2015年最新美国数学建模试题原题-ICM-D
2015 ICMProblem DIs it sustainable?Problem backgroundOne of the largest challenges of our time is how to manage increasing population and consumption with the earth’s finite resources. How can we do this while at the same time increasing equity and eradicating poverty? Since the beginning of the modern envi ronmental movement in the 1960’s, balancing human needs with the earth’s health has been a topic of considerable debate. Are economic development and ecosystem health at odds? In order to reconcile this difficult balance, the concept of sustainable develo pment was introduced in the 1980’s. Sustainable development is defined by the 1987 Brundtland Report as “development that meets the needs of the present without compromising the ability of future generations to meet their own needs.” Since its conception, sustainable development has become a goal for international aid agencies, planners, governments, and non-profit organizations. Despite this, striving towards a sustainable future has never been more imperative. The United Nations (UN) predicts the world’s population will level at 9 billion people by 2050. This, coupled with increased consumption, places a significant strain on the earth’s finite resources. Understanding that the earth is a system that connects both time and space is critical to sustainable development. Development must focus on needs (e.g., reducing the vulnerability of the world’s poor) and limitations (e.g., the environment’s ability to detoxify wastes). In 2012, the UN conference on sustainable development recognized that: “that poverty eradication, changing unsustainable and promoting sustainable patterns of consumption and production and protecting and managing the natural resource base of economic and social development are the overarching objectives of and essential requirements for sustainable development.” Decreasing personal poverty and vulnerability, encouraging economic development, and maintaining ecosystem health are the pillars of sustainable development.Problem statementThe International Conglomerate of Money (ICM) has hired you to help them use their extensive financial resources and influence to create a more sustainable world. They are particularly interested in developing countries, where they believe they can see the greatest results of their investments.Task 1: 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. It can also serve to inform the ICM on those countries that need the most support and intervention. Some factors may include human health, food security, access to clean water, local environmental quality, energyaccess, livelihoods, community vulnerability, and equitable sustainable development. Your model should clearly define when and how a county is sustainable or unsustainable.Task 2: Select a country from the United Nations list of the 48 Least Developed Countries (LDC) list(/en/pages/aldc/Least%20Developed%20Countries/UN-list-of-Least-Developed-Countries.aspx). Using your model and research from Task 1, create a 20 year sustainable development plan for your selected LDC country to move towards a more sustainable future. This plan should consist of programs, policies, and aid that can be provided by the ICM within a country based on their demographic, natural resources, economic, social and political conditions.Task 3: Evaluate the effect your 20-year sustainability plan has on your country’s sustainability measure created in Task 1. Predict the change that will occur over the 20 years in the future by implementing your plan in your evaluation. Based on the selected country, you may need to consider additional environmental factors such as climate change, development aid, foreign investment, natural disasters, and government instability. The ICM would like to get the “most bang for their buck”, so determine which programs or policies produce the greatest effect on the sustainability measure for your country. Identifying highly effective strategies to be implemented is the ultimate goal of the ICM to create a more sustainable world.Task 4: Write a 20-page report (summary sheet does not count in the 20 pages) that explains your model, your sustainability measure, your sustainability development plan, and the effect of your plan based on your model and the country’s environment. Be sure to detail the strengths and weaknesses of the model. The ICM will use your report to invest in sustainability development intervention strategies for specific LDC countries. Good luck in your modeling work!Possible ResourcesUN sustainable development knowledge platform()Ecological footprint(/en/index.php/GFN/page/footprint_basics_overvi ew/)World Bank Data ()International Institute for Sustainable Development (https:///sd/)ReferencesWorld Commission on Environment and Development (WCED). 