is the 6 powerfunction model (εfor random error). （9）Figure 2 is obtained by MATLAB fitting curve, the fitting found that2x and 1y is the 8 power function model（10）Figure 3 is obtained by MATLAB fitting curve, the fitting found that3x and 1y is the 8 power function model（11）Combined with the above analysis, the model (9) (10) (11) established the following regression model（12）Directly using the MATLAB statistics toolbox in the command regress solution, the format is[b,bint,r,rint,stats]=regress(x,y,alpha)61011n n n y x ββε==++∑81021n n n y x ββε==++∑31031n n n y x ββε==++∑33121212312456683999103331231131111n n n n n n n n n n n n n n n y x x x x x x βββββε=======+++++∑∑∑∑∑∑Output value of b for the estimation of the regression coefficientβ, bint is the confidenceintervals for b and r is the residual vector, rint is the confidence interval of r , stats is regression model test statistics, in the first number is a regression equation with coefficient of determination 2R ;The regression coefficients of the model (12) are estimated and their confidence intervals(confidence level α=0.05), test statistic 2R , F , ρ, and the results are shown in table.Table 1 Surface water regression coefficientCan get the regression coefficient from the figure, the estimated value of the regression coefficient into the model (12) forecast equation（13）3.3.2 Total groundwater resourcesFactors that affect the2y include 1x ,2x , in order to determine the relationship between 2y and 1x ,2x , first use the data in the appendix table to make the A3 and A4 and A5 of the scatterdiagram, as shown in figure:^9665444111138273322223724 1.7610 1.0610 1.8910 1.18103.8410 2.610 3.2910 1.0110y x x x x x x x x x --------=+⨯-⨯+⨯+⨯-⨯+⨯-⨯+⨯Figure 4 the amount of groundwater resources Figure 5 the amount of groundwater resources and annual average temperatureand the average annual rainfallFigure 4 is obtained by MATLAB fitting curve, the fitting found that1x and 2y is the 6 powerfunction model (ε for random error), （14）Figure 5 is obtained by MATLAB fitting curve, the fitting found that2x and 2y is the 8 power function model.（15）Combined with the above analysis, the model (9) (10) (11) established the following regression model.（16） Directly using the MATLAB statistics toolbox in the command regress solution, the format is[b,bint,r,rint,stats]=regress(x,y,alpha)Output value of b for the estimation of the regression coefficientβ, bint is the confidence intervals for b ,and 2R is the residual vector, rint is the confidence interval of r , stats is regressionmodel test statistics, in the first number is a regression equation with coefficient of determination 2R ;The regression coefficients of the model (12) are estimated and their confidence intervals(confidence level α=0.05), test statistic 2R , F , ρ, and the results are shown in table.62011n n n y x ββε==++∑82021n n n y x ββε==++∑121212123468992013121111n n n n n n n n n n y x x x x ββββε=====++++∑∑∑∑Table 2 Regression coefficients of groundwater resourcesCan get the regression coefficient from the figure, the estimated value of the regression coefficient into the model (16) forecast equation（17）Its image is shown in Figure 6Figure 6 groundwater resources3.3.3 Total industrial water consumption functionFactors that affect 3y is 4x , in order to determine the relationship between 3y and 4x , thefirst use of the data in the appendix table to make the X and the scatter diagram, as shown in figure:^9665445111123821000 1.8210 1.3410 3.37108.49101.3610y x x x x x -----=+⨯-⨯+⨯+⨯-⨯Figure 7 industrial water consumption and GDPFigure 8 industrial water useFigure 7 is obtained by MATLAB fitting curve, the fitting found that4x and 3y is a function model(εfor random errors), （18）The regression coefficient can be got from the following chartTable 3 Regression coefficient of industrial water consumptionAccording to the above analysis, combined with the model to establish the following regression model, regression coefficient estimation values are substituted into the model (18) to forecast equation.（19）Image as figure 8 3.3.4 Total agricultural water consumption functionFactors that affect the 4y are 1x , 5x , in order to determine the relationship between 4y and 1x , 5x , first using the data in the appendix table to make the 4y and 1x , 5x scatter diagram, asshown in figure:3014y x ββε=++^443105.2888410y x -=+⨯Figure 9 total agricultural water consumption Figure 10 the amount of agricultural water and the average annual rainfalland populationFigure 9 is obtained by MATLAB fitting curve, the fitting found that4x and 4y is a function model(εfor random errors), （20）Figure 10 is obtained by MATLAB fitting curve, the fitting found that5x and 4y is a function model (εfor random errors),（21）Combined with the above analysis, the model (20) (21) established the following regression model.（22）Directly using the MATLAB statistics toolbox in the command regress solution, the format is[b,bint,r,rint,stats]=regress(x,y,alpha)Output value of b for the estimation of the regression coefficientβ, bint is the confidence intervals for b ,and 2R is the residual vector, rint is the confidence interval of r , stats is regressionmodel test statistics, in the first number is a regression equation with coefficient of determination 2R ;The regression coefficients of the model (12) are estimated and their confidence intervals(confidence level α=0.05), test statistic 2R , F , ρ, and the results are shown in table.3014y x ββε=++74051n n n y x ββε==++∑121212123468994013121111n n n n n n n n n n y x x x x ββββε=====++++∑∑∑∑Table 4 regression coefficients of agricultural water useAccording to the above analysis, combined with the model to establish the following regression model, regression coefficient estimation values are substituted into the model (22) to forecast equation.