2016数学中国国际赛论文参考模版.doc

Team # 4488 Page 15 of 15第五届“认证杯”数学中国数学建模国际赛承 诺 书我们仔细阅读了第五届“认证杯”数学中国数学建模国际赛的竞赛规则。我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。我们知道，抄袭别人的成果是违反竞赛规则的, 如果引用别人的成果或其他公开的资料（包括网上查到的资料），必须按照规定的参考文献的表述方式在正文引用处和参考文献中明确列出。我们郑重承诺，严格遵守竞赛规则，以保证竞赛的公正、公平性。如有违反竞赛规则的行为，我们将受到严肃处理。我们允许数学中国网站()公布论文，以供网友之间学习交流，数学中国网站以非商业目的的论文交流不需要提前取得我们的同意。我们的参赛队号为：我们选择的题目是： 参赛队员 (签名) ：队员1： 队员2：队员3： 参赛队教练员 (签名)： 第五届“认证杯”数学中国数学建模国际赛编 号 专 用 页参赛队伍的参赛队号：（请各个参赛队提前填写好）：竞赛统一编号（由竞赛组委会送至评委团前编号）：竞赛评阅编号（由竞赛评委团评阅前进行编号）：TITLEAbstract: Key words: Contents1. Introduction.5 1.1 what is the cause of the Ozone depletion? .5 1.2 What is the origin of the air pollution for ozone layer? 5 1.3 The protection measurements of ozone layer.5 1.4 The recent development of ozone protection.6 1.5The importance of ozone layer.62. The Description of Problem. 2.1 Hypothesis of this problem.72.2 analysis of this problem 2.2.1 part 1： .8 2.2.2 part 2: .8 2.2.3 part 3:.8 2.2.4 part 4:.8 2.2.5 part 5:.83. Models.73.1 Basic Model.7 3.1.1 Symbols and Definitions.7 3.1.2 Assumptions.8 3.1.3 The Foundation of Model.9 3.1.4 Solution and Result.11 3.1.5 Analysis of the Result.11 3.1.6 Strength and Weakness.133.2 Improved Model.14 3.2.1 Extra Symbols.14 3.2.2 Additional Assumptions.14 3.2.3 The Foundation of Model.14 3.2.4 Solution and Result.15 3.2.5 Analysis of the Result.18 3.2.6 Strength and Weakness.194. Conclusions.19 4.1 Conclusions of the problem.194.2 Methods used in our models.19 4.3 Application of our models.195. Future Work.19 5.1 Another model19 5.2 Another layout of .23 5.3 The newly- adopted methods.236. References.237. Appendix.23 Programs and codes.24I. IntroductionIn order to indicate the origin of problems, the following background is worth mentioning.1.1 What is the cause of the ozone depletion? Theozone layerorozone shieldis a region of Earthsstratospherethat absorbs most of theSunsultraviolet(UV) radiation. It contains high concentrations ofozone(O3) in relation to other parts of the atmosphere, although still small in relation to other gases in the stratosphere. The ozone layer contains less than 10 parts per million of ozone, while the average ozone concentration in Earths atmosphere as a whole is about 0.3 parts per million. The ozone layer is mainly found in the lower portion of the stratosphere, from approximately 20 to 30 kilometers (12 to 19mi) above Earth, although its thickness varies seasonally and geographically.The ozone layer can be depleted by free radical catalysts, includingnitric oxide(NO),nitrous oxide(N2O),hydroxyl(OH), atomicchlorine (Cl), and atomicbromine(Br). While there are natural sources for all of thesespecies, the concentrations of chlorine and bromine increased markedly in recent decades because of the release of large quantities of man-madeorganohalogencompounds, especiallychlorofluorocarbons(CFCs).These highly stable compounds are capable of surviving the rise to thestratosphere, where Cl and Brradicalsare liberated by the action of ultraviolet light. Each radical is then free to initiate and catalyze a chain reaction capable of breaking down over 100,000 ozone molecules. By 2009, nitrous oxide was the largest ozone-depleting substance (ODS) emitted through human activities.Levels of atmospheric ozone measured by satellite show clear seasonal variations and appear to verify their decline over time.The breakdown of ozone in the stratosphere results in reduced absorption of ultraviolet radiation. Consequently, unabsorbed and dangerous ultraviolet radiation is able to reach the Earths surface at a higher intensity. Ozone levels have dropped by a worldwide average of about 4 percent since the late 1970s. For approximately 5 percent of the Earths surface, around the north and south poles, much larger seasonal declines have been seen, and are described as ozone holes.The discovery of the annual depletion of ozone above the Antarctic was first announced byJoe Farman,Brian GardinerandJonathan Shanklin, in a paper which appeared inNatureon May 16, 1985.1.2 What is the origin of the air pollution for ozone layer?This kind of air pollution is consists of chlorfluorocarbons(CFCs) mainly, which originated from the manufactures of aerosols, refrigerant, foaming agent and chemical solvents.Whats more, nitrogen oxides also can affect the quality of ozone layer to some degree, which is derived from fire extinguisher.1.3 The protection measurements of ozone layerIn 1978, the United States, Canada and Norway enacted bans on CFC-containing aerosol sprays that damage the ozone layer. The European Community rejected an analogous proposal to do the same. In the U.S., chlorofluorocarbons continued to be used in other applications, such as refrigeration and industrial cleaning, until after the discovery of the Antarctic ozone hole in 1985. After negotiation of an international treaty (the Montreal Protocol), CFC production was capped at 1986 levels with commitments to long-term reductions.Since that time, the treaty was amended to ban CFC production after 1995 in the developed countries, and