1987. Our Common Future. New York: Oxford University Press, 1987, 8.United Nations. The future we want. Resolution adopted by the General Assembly. 66th Session of the General Assembly, 123rd plenary meeting; 2012 July 27. New York: UN; 2012 Sep 11 (Resolution A/RES/66/288) [cited 2013 Jul 23]. Available at:/ga/search/view_doc.asp?symbol=A/RES/66/288&Lang=E. Other useful SourcesBell, Simon and Stephen Morse. 2008. Sustainability Indicators: measuring the immeasurable. Earthscan, London.Daly, Herman. 1990. Towards some operational principles of sustainable development. Ecological Economics, 2(1990) 1-6.Kates, Robert W., Thomas M. Parris, and Anthony A. Leiserowitz. 2005. What is sustainable Development: Goals indicators, values, and practices. Environment: Science and Policy for Sustainable Development, Volume 47, Number 3, pages 8–21.。
美国数学建模大赛比赛规则
数学中国MCM/ICM参赛指南翻译（2014版）MCM:The Mathematical Contest in ModelingMCM：数学建模竞赛ICM:The InterdisciplinaryContest in ModelingICM：交叉学科建模竞赛ContestRules, Registration and Instructions 比赛规则，比赛注册方式和参赛指南(All rules and instructions apply to both ICM and MCMcontests, except where otherwisenoted.)（所有MCM的说明和规则除特别说明以外都适用于ICM）每个MCM的参赛队需有一名所在单位的指导教师负责。
指导老师：请认真阅读这些说明，确保完成了所有相关的步骤。
每位指导教师的责任包括确保每个参赛队正确注册并正确完成参加MCM/ ICM所要求的相关步骤。
请在比赛前做一份《参赛指南》的拷贝，以便在竞赛时和结束后作为参考。
组委会很高兴宣布一个新的补充赛事（针对MCM/ICM 比赛的视频录制比赛）。
点击这里阅读详情！1.竞赛前A．注册B．选好参赛队成员2.竞赛开始之后A．通过竞赛的网址查看题目B．选题C．参赛队准备解决方案D．打印摘要和控制页面3.竞赛结束之前A.发送电子版论文。
4.竞赛结束的时候,A. 准备论文邮包B．邮寄论文5.竞赛结束之后A. 确认论文收到B．核实竞赛结果C．发证书D．颁奖I. BEFORE THE CONTEST BEGINS:（竞赛前）A.注册所有的参赛队必须在美国东部时间2014年2月6号（星期四）下午2点前完成注册。
届时，注册系统将会自动关闭，不再接受新的注册。
任何未在规定时间内注册的参赛队都没有参加2014年MCM/ICM的资格。
不存在例外情况。
1参赛队通过下面的网站在线注册：/undergraduate/contests/m cma.如果您刚刚开始注册竞赛的第一个参赛队，请点击网页左边的Register for2014 Contest 。
华工第十六届数理大赛赛题发布会
2014全国数学建模竞赛题目 2015美国数学建模竞赛题目
2014全国数学建模竞赛题目 A题 嫦娥三号软着陆轨道设计与控制策略 B题 创意平板折叠桌 C题 生猪养殖场的经营管理 D题 储药柜的设计
2015 MCM&ICM Problems • Problem A:Eradicating Ebola • Problem B:Searching for a lost plane • Problem C:Managing Human Capital in Organizations • Problem D:Is it sustainable?
• Convex Optimization • Duality-Theory • Lagrange Multipliers • Kernels function
Deep Learning Neural Network
• • • • AlphaGo Zero强化学习战胜AlphaGo 人工智能推动数学建模 数学建模制造新的信息机器 丘成桐：工程上取得很大发展 但理论基础仍非常 薄弱 • 人工智能需要一个可以被证明的理论作为基础。 • 人工智能需要新数学理论
SVHN – real world image dataset
Image classification
Convolutiona Neural Network
全 连 接 卷 积
池 化
CNN- 图像分类和场景特色
数学建模生产的图形处理机器
LSTM- 翻译语言和语音识别机器
RNN - 语音识别和自然语言分析
2017A题
CT系统参数标定及成像
• 请建立相应的数学模型和算法，解决以下问题： • (1) 在正方形托盘上放置两个均匀固体介质组成的标定模板，模板的 几何信息如图2所示，相应的数据文件见附件1，其中每一点的数值反 映了该点的吸收强度，这里称为“吸收率”。对应于该模板的接收信 息见附件2。请根据这一模板及其接收信息，确定CT系统旋转中心在 正方形托盘中的位置、探测器单元之间的距离以及该CT系统使用的X 射线的180个方向。 • (2) 附件3是利用上述CT系统得到的某未知介质的接收信息。利用(1) 中得到的标定参数，确定该未知介质在正方形托盘中的位置、几何形 状和吸收率等信息。另外，请具体给出图3所给的10个位置处的吸收 率，相应的数据文件见附件4。 • (3) 附件5是利用上述CT系统得到的另一个未知介质的接收信息。利 用(1)中得到的标定参数，给出该未知介质的相关信息。另外，请具 体给出图3所给的10个位置处的吸收率。 • (4) 分析(1)中参数标定的精度和稳定性。在此基础上自行设计新模 板、建立对应的标定模型，以改进标定精度和稳定性，并说明理由。
2017年美赛题目
2017年美赛题目2017年美赛（MCM/ICM）共有6个题目，分别是：1. Problem A: The Art of Archery.这个问题涉及到弓箭射击的技术和策略。
要求团队通过建立数学模型，分析射击的精度和效率，并给出最佳的射击策略。
2. Problem B: The Search for the Lost Dutchman's Gold Mine.这个问题要求团队通过模拟和优化算法，规划一次寻找失落的荷兰人金矿的探险。
团队需要考虑资源分配、路线选择和风险评估等因素。
3. Problem C: The Great American Potato Chip Factory.这个问题要求团队分析和优化一个薯片工厂的生产过程。
团队需要考虑原材料采购、生产调度和产品分配等方面，以提高工厂的效率和利润。
4. Problem D: The Mathematics of Music.这个问题要求团队通过数学模型和计算方法，分析和优化音乐的和声和旋律结构。
团队需要考虑音乐的音高、音长和节奏等因素，并给出最佳的音乐创作建议。
5. Problem E: The Internet of Things.这个问题要求团队分析和优化物联网中的传感器网络。
团队需要考虑传感器的部署、数据传输和能源管理等问题，以提高网络的覆盖范围和性能。
6. Problem F: The Impacts of Tourism.这个问题要求团队通过建立模型，分析旅游业对一个地区的经济、环境和社会影响。
团队需要考虑游客数量、旅游收入和环境保护等因素，并给出合理的政策建议。
以上是2017年美赛的题目概述，每个题目都涉及不同的领域和问题，需要团队综合运用数学建模、数据分析和优化方法来解决。
2013年美国大学生数学建模大赛B题获奖论文