（22）Its image is shown in Figure 11Figure 11 function of agricultural water3.3.5 Assessment of water supply capacityAccording to the data model obtained in 3.2.3, Shandong Province in China, the relevant data and the above function is brought into the model and calculated results:By the conclusion of the model, 1λ< shows that the ability to provide clean water in Shandong province is weak.3.4 Cause Analysis and Treatment Measures Water Shortage.3.4.1 the causes of water shortage in Shandong.^737424155514 1.010 2.110510910 2.56810y x x x x ----=⨯-⨯+⨯-⨯+⨯216.030.741289.69X Y λ===<（1）Water and soil erosion in hilly areas is serious, and water cannot be brought together into a river （2）Shandong is a temperate monsoon climate. Instability is one of the characters of the monsoon climate. Shandong is located in a part a Plain, and it is short of water. It is a big agricultural province. The water used in industry and agriculture is a lot.（3）Water shortage is the basic situation in the province of Shandong, the contradiction between water supply and demand have become increasingly prominent.（4）Total water resources shortage, average, low mu water resources, less water and more and more people, water resources and population, cultivated land resources serious imbalance, which is the main reason caused by a very prominent contradiction between water supply and demand in Shandong. （5）Have a great relationship with the natural geographical location. Shandong is located at the junction of the north and the south, which is a warm temperate monsoon climate. From the rainfall, the first is the uneven distribution of rainfall during the year.（6）As to rainfall distribution, in the southeast of Shandong Province annual rainfall average is up to 8.5 mm, and northwest region's annual average rainfall is only 550 millimeters, basically showing decreases from the southeast Shandong Province to the northwest of successive trend.（7）East Province is a coastal province, but the sea is not the water for drinking. A lot of rain in the coastal areas is typhoon. The available water in these areas is actually very little.（8）Groundwater levels continue to decline due to over exploitation of underground water in many places. The eastern provinces have formed a number of super mining areas. A series of environmental geological problems, such as groundwater pollution, are formed by the formation of the super mining area.（9）Water must not lack of water in the Yellow River in Shandong province. However, the amount of water in the Yellow River is declining year by year, and the available amount is decreasing.（10）Water conservancy project aging, degradation, water supply reduction3.4.2 Remediation Measures（1）With more rain and floods, water conservation, improvement of water cycle, reserve of groundwater resources, to achieve the use of abundant dry.（2）In strict accordance with the requirements of the state on the implementation of the most stringent water management system, around the allocation of water resources, conservation and protection, clear water resources development and utilization of red line, strict implementation of the total amount of water control. Clear red line water functional areas to limit the, strictly controlling the total discharge of the river; Clear water efficiency control of the red line, and resolutely curb the waste of water.（3）To strengthen the unified management of water resources（4）To carry out planned water and water saving.（5）Increasing the provision of new water sources, while strengthening the protection of water sources 3.5 Forecast for the next 15 yearsAccording to the investigation of the actual situation, it is assumed that the water resources in Shandong province will not be exhausted in a short time, and there will not be a large demand for water in short time.The first to do is to predict the data. According to the model of task 1, on water supply capacity。
2016美赛题目A、B翻译
A热水浴一个人从一个水龙头里放热水灌满浴缸，然后安顿在浴缸中，清洗和放松。
不幸的是，浴缸不是一个具有二次加热系统和循环射流的水疗式浴缸，而是一个简单的水容器。
过了一会儿，洗澡水就明显地变凉，所以这人让水龙头一直滴热水以重新加热洗澡水。
该浴缸的设计方式是，当浴缸达到容量，多余的水将通过排水管溢出。
在空间和时间上开发一个浴缸的水的温度模型，以确定最佳的策略使浴缸的人采纳，即使整个浴缸保持同样温度并且尽可能接近的初始温度，而没有浪费太多的水。
使用你的模型来确定你的策略在多大程度上取决于浴缸的形状和体积，浴缸的形状/体积/温度，浴缸中的人的运动。
如果这个人最初填充浴缸时使用了泡泡浴剂以协助清洗，这将如何影响你的模型的结果？除了要求的一页MCM提交摘要，你的报告必须包括给所有浴缸使用者的一页的非技术性说明以描述你的策略并解释为什么难以使洗澡水温度保持均匀。
B 太空垃圾在地球轨道上的小碎片数量已成为日益严重的关注焦点。
据估计，超过5000块的空间碎片，也被称为轨道碎片，目前被锁定为对空间飞行器构成潜在危险的目标。
在2009年二月十号俄罗斯卫星kosmos-2251和美国卫星iridium-33相撞后，在新闻媒体上这个问题受到了更广泛的讨论。
已经有人提出消除碎片的一些方法。
这些方法包括用小型空间运载的喷水装置和高能激光瞄准碎片的特定位置，还有设计大卫星来清扫这些小碎片。
太空垃圾的范围包括从涂料碎片到废弃卫星，尺寸和质量也有很大变化范围。
碎片的高速度轨道使得捕捉变得困难。
开发一个随时间变化的模型，以确定一个私营企业可以采纳的最佳方案选择或组合方案，该企业将把解决空间碎片问题作为商业机会。
你的模型应该包括对成本，风险，收益，以及其他重要因素定量或定性的估计。
你的模型应该能够评估单独的解决方案，以及解决方案的组合，并能够探讨各种重要的可能情景。
使用你的模型，确定商机是否存在。
如果存在一个可行的商业机会作为可选的解决方案，请提供其与其他备选解决方案的比较，并且给出移除碎片的具体建议。
2016年美国大学生数学建模竞赛题目
2016年美国大学生数学建模竞赛题目第５卷第２期２０１６年６月、・．．．．・‘．¨．．．‘－．．．．．’．．．Ⅲ’¨．．．．‘．．．．．．‘．．．¨．！数学建模及其应用ＭａｔｈｅｍａｔｉｃａＩＭＯｄｅ¨ｎｇａｎｄｌｔｓＡｐｐＩｉＣａｔｉＯｎｓＶＯＩ．５Ｎｏ．２Ｊｕｎ．２０１６｛竞赛论坛｝＾¨Ｉ・。