later in developing countries. Today, all of the worlds 197 countries have signed the treaty. Beginning January 1, 1996, only recycled and stockpiled CFCs were available for use in developed countries like the US. This production phaseout was possible because of efforts to ensure that there would be substitute chemicals and technologies for all ODS uses.On August 2, 2003, scientists announced that the global depletion of the ozone layer may be slowing down because of the international regulation of ozone-depleting substances. In a study organized by the American Geophysical Union, three satellites and three ground stations confirmed that the upper-atmosphere ozone-depletion rate slowed down significantly during the previous decade. Some breakdown can be expected to continue because of ODSs used by nations which have not banned them, and because of gases which are already in the stratosphere. Some ODSs, including CFCs, have very long atmospheric lifetimes, ranging from 50 to over 100 years. It has been estimated that the ozone layer will recover to 1980 levels near the middle of the 21st century.A gradual trend toward healing was reported in 2016.Compounds containing CH bonds (such as hydrochlorofluorocarbons, or HCFCs) have been designed to replace CFCs in certain applications. These replacement compounds are more reactive and less likely to survive long enough in the atmosphere to reach the stratosphere where they could affect the ozone layer. While being less damaging than CFCs, HCFCs can have a negative impact on the ozone layer, so they are also being phased out. These in turn are being replaced by hydrofluorocarbons (HFCs) and other compounds that do not destroy stratospheric ozone at all.1.4 The recent development of ozone protectionAlthough mankind has taken many measures to protect the ozone layer, but the ozone hole over the Antarctic is still very big, in other word, the ozone layer repairs slower than expected. NASA, Americas national oceanic and atmospheric administration and the national center for atmospheric research in the United States believes that a study of the Antarctic ozone hole will be continued until 2068, which scientists had forecast the ozone hole will disappear completely after 2050.Now the humanity has not found the way to repair the damaged parts of ozone layer yet, but governments are taking action to limit the damage to the ozone layer actively. The United States and the European Community has decided to stop the production of freon deadlines in 2000. On the other hand, scientists are working on the researches about harmless refrigerant, foaming agent. The consumers who concerned about the problems are protecting the ozone layer by using non-freon freezers, etc.1.5 The importance of ozone layerFirstly, protective effects: ozone layer can absorb the ultraviolet ray whose wavelength is below 300 m in sunlight to protect the lives in earth from the damage of uvb radiation.Secondly, heating effects: ozone absorbs the ultraviolet ray from sunlight and converts it to heat energy to heat the atmosphere, the temperature of the atmospheric structure has an important influence to atmospheric circulation.Thirdly, regulating effects: at the top of the troposphere and bottom of the stratosphere, which is as same as in the part with low temperature, ozone layer also plays a significant role. If the density of ozone in this level declined, it will lead to the decrease of ground temperature II. The Description of the Problem2.1 Hypothesis of this problemCombined with the practice, in order to ensure the accuracy and rationality of the model, we exclude the interference of some other factors, put forward the following hypothesis:1. the number of industrial enterprises of city A,the value of profits of city A, and the comprehensive energy consumption of ozone data of city A is true and valid, and were all in the allowable error range;2.The assumption that the data A representative city industrial enterprises, the consumption structure of the randomly selected part of industrial enterprises can represent the city industrial enterprises A industrial structure, energy and industrial development level of ozone;3.If only the comprehensive energy consumption of ozone in resource endowment, does not take into account the social resources and natural resources;4.The assumption that each industrial energy consumption and the total ozone amount does not exceed the total energy consumption of ozone city A.2.2 analysis of this problemFirst aspect analysis:The problem requires us to make a quantitative analysis of the industrial structure and energy consumption characteristics of urban A industrial enterprises, and to establish a comprehensive evaluation of the development level of urban A industrial enterprises. First of all, reading a lot of literature to understand the concept of industrial structure and energy loss characteristics of ozone, analysis of the relationship between energy consumption and industrial structure development of ozone; secondly, through the