For office use onlyT1________________ T2________________ T3________________ T4________________Team Control Number22599Problem ChosenAFor office use onlyF1________________F2________________F3________________F4________________ 2013Mathematical Contest in Modeling(MCM/ICM)Summary Sheet(Attach a copy of this page to your solution paper.)Heat Radiation in The OvenHeat distribution of pans in the oven is quite different from each other,which depends on their shapes.Thus,our model aims at two goals.One is to analyze the heat distri-bution in different ovens based on the locations of electrical heating cubes.Further-more,a series of heat distribution which varies from circular pans to rectangular pans could be got easily.The other is to optimize the pans placing,in order to choose a best way to maximize the even heat and the number of pans at the same time.Mathematically speaking,our solution consists of two models,analyzing and optimi-zing.In part one,our whole-local approach shows the heat distribution of every pan.Firstly,we use the Stefan-Boltzmann law and Fourier theorem to describe the heat distribution in the air around the electrical heating tube.And then, based on plane in-tercept method and simplified Monte Carlo method,the heat distribution of different shapes of pans is obtained.Finally,we explain the phenomenon that the corners of a pan always get over heated with water waves stirring by analogy.In part two,our discretize-convert approach optimizes the shape and number of the pans.Above all,we discre-tize the side length of the oven, so that the number and the average heat of the pans vary linearly.In the end,the abstract weight P is converted into a specific length,in order to reach a compromise between the two factors.Specially,we create a unique method to convert the variables from the whole space to the local section.The special method allows us to draw the heat distribution of every single section in the oven.The algorithm we create does a great job in flexibility,which can be applied to all shapes of pans.Type a summary of your results on this page.Do not includethe name of your school,advisor,or team members on this page.Heat Radiation in The OvenSummaryHeat distribution of pans in the oven is quite different from each other,which depends on their shapes.Thus,our model aims at two goals.One is to analyze the heat distri-bution in different ovens based on the locations of electrical heating cubes.Further-more,a series of heat distribution which varies from circular pans to rectangular pans could be got easily.The other is to optimize the pans placing,in order to choose a best way to maximize the even heat and the number of pans at the same time.Mathematically speaking,our solution consists of two models,analyzing and optimi-zing.In part one,our whole-local approach shows the heat distribution of every pan. Firstly,we use the Stefan-Boltzmann law and Fourier theorem to describe the heat distribution in the air around the electrical heating tube.And then,based on plane in-tercept method and simplified Monte Carlo method,the heat distribution of different shapes of pans is obtained.Finally,we explain the phenomenon that the corners of a pan always get over heated with water waves stirring by analogy.In part two,our discretize-convert approach optimizes the shape and number of the pans.Above all, we discre-tize the side length of the oven,so that the number and the average heat of the pans vary linearly.In the end,the abstract weight P is converted into a specific length,in order to reach a compromise between the two factors.Specially,we create a unique method to convert the variables from the whole space to the local section.The special method allows us to draw the heat distribution of every single section in the oven.The algorithm we create does a great job in flexibility, which can be applied to all shapes of pans.Keywords:Monte Carlo thermal radiation section heat distribution discretizationIntroductionMany studies on heat conduction wasted plenty of time in solving the partial differential equations,since it’s difficult to solve even for computers.We turn to another way to work it out.Firstly,we study the heat radiation instead of heat conduction to keep away from the sophisticated partial differential equations.Then, we create a unique method to convert every variable from the whole space to section. In other words,we work everything out in heat radiation and convert them into heat contradiction.AssumptionsWe make the following assumptions about the distribution of heat in this paper.