・－．．哪・．．．岫・．．．嘶・．．－‘・‘・．．．Ⅵ・‘‘“・・Ｉ２０１６年美国大学生数学建模竞赛题目韩中庚译（解放军信息工程大学四院，河南郑州４５０００１）问题Ａ：热水澡人们经常会通过用一个水龙头将浴缸注满热水，然后坐在浴缸里清洗和放松。
这个浴缸不是带有二次加热系统和循环喷流的温泉式浴缸，而是一个简单的水容器。
过一会儿，洗澡水就会明显变凉，所以洗澡的人需要不停地从水龙头注入热水，以加热洗浴的水。
该浴缸的设计是这样一种方式，即当浴缸里的水达到容量极限时，多余的水就会通过溢水口流出。
考虑空间和时间等因素，建立一个浴缸的水温控制模型，以确定最佳策略，使浴缸里的人可以利用这个策略让整个浴缸中的水保持或尽可能接近初始的温度，而且不浪费太多的水。
利用你们的模型来确定这个策略对浴缸的形状和体积，以及对浴缸中人的形状、体积、温度和活动等因素的依赖程度。
如果这个人一开始用了一种泡泡浴剂加入浴缸中以助清洗，这会对你们的模型结果有怎样的影响？除了要求提交１页的ＭＣＭ摘要之外，你们的报告必须包括１页为浴缸用户准备的非技术性的说明书，来阐述你们的策略，同时解释为什么保持洗澡水的恒温如此之难。
问题Ｂ：太空垃圾地球轨道上的小碎片数量已引起人们越来越多的关注。
据估计，目前有超过５０００００块的空间碎片，也被称为轨道碎片，由于被认为对空间飞行器是潜在的威胁而正在被跟踪。
２００９年２月１０日，俄罗斯卫星Ｋｏｓｍｏｓ一２２５１和美国卫星Ｉｒｉｄｉｕｍ一３３相撞之后，该问题受到了新闻媒体更广泛的讨论。
太空垃圾吸成器英语作文
太空垃圾吸成器英语作文Space Junk Incinerator: A Solution to the OrbitalDebris Menace.The rapid advancement of space exploration andsatellite technology has brought with it a significant problem: space junk. Space junk, also known as orbital debris, consists of discarded spacecraft, rocket bodies,and other man-made objects that remain in orbit around Earth. This debris poses a serious threat to activesatellites and spacecraft, as even small pieces of debris can cause catastrophic damage upon impact.The amount of space junk has been steadily increasing over the years, with an estimated 128 million pieces of debris larger than 1 centimeter currently orbiting our planet. The vast majority of this debris is concentrated in low Earth orbit (LEO), the region of space closest to Earth, where most satellites operate.The consequences of a collision between a satellite and a piece of space junk can be devastating. In 2009, a defunct Russian satellite collided with an active Iridium communications satellite, resulting in the destruction of both satellites and the creation of thousands of additional pieces of debris. Such collisions pose a significant risk to the safety and reliability of space-based systems, including those that are vital for communications, navigation, and weather forecasting.Recognizing the urgent need to address the space junk problem, scientists and engineers have proposed a range of innovative solutions, including the development of space junk incinerators. These devices are designed to capture and destroy space junk, reducing the amount of debris in orbit and mitigating the risk of collisions.One concept for a space junk incinerator involves using a large, parabolic dish to focus sunlight onto the debris. The intense heat generated by the concentrated sunlight would rapidly vaporize the debris, removing it from orbit. Another approach involves using a laser to vaporize thedebris. The laser would be mounted on a satellite or spacecraft and would be used to target and destroy individual pieces of debris.A third concept for a space junk incinerator is to use a plasma torch to incinerate the debris. The plasma torch would generate a high-temperature plasma that would melt and vaporize the debris. This method would be particularly effective for incinerating large pieces of debris, such as defunct satellites or rocket bodies.The development of space junk incinerators is a challenging but necessary endeavor. These devices have the potential to significantly reduce the amount of debris in orbit and mitigate the risk of collisions. However, there are a number of technical challenges that need to be overcome before space junk incinerators can become a reality.One challenge is the need to develop a reliable and efficient way to capture space junk. The debris is spread over a large area of space and is often moving at highspeeds. Capturing the debris without damaging it or creating additional debris is a complex task.Another challenge is the need to develop a power source that is capable of generating the intense heat required to incinerate the debris. Solar power is a potential option, but it would require a large and expensive parabolic dish. Laser systems require a significant amount of electrical power, which would need to be provided by batteries or solar panels. Plasma torches require a steady supply of fuel, which could be hydrogen or methane.Despite these challenges, the development of space junk incinerators is a promising area of research. These devices have the potential to make space exploration and satellite operations safer and more reliable. As the amount of space junk continues to grow, it is essential that we develop innovative solutions to address this problem. Space junk incinerators are one of the most promising solutions, and they could play a vital role in ensuring the future of space exploration.In addition to the technical challenges, there are also legal and regulatory issues that need to be considered. The development and deployment of space junk incinerators would require international cooperation and coordination. It would also be necessary to develop clear rules and regulations governing the use of these devices.Despite the challenges, the development of space junk incinerators is a necessary step towards ensuring the safe and sustainable use of space. These devices have the potential to significantly reduce the amount of debris in orbit and mitigate the risk of collisions. As the amount of space junk continues to grow, it is essential that we pursue all available solutions to address this problem.。
2016美国数模竞赛题目中文翻译
A: 一个人充满热水的浴缸从一个单一的水龙头，并落户到浴缸里清洁和放松。
不幸的是，浴缸不是温泉式浴盆与辅助加热系统和循环飞机，而是一个简单的水安全壳。
一段时间后，在浴变得明显冷却器，所以该人增加的热水恒定涓流从龙头再加热洗澡水。
所述浴缸的设计以这样的方式，当所述桶达到其容量，过量的水逸出通过溢流漏极。