analysis, calculation and comparison of A city industrial enterprises, output value, tax and comprehensive energy consumption of ozone table roughly determine the classification and energy consumption characteristics of the A industry the structure of the city; finally, the A industrial enterprises to carry out comprehensive cluster analysis using SPSS software, the industrial enterprises in A city classification, through the analysis of the characteristics of similar data of industrial enterprises, summed up the characteristics of the industrial structure and energy consumption of ozone in various industrial enterprises, comprehensive evaluation of the comprehensive analysis of these types of industrial enterprises in A city the development level of ozone.Second aspects of analysis:The total consumption of city A this year ozone decreased by 5% compared with last year, the impact on A citys industrial output value of enterprises, profits, employees were the least, establish the mathematical model for the allocation of the ozone energy industrial enterprises A. First of all, we should make clear the A industrial output value of enterprises, profits and the number of ozone will affect the total energy consumption, but the total energy distribution requirements of ozone respectively with minimal impact on A industrial output value of enterprises, profits and employees, then we need to consider individual factors can affect the total consumption of ozone source; secondly, we can make the ozone consumption each enterprise as reference sequence, every industrial enterprise value, and the number of taxes as comparative sequence grey relational analysis, correlation of all industrial enterprises, and the value of the number of taxes and ozone consumption, according to the degree of various industrial enterprises, and the value of the number of taxes and energy consumption were established three ozone the total energy distribution model.Third aspects of analysis:For this years consumption of energy in the city of A total 5% lower than last years situation, need to establish the mathematical model of A, the industrial enterprise energy distribution, the output and profits of industrial enterprises, employees of the citys comprehensive influence of the minimum. First of all, the production and profit of industrial enterprises and the number will affect the total energy distribution of ozone, compared to A industrial enterprises output value and profits, the number of data comparison judgment matrix; secondly according to the comparative judgment matrix to establish the AHP model, get the weight vector to determine the A City Industrial enterprises output value and profits, the number of the importance of energy consumption of ozone of the total; finally, according to the weight vector of A, various industrial enterprises share of the total energy consumption of ozone, determine the total energy allocation scheme of various industrial enterprises in the city of A.Fourth aspects of analysis:Through access to information, the establishment of distribution model of total ozone energy, and the next two years the citys profit and tax levels for quantitative analysis. First of all, all industrial enterprises in A city is divided into two categories according to the unit energy consumption of ozone output value A city industrial enterprises; secondly, the establishment of energy consumption goal programming model according to the information given in the total energy consumption of ozone target and A, the growth rate of the total output value of industrial enterprises, two industrial enterprises to determine the allocated amount of energy E1, E2 then, the total energy of E1 and E2 were assigned to the class belonging to two industrial enterprises of various industrial enterprises; finally, through the analysis of energy consumption and output of ozone on tax effect, A city tax in the future development of water within two years, every 10 years as a benchmark, and can predict the future ozone depletion 50 years.Fifth aspects of analysis:Under the premise of total energy control, the reasonable distribution of energy resources to urban A industrial enterprises is to improve the efficiency and quality of ozone energy utilization. First of all, the need for different requirements of different ozone energy distribution model is established, and a simple description of the implementation methods and effect; secondly, put forward policy recommendations to improve the ozone ozone distribution model of energy efficiency and reduce city A ozone depletion.III. Models3.1 Basic Model3.1.1 Terms, Definitions and SymbolsThe signs and definitions are mostly generated from queuing theory. l l l l l 3.1.2 Assumptionsl l l l l3.1.3 The Foundation of Model1) The utility functionl The cost of : l The loss of : l The weight of each aspect: l Compromise: 2) The integer programmingAccording to theory, we can calculate the statistical properties as follows.3) The overall optimization and the local optimizationl