·Initially two racks in the oven,evenly spaced.·When heating the electrical heating tubes,the temperature of which changes from room temperature to the desired temperature.It takes such a short time that we can ignore it.·Different pans are made in same material,so they have the same rate of heat conduction.·The inner walls of the oven are blackbodies.The pan is a gray body.The inner walls of the oven absorb heat only and reflect no heat.·The heat can only be reflected once when rebounded from the pan.Heat Distribution ModelOur approach involves four steps:·Use the Fourier theorem to calculate the loss energy when energy beams are spread in the medium.So we can get the heat distribution around each electrical heating tube.The heat distribution of the entire space could be go where the heat of two electrical heating tubes cross together.·When different shapes of the pans are inserted into the oven,the heat map of the entire space is crossed by the section of the pan.Thus,the heat map of every single pan is obtained.·Establish a suitable model to get the reflectivity of every single point on the pan with the simplified Monte Carlo method.And then,a final heat distribution map of the pan without reflection loss is obtained.·A realistic conclusion is drawn due to the results of our model compared with water wave propagation phenomena.First of all,the paper will give a description of the initial energy of the electrical hea-ting tube.We see it as a blackbody who reflects no heat at all.Electromagnetic know-ledge shows that wavelength of the heat rays ranges from um 110−to um 210as shown below[1]:Figure 1.Figure 2.We apply the Stefan-Boltzmann’s law[2]whose solution is ()1/512−=−T c b e c E λλλ(1)()λλλλλd e c d E E T c b b ∫∫∞−∞−==0/51012(2)Where b E means the ability of blackbody to radiate. 1c and 2c are constants.Obviously,,the initial energy of a black body is )(0122398.320m w e E b ×+=.Combine Figure 1with Figure 2,we integrate (1)from 1λto 2λto get the equation as follow:λλλλλλd E E b b ∫=−2121)((3)Figure 3.From Figure 3,it can be seen how the power of radiation varies with wavelength.Secondly,based on the Fourier theorem,the relation between heat and the distance from the electrical heating tubes is:dxdt S Q λ−=(4)Where Q is the power of heat (W s J =/),S is the area where the energy beamradiates (2m ),dxdt represents the temperature gradient along the direction of energy beam.[3]It is known that the energy becomes weaker as the distance becomes larger.According to the fact we know:dxdQ =ρ(5)Where ρis the rate of energy changing.We assume that the desired temperature of electrical heating tube is 500k.With the two equations,the distribution of heat is shown as follow:Figure 4.(a)Figure 4.(b)In order to draw the map of heat distribution in the oven,we use MATLAB to work on the complicated algorithm.The relation between the power of heat and the distance is shown in Figure4(a).The relation between temperature and distance is presented in Figure4(b).The spreading direction of energy beam is presented in Figure5.Figure5.The shape of electrical heating tube is irregular.The heat distribution of a single electrical heating tube can be draw in3D space with MATLAB.The picture is shown in Figure6.After superimposing,the total heat distribution of two tubes is shown below in Figure7and Figure8.Figure6.Figure7.Figure8.The pictures above show the energy in an oven with no pan.We put in a rectangular pan whose area is A,and intercept the maps with MATLAB.The result is show in Figure9.Figure9.Figure10.Put in a circular pan to intercept the maps,whose area is A,also.The distribution of heat is shown in Figure11.Figure11.When put in a pan in transition shape,which is neither rectangular nor circular.The area of it is A,also.The heat distribution on such a pan is shown as follow:Figure12(a)Figure12(b).Figure13.Next,learning from the Monte Carlo simulation[4],a model is established to get obtain the reflectivity.We generate a random number between0and1to determine if the energy beam on certain point is reflected.