开发浴缸水的空间和时间，以确定该人在浴缸可以采用，以保持温度甚至整个浴缸和尽可能接近到初始温度，而不会浪费过多的水的最佳策略的温度的模型。
使用模型确定哪个你的策略取决于形状和桶，该人在浴缸的形状/体积/温度的体积，并且由该人在浴缸所作的运动的程度。
如果对方使用了泡泡浴的添加剂，而最初填补了浴缸，以协助清洁，怎么会变成这样影响模型的结果吗？除了必需的单页摘要您的MCM提交，你的报告必须包括一份一页纸的非技术性解释浴缸的用户描述你的策略，同时解释了为什么它是如此难以得到整个均匀保持温度浴缸里的水。
B: 小碎片在轨道上绕地球金额已日益受到关注。
据估计，超过50万件的空间碎片，也被称为轨道碎片，目前都被跟踪的潜在危害航天器。
这个问题本身变得更广泛的讨论，在新闻媒体时，俄罗斯卫星的Kosmos-2251和美国铱卫星-33相撞2009年2月10日。
有许多方法以除去碎片已被提出。
这些方法包括小的，基于空间的水射流和用于针对特定的碎片高能激光器和设计，以清扫杂物，其中包括大型卫星。
从漆片的废弃卫星的大小和质量的碎片范围。
碎片“高速轨道进行采集困难。
开发时间依赖模型来确定的替代品，私人公司可以采取作为一个商业机会，以解决空间碎片问题的最佳替代品或组合。
您的模型应该包括成本，风险，效益的定量和/或定性的估计，以及其他重要的因素。
您的模型应该能够评估独立的替代品的替代品，以及组合和能够探索各种重要的“如果？”的情景。
使用模型，确定了经济上有吸引力的机会是否存在，或没有这样的机会是可能的。
如果一个可行的商业机会的存在作为一种替代解决方案，提供了不同的选择去除杂物进行比较，并包括具体建议，以碎片应该如何去除。
太空垃圾吸成器作文
太空垃圾吸成器作文英文回答：Space debris, also known as space junk, is becoming a major concern for space agencies and scientists around the world. As the number of satellites and other objectsorbiting the Earth continues to increase, so does the amount of space debris. This poses a significant risk to both operational satellites and future space missions.To tackle this problem, scientists have been developing a space debris collector, also known as a space junk sweeper or space garbage collector. This device is designed to capture and remove space debris from orbit, thusreducing the risk of collisions and the creation of more debris.The space debris collector works by using various techniques to capture and collect space junk. One method involves using a net or a harpoon to capture larger objects,such as defunct satellites or spent rocket stages. Another method involves using a robotic arm or a grappling hook to capture smaller objects, such as screws or bolts. Once captured, the space debris is then brought back to Earth or directed towards a controlled re-entry, where it will burn up in the Earth's atmosphere.The development of a space debris collector is crucial for the sustainability of space activities. Without effective measures to remove space debris, the risk of collisions will continue to rise, making space exploration and satellite operations increasingly dangerous. By removing space junk from orbit, we can ensure the safety and longevity of our space assets.中文回答：太空垃圾，也被称为太空碎片，正成为全球航天机构和科学家们关注的重要问题。
【外刊精读】76. 太空垃圾
【外刊精读】76. 太空垃圾导读：报告显示太空垃圾数量在不断增加。
在过去的几十年里，卫星和火箭被发射到太空中，随之在太空中产生垃圾。
本文介绍人们如何清理太空垃圾。
一、语篇泛读Many of us ponder what lies in outer space. When we look up at the night sky, we see stars, the twinkle of a moving satellite and occasionally a distant planet. But one thing we don’t see is the millions of pieces of junk filling up space. It’s this debris that’s causing problems for the existing technology that’s up there and which we rely on.The amount of space junk is increasing. Over the last few decades, satellites and rockets have been launched into space, littering the cosmos as they go. It’s estimated there are now millions of discarded pieces of metal and other materials in orbit–everything from old rocket segments to accidentally dropped astronaut tools, and even flecks of paint. The fear is that if we don’t start taking this litter out of the sky soon, it will become a significant threat to active satellites. Nobu Okada, Chief Executive of Astroscale –a company working on ways to clean up space junk –says hitting “even a small paint fleck…has enough power to blow up other satellites.”Several ideas are being looked at to capturethe debris floating around in space. In 2018, the RemoveDebris spacecraft carried out various experiments, including testing a net that could snare a satellite and firing a harpoon at a target in orbit to try to catch it.This year the UK Space Agency is helping to fund new approaches to tracking satellites and debris in space. Jacob Geer from UKSA told the BBC: “Space surveillance and tracking is one of the key things we can do to keep safe those satellites we rely on now, and to make sure certain orbits don’t become inaccessible for future generations because there’s too much debris in them.”It’s clear that a solution is needed so a celestial deep clean can take place. But looking to the future, like any litter problem, we need to look at ways of creating less –and that shouldn’t be the stuff of science fiction.二、词汇表outer space 外层空间，太空twinkle 闪烁，闪耀satellite 人造卫星junk 废弃的旧东西，垃圾debris 碎片，残片rocket 火箭launch 发射litter 丢弃垃圾the cosmos 宇宙orbit （天体围绕行星或恒星运行的）轨道segment （事物的）部分，段astronaut 宇航员float 漂浮spacecraft 宇宙飞船snare 用罗网捕捉space surveillance and tracking 宇宙空间监视跟踪系统celestial 天空的，天外的deep clean 深层清洁science fiction 科幻小说，科幻电影三、测试与练习1. 阅读课文并回答问题。
关于宇航员太空垃圾的作文
关于宇航员太空垃圾的作文英文回答：Space debris, also known as space junk, is a growing concern for astronauts and space agencies around the world. As an astronaut myself, I have witnessed firsthand the impact that space debris can have on our missions and the potential dangers it poses to both human life and space exploration.One of the biggest challenges with space debris is its sheer quantity. There are currently thousands of pieces of debris orbiting the Earth, ranging in size from small screws to defunct satellites. These objects travel at incredibly high speeds, posing a significant risk to spacecraft and the astronauts on board. Just a small piece of debris can cause significant damage to a spacecraft, potentially leading to catastrophic consequences.To illustrate this point, let me share a personalexperience. During one of my missions, we encountered a piece of debris that was about the size of a tennis ball. It was traveling at such a high velocity that it could have easily penetrated the hull of our spacecraft. Luckily, our onboard systems detected the debris in time, and we were able to maneuver out of its path. This incident served as a stark reminder of the constant threat that space debris poses to our safety.In addition to the immediate risks, space debris also has long-term implications for space exploration. As more debris accumulates in Earth's orbit, it becomesincreasingly difficult to launch new missions and satellites. The risk of collisions is so high that space agencies often have to adjust their launch schedules and trajectories to avoid potential debris fields. This not only adds to the complexity and cost of space missions but also limits our ability to explore and utilize space for scientific and commercial purposes.中文回答：太空垃圾，也被称为宇宙垃圾，是全球宇航员和航天机构关注的一个日益严重的问题。
What_Is_Space_Junk
There ’s space junk orbiting 2Earth,and it ’s getting more and more every year.Space junk is the name that scientists give to the thousands of pieces of broken satellites 3and spacecraft 4.It takes up the Earth ’s orbit.Space junk can be as small as a piece of paint or as large as a broken rocket 5.No matter the size,it is a great danger to the astronauts 6and spacecraft that work in Earth ’s orbit.太空垃圾在围绕地球飞行，而且每年都在增加。
太空垃圾是科学家们给成千上万颗破碎的卫星和航天器取的名字。
它占据了地球的轨道。
太空垃圾可以小到一块油漆，也可以大到一枚破碎的火箭。
无论大小，它对在地球轨道上工作的宇航员和航天器来说都是巨大的危险。
The space junk in orbit becomes more hand -in -hand with the growth of the space industry 7on Earth.A group of international researchers wrote an articleand showed people the growing problem of space junk.They called for a treaty 8to “help protect Earth ’s orbit ”before it becomes completely polluted 9with junk.轨道上的太空垃圾与地球上航天工业的发展越来越紧密。
关于宇航员太空垃圾的作文
关于宇航员太空垃圾的作文英文回答：Space junk, also known as orbital debris, is a growing concern for astronauts in space. With the increasing number of satellites, spacecraft, and other objects in orbitaround the Earth, the risk of collisions with space junk is also on the rise. This poses a serious threat to the safety of astronauts and the integrity of their spacecraft.One of the main contributors to space junk is the remnants of old satellites and rocket stages that have been left in orbit. These pieces of debris can range in sizefrom tiny paint flecks to large chunks of metal, and theyall pose a potential hazard to astronauts and their equipment. In fact, even a small piece of debris travelingat high speeds can cause significant damage to a spacecraft.To address this issue, space agencies and organizations are working on ways to track and monitor space junk, aswell as develop technologies to remove it from orbit. Some proposed solutions include using robotic arms to capture and de-orbit debris, or using lasers to nudge objects out of harm's way.中文回答：太空垃圾，也被称为轨道碎片，是太空中宇航员日益关注的问题。
2016美赛E题参考答案
Team Con trol NumberFor office use only T1For office use only 52766F1T2 F2T3 Problem Chose n F3T4 F42016MCM/ICMSummary SheetIn order to predict the water scarcity and optimize the con figurati on reas on ably, we analyze the situation of water scarcity by establishing a mathematical model, and propose the feasible suggesti ons on optimizati on. All the work is based on thesufficie nt data we collect.Firstly, the local situation of water scarcity is estimated by introducing the water lack ing rate in dex. Sec on dly, the local water con sumpti on is predicted from personal liv in g, in dustry, agriculture and ecology. Mean while, the local water con sumpti on is predicted through establish ing a compo und model which based on an improved Logistic Model and the statistical regression analysis. Thirdly, the Gray PredictionMetabolism Model is used for predicting the amount of local water supply. At last, wecomprehe nsively an alyze the experime ntal results, and predict the ability of watersupply in this local area.To verify the availability of the model, we choose the North China as the object of study. We conclude that this area is seriously scarce before 2010 on the basis ofmass data. The water scarcity will steadily remit and reach balance in 2025. This isdue to China has finished the South-to-North Water Diversion and the North Chinagains large water resources from outside. The results call in side with the truth, so the model is reliable.The n we try to optimize the water suppl ying and dema nding structure in the North China, so that it can realize the internal self-sufficiency. We use analytichierarchy process (AHP) to assess the four schemes of water storage, water tran sfer, wastewater treatment and desalination from four aspects of timeliness, sustainability,econo mic, en vir onmen tal ben efits, so a more scie ntific water suppl ying system isdeveloped. Fin ally, by means of adjust ing the in dustrial structure, optimiz ing themode of agricultural irrigatio n and improvi ng the water con servatio n aware ness ofcitizens, we propose a water resources allocation model to optimize the water supplysystem in the North China. In this way, the water scarcity in the North China can besolved five years ahead of the orig inal schedule.Key wordsWater scarcity; water lack ing rate in dex; improved Logistic Model;Metabolism Model ; statistical regression; analytic hierarchy process (AHP)Gray Predicti onContents1 I NTRODUCTION & B ACKGROUNDS (1)2 P ROBLEM A NALYSIS (1)2.1 Problem Restateme nt (1)2.2 Problem solving (2)3 A SSUMPTIONS (2)4 N OTATIONS (3)5 B ASIC MODEL (3)5.1 Model of the water con sumpti on (3)5.1.1 Compound population Model based on Logistic Model (4)5.1.2 Model of Industrial water consumption (5)5.1.3 Model of total water consumption of a region (6)5.2 Model of the Gray Metabolism Model GM (1, 1) (6)5.2.1 Principle of common Gray GM (1, 1) Model (6)5.2.2 Principle of Gray Metabolism Model GM (1, 1) [2] (8)5.2.3 Accuracy testing (8)5.3 Model of water supply capacity of a regi on (9)5.4 Stre ngths & Weakness (10)6 C HOOSE A REGION TO ANALYZE (10)6.1 Brief in troducti on (10)6.2 Physical scarcity: (11)6.3 Economical scarcity: (12)7 P REDICTION MODEL FOR THE N ORTH C HINA (12)7.1 Model of water con sumpti on in North China (12)7.2 Water supply model in the North China (17)7.3 The comprehensive evaluation to the future water resources in the North China (19)7.4 Stre ngths and Weak nesses (21)8 O PTIMIZATION OF WATER RESOURCES A LLOCATION (21)8.1 Optimization of water supply allocation (21)8.1.1 Construct the model of hierarchical structure (21)8.1.2 Construction of comparison matrix of target-criterion layer (22)8.1.3 Construction of comparison matrix criterion - target layer (23)8.1.4 Total sorts of hierarchy and consistency check (27)8.1.5 Interpretation of result (28)8.2 Optimizati on of water con sumpti on allocati on (29)8.2.1 Construction of water resources allocation model (30)8.2.2 Main constraint equations (30)8.2.3 Model Solution (32)C ONCLUSIONS (34)F URTHER DISCUSSIONS (35)R EFERENCE (35)A PPENDIX (36)Strategy of Conquering Thirst1 Introduction & BackgroundsAn effective plan of solving the water scarcity problem is crucial to human society. According to the United Nations, today more than one billion people lackaccessto safe, clea n drinking water, and just 10 coun tries share 60 perce nt of theworld ' s natural, renewable water resources; what re, water use ihas been growing at twice the rate of population over the last century. A model of water scarcity of the world shows the serious situation. (See Figure 1)Figure 1: the map of the world ' s water scarcityAt the same time, our societal and economic growth is largely driven by the productive use of water. Actually, the world tripled its water use in the last 50 yearsalone. Our world population is increasing, yet we still share one water resource-and it ' s limited. If we ' re going toagieeil t heal, industrial and residential needs of this grow ing world, we must use our water in effective, efficie nt ways.2 Problem Analysis2.1 Problem RestatementDevelop a model that provides a measure of the ability that a region cab provide clean water to meet the needs of its population. Doing all this work with considering the dyn amic n ature of the factors that affect both supply and dema nd.Pick one country or region where water is either heavily or moderately overloaded. Expla in why and how water is scarce in that regi on.Show what the water situation will be in 15 years, and predict how this situation impact the lives of citizens of this region. Design an intervention plan taking all the drivers of water scarcity into account according to the situation, to help with the water scarcity and optimizing the model.Estimate the optimized model and predict the results.2.2 Problem solvingWe address the problem of optimiz ing water use of a regi on through an alyz ing the water situation, which provides a measure of the ability of a region to provide clean water to meet the needs of its population. The model consists of two big modules: water supply and water consumption. Water supply module is mainly composed of surface water and groun dwater, the degree of en vir onmen tal gover nance, storage capacity, precipitation, etc. Water module is mainly composed of personal living water, agricultural water, industrial water and ecological water use, etc. Finally we compare the model of water supply with the model of water consumption, then take a certa in evaluatio n in dex to measure the regio n's water supply capacity.Next, since the region of North China (include Beijing, Tianjin, Hebei, Shanxi, Inner Mon golia) meets the requireme nt of being heavily or moderately overloaded on using water, we choose the North Chi na as the researchi ng regi on. We expla in the social and en vir onmen tal reas ons of the scarcity from physical and econo mical sides, to dissect what facts impact the water scarcity.Then we make quantitative and qualitative analysis of the water supply and consumption in this region, to get what the characteristics of the situation in 15 years.At last, according to the fourth and fifth question, we optimize the model from impro ving water supply and reduc ing water con sumpti on, to solve the problem of water shortage. We con sider about impro ving the water supply by the con struct ion of reservoirs, water diversion works, water desalination, wastewater treatment, and political, econo mic and social con sideratio ns. On the other side, we reduce the water con sumptio n from rais ing aware nessabout sav ing water and impro ving agricultural irrigati on methods, adjust ing the structure of in dustrial water, impro ving ecologicalaspects to con sider aut onomy ability. Then un der the optimizati on of water supply and water con sumpti on we set up a water allocati on optimizati on model, which is used for exploitati on and utilizati on pla nning of water resources, mean while predict the situati on of water resources using in the future.3 Assumptions☆Ignore the impacts of the extreme disasters.☆Ignore the impacts of the migrati on of populati on.☆Ignore the admi nistrati on cost in late period of water diversi on project☆Ignore the effects of the other polluting factors in the wastewater when con sider about the polluted degree.☆Ignore the tran sportati on cost of the water supply whe n con sider about the sea water desali nati on.☆we assume that the gross of the populati on N (t)is large eno ugh.☆We assume that there is no big revolution in the configuration of water supply.4 NotationsTable 1:Notations and DescriptionsNotations Descriptionst time unitN(t) Gross population of time tN(t o) Gross populati on of time t0M Allowed max populati on in a regi ona Natural populati on growth rateP(t) Population net growth rate of time tB Coefficie nt of lifeS Relative sta ndard deviati onW Water con sumpti on per capitaA(t) Gross of the pers onal water con sumpti onu Water lack ing rateU() Upstream collection of objectsXZTL Sewage water back to the rema ining amountXRSV Reservoir capacity of the surface waterPZBC1 Agricultural producti on function coefficie ntXZGO Lateral groun dwater runoffPZGU Groun dwater mining upper limitPRSF InflowPCSD Channel of water proporti onPZWE River ecological water requireme ntPNSF At the end of the river cha nnel con trol in flowXCSO The dodger ' s river water amount5 Basic model5.1 Model of the water consumptionThe water con sumptio n of one regi on mai nly con sists of pers onal con sumptio n agricultural con sumpti on, in dustrial con sumptio n, ecological con sumpti on and etc. And the agricultural con sumpti on , in dustrial con sumpti on cha nges with the en vir onment cha nging, populati on in creas ing, and econo mics develop ing. Therefore we n eed to develop mathematical model for the four facts to research.Pers onal con sumpti on refers to a sin gle pers on use water to drink, bath and so on for daily life.5.1.1 Compound population Model based on LogisticModelLogistic Model fits for continuous population growth, but also can appear n egative growth in some coun tries. We establish a compo und populati on model based on Logistic Model, the n build the model of populatio n net growth rate in on e-place linear, by researching the law of population growth.According to Logistic Model, the model of the population growth rate can express as the in itial value problem of differe ntial equatioK"：(1)N(t°)讥Postulate 二，N(t)二P(t), and P(t) denotes the population net growth rate,-■ denotes the natural population growth rate, : denotes the coefficient of life,N(t) denotes the gross population, N(t0) denotes the gross population of initial time.Formula (1) represents an initial value problems of Bernoulli equation, and we can obtain the solution. However, due to the limited data information, we cannot confirm the parameters :- and : . Thus even if we have obtained the solutions, it made no con tributi on to predict the gross of populati on. Therefore we assume that the populati on net growth rate has lin ear relati on ship with time; that is the model of the populati on net growth rate:a,b are uncertain constant. The results of a multiply b is less than zero.Putting equation (2) into equation (1), we can get the model that reflects the gross of the populati on.呼g b）呵I N(t o) = N°By solving the initial value of the differential equation problem, we can get the composite model of populati on growth:N(t) =N°2In this differe ntial equatio n, guess in g d ^(t ^ at b N t , because^ t isb greater than zero, t becomes the only stable point of function N t , then we apoi nt.When constant a is less than zero, and constant b is greater than zero, we get(_blN t is a monotonic increasing function in 0, , and a monotonic decreasing l a 」 戈 ：：,so N t achieves the maximum value N —IL a . aso N t achieves the minimum value N Since the gross of personal water consumption A(t)二 W * N (t), then we put (4) into it, we get the equati on of the gross of pers onal water con sumpti on:I" f t 2A(t )=W* N 0 *exp |- bt 0+空 .I 2丿」5.1.2 Model of Industrial water consumptionAccord ing to the n ati onal in dustrial water con sumpti on statistics from various coun tries, the value prese nts a lin ear trend. We determ ine the in dustrial water consumption B(t) through linear fitting.We use least square method for fitting. The method makes parameter Q infunction Q Y 7 a bX i2 reaches the minimum value. a and b are called i =1 -the Least squares estimators. Due to the necessary condition of the extremum in the calculus, we obta ina and b:draw the con clusi on that whe n t =-N t gets the maximum absolute valuefun cti on in whe n;Whe n a is greater tha n zero, and b is less tha n zero, N t is a monotonicdecreas ing function inand a monotonic in creas ing fun ctio n inwhent 二|* exp bt +巴=-2 ： ||Y - a bX i=0da i i -竺二 -2 ：||Y j_ a bX j X j =0db ij -t t'、X i —X Y -Y 、 X i -X Yi -4i 4亠「—r' X i-X ' X i-Xy i =a =Y -bXAccord ing to the in dustrial water con sumpti on in each year, we can fit the in dustrial water con sumpti on B(t).5.1.3 Model of total water consumption of a regionSince it is the same for the agricultural consumption c(t) and ecological con sumptio n D(t) to calculate as it does in in dustrial con sumpti on B(t), we can determine the model of total water consumption. Based on the model of personal con sumpti on, in dustrial con sumpti on, agricultural con sumpti on, and ecological consumption, we can determine the model of total water consumption of a region E(t) as follows:at 2at2"2°)]*exp( bt y ) B(t) C(t) D(t)5.2 Model of the Gray Metabolism Model GM (1,1)5.2.1 Principle of common Gray GM (1, 1) ModelGray System theory holds the view that all the random quantities are gray variables and process within certain range and time interval. The model is established after process ing these data in certa in ways and ranking in to regular time series.Gray SystemPrediction Model GM (1, 1) is a first order differential equation with one variable, it is fit for prediction to the development of systematic behavior eigenvalue. Gray System Prediction Model GM (1, 1) produces random number and transformsE(t)二W* N0*exp[ -(bt0them into ordered data, and then establishes differential equation, later, it seeks for the regulation of producing the data and then restore the operating results. The specific steps are followi ng:We accumulate the variablex ⑴二{x ⑴(1),x ⑴(2), ||(,x ⑴(N)}t hereinto, we get x ( 1( t)=£ iSo we can establish a differential equation in the form of an albino as fellow:dx ⑴*⑴ ax u dtThe bleaching solution of differential equation are as follows ( disperseresponse :x ⑴(t)=[x (0)(1)丄]e 」(t」)ua a Parameter k deno tes time series, can be year, seas on or month.Mark parameter sequences asj , U =；：.We obtain U from these equations:；?1 U = [q8 一While B represents data matrix y denotes data column.-1[x (1)(2)x (1 ( 1) ] 1 -1[x (1)(3|x (1)(2)] 1 : 1-1[X (1)(N )x (N- 1)] 1Because we get cumulative amount by GM Model is for once, and it is thepredicted value when t {n 1,n 2,...} , we must restore the obtained data ?(1)(t 1) (or x?(1) (t)) to x (0)(t 1) (or 00)(t) ) through repeatedly minus with determining (I — AGO): t0)(t)八 0)(i)i =iX (0) ={X (0)(1),X (0)(2),川，X (0)(N)} to getX (0()学 x (悝 1) ,4( 1,2 ,n ..,)= (B T B)‘B Ty _X (0()2)1X (°(3) X (0^N)t J八 x (0f i)・ ?x (0()t)i Jt 」X^ft^/xTH)瓦? x (f 6i 4t JSi nee X ⑴(t-1)八?(0)(i) , we get 4(t 1)=G )(t 1)-X ⑴(t),(t =0,1,2,…).i 45.2.2 Principle of Gray Metabolism Model GM (1, 1)[2]After making a gray predietion and getting the latest information , it adds this information into the original data series and wipes off the oldest information at the same time.Then, using the new one as original series, it repeats the above step 1.1 to set up GM (1,1) Model , so on and so forth, un til the fulfillme nt of all the predict ion objectives, and that is theGray Metabolism Model we wanted5.2.3 Accuracy testingRelative error and posterior differe nee ratio C are two most com monly used way to test the model, and its basic process is follow ing:x (0)is original series, X (0)is the series simulated by GM Model and ； is residualseque nce With in it is 欽t) =x (0)(t) _00)(t) , the relative error seque nceis p =1 - ：, andthus the total water resource amount in t 1 yean -(」，—，…，二 n)-1 nerror of the point, andkis the average relative error.n tmas the predictio n accuracy, which is displayed in perce ntage.,■S1 :,；n TnS「(x (0)(t)-x (0) )2-(0) vx (0)(k)S 2 :,xn TnC = -dS2could be obtained. Hereinto we have t|, and L is the simulated relativep = 1 is definedWhere S1is the mean variance of residua；S2is the mean variance of originalseries; C is the posterior differenee ratio.Here is a referenee table attached that illustrates the model accuracy classification in details:accuracy could be gain ed.5.3 Model of water supply capacity of a region唱 *100%For measuring the degree of water lacking in this region, we set 4th level evaluati on on the basis of water shortage ratethe sta ndard see table 3:Strengths: r at2 丫at 2、 F(t )=Y(t )—W*N 0*exp |-bt 。
阅读《太空垃圾——人类自设的隐患》附答案
阅读《太空垃圾——人类自设的隐患》附答案阅读《太空垃圾——人类自设的隐患》附答案阅读《太空垃圾——人类自设的隐患》，完成14—16题。
（10分）人类为了追求更加清洁、优美的生活环境，采取了各种各样的方法治理地球上的垃圾等有害物质。
但鲜为人知的是，在太空，成千上万吨垃圾正在不断地蔓延。
它不仅影响航天事业的发展，而且还给地球增加一层污染源，其中更令人不安的是，这些垃圾存在大量放射性物质时刻威胁着人类的生命安全。
太空垃圾是人类在进行航天活动时遗弃在太空的各种物体和碎片。
如各种卫星的零部件，各种火箭发动机在空间爆炸产生的残骸，核动力卫星及其产生的放射性碎片；宇航员在太空行走时丢弃的螺母、螺栓和螺丝刀等各种物体。
这些东西如人造卫星一般按一定的轨道环绕地球飞行，形成一条危险的垃圾带。
据统计，目前约有数千吨太空垃圾在绕地球“运行”，且数量正以每年2％至5％的速度递增。
科学家们对太空中可能存在的近10万块废弃物表示担忧。
由于这些物体通常以每秒10公里以上的速度运行，因此如果与其他物体相撞，每小块将产生相当于一颗手榴弹的爆炸力。
一块仅有阿司匹林药片大的残骸可将人造卫星撞成“残废”，可将造价数亿美元的航天器送上绝路。
1983年，美国航天飞机“挑战者”号与一块直径0．2毫米的涂料剥离物相撞，导致舷窗被损，只好停止飞行。
当宇航员在太空行走时，一块迎面而来、直径仅为0．5毫米的金属微粒足以戳穿密封的宇航服，人们肉眼很难看清的油漆片和涂料粉末也能给宇航员带来生命危险。
科学家还认为，大块的宇宙飞船残块将不断下落，进入大气层，一部分在大气层中烧毁，另一部分则掉在地球上。
然而，飘荡在地球上空的核动力装置，尤其是核动力发动机的`脱落更具有特别的危险性，它将对地球造成严重的放射性污染。
据统计，到下个世纪，将会有100多个这种装置，含有1吨以上的放射性物质。
1978年苏联带有核装置的“宇宙一954”星掉在了加拿大北部的土地上；1983年，“宇宙1420”号的反应堆芯落入南大西洋。
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太空垃圾
在地球轨道上的小碎片已成为越来越多的关注。
据估计，超过500000块的空间碎片，也被称为轨道碎片，目前正在跟踪潜在危险的空间飞行器。
在新闻媒体报道2009。
2.10俄罗斯卫星和美国卫星kosmos-2251 iridium-33相撞后，该问题引起更广泛的讨论。
已提出的许多方法，以消除碎片。
这些方法包括小的，空间为基础的水射流，并用于针对碎片的特定部分高能激光器和大型卫星，扫描碎片，还包括其他一些方法。
碎片的大小和质量从油漆薄片到废弃的卫星不等。
碎片的高速度轨道使得捕捉变得困难。
开发一个随时间变化的模型，以确定最佳的替代或组合的替代品，私营企业可以发掘一个商业机会，以解决空间碎片问题。
您的模型应该包括定量和/或定性的估计成本，风险，收益，以及其他重要因素。
您的模型应该能够评估独立的替代品，以及组合的替代品，并能够探索各种重要的“如果？“情景。
使用您的模型，确定能否有机会使该项目有经济吸引力成为可能。
如果存在一个可行的商业机会作为替代解决方案，提供用于去除碎屑的不同选项的比较，用于去除碎片，并包括一个具体的建议，如何消除碎片。
如果没有这样的机会是可能的，然后提供用于避免碰撞的创新方案。
除了要求的一页摘要提交，你的报告必须包括一个两页的执行总结，介绍了考虑的方案和主要的建模结果，并适当的从你的工作提取出一个特定的行动建议，联合行动，或不采取行动，。
执行总结是用来给那些高层政策制定者和新闻媒体分析人士等不具备技术背景的人看的。