•Firstly,to demonstrate the question better,we construct a simple model:Figure 14.Where θis the viewing angle from electrical heating tube to the pan.360θ=R is the proportion of the beams radiated to the pan.•What is more,we assume the total beam is 1M .Ideally,the number of absorption is3601θ×M .Then,each element of the pan is seen as a grid point.Each grid point can generate a-3601θ×M -random-number vector between 0and 1in MATLAB.•After MATLAB simulating,the number of beams decreased by 2M ,due to thereflection.So we define a probability θρ12360M M ×=to describe the number of beams reflected.The conclusion is :•If R ≤ρ,the energy beam is absorbed.•If R >ρ,the energy beam is reflected.[5]Based on the analysis above,our model get a final result of heat-distribution on the pan as shown below:Figure 15(a)Figure15(b).The conclusion is known that the closer the shape of pans is to circle,the more evenly the heat is distributed.Moreover,the phenomenon that the corners always get over heated can be explained by water wave propagation in different containers.When there is a fluctuation in the center of the water,the ripples will fluctuate and spread in concentric circles,as shown in Figure16.The fluctuation stirs waves up when contacting the pared with the waves with one boundary,the waves in corner make a higher amplitude.The thermal conduction on the pan is exactly the inverse process of the waves propagation.The range of thermal motion is much smaller than it on the side.That’s why the corners is easy to get over heated.In order to make the heat evenly distributed on the pan,the sides of the pan should be as few as possible.Therefore,if nothing is considered about the utilization of space,a circle pan is the best choice.Figure16,the water waves propagation[6]According to the analysis above and Figure7,the phenomenon shows that the heat conduction is similar to water waves propagation.So it is proved that heatconcentrates in the four corners of the rectangular pan.The Super Pan ModelAssumptions•The width of the oven(W)is mm100,the length is L.•There are three pans at most in vertical direction.•Each pan’s area is A.The first part.Calculate the maximum number of pans in the oven.Different shapes of pan have different heat distribution which affects the number of pans,judging from the previous solution.According to the conclusion in the first model,the heat is distributed the most evenly on a circular pan rather than a rectangular one.However, the rectangular pans make fuller use of the space the space than circular ones.Both factors considered,a polygonal pan is chosen.A circle can be regard as a polygon whose number of boundaries tends to infinity. Except for rectangle,only regular hexagon and equilateral triangle can be closely placed.Because of the edges of equilateral triangle,heat dissipation is worse than rectangle.So,hexagonal pans are adopted after all the discussion.Considering the gaps near boundaries,we place the hexagonal pans closely attached each other on the long side L.There are two kinds of programs as shown below.Program1.Program2.Obviously,Program2is better than Program1when considering space utilization.So scheme 1is adopted.Then,design a size of each hexagonal pan to make the highest space utilization.With the aim of utilization,hexagonal pans has to be placed contact closely with each other on both sides.It is necessary to assume a aspect ratio of the oven to work out the number of pans(N ).Assume that the side length of a regular hexagon is a ,the length-width ratio of the oven is λand L ∆is the increment in discretization.Because the number of pans can not change continuously when ⋅⋅⋅=+∈3,2,1),1,(m m m n ,the equations would be as follows.⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎧⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⋅−====∆⋅+<⎥⎦⎤⎢⎣⎡∆⋅+−∆⋅+≤⋅=∆∆⋅+=<<=a W L n W L N Lk L W W L k L W L k L a L L k L L L W aW 23,810;23105000λ(6)Result:⎪⎪⎩⎪⎪⎨⎧⋅⋅⋅==⋅+=⋅⋅⋅=−=+−⋅+=3,2,1,2233,2,1,1212130201k k n n N N k k n n N N Where 1N represents the number of pans when n is odd,2N represents the number of pans when n is even.The specific number of pans is depended on the width-length ratio of oven.The second part.Maximum the heat distribution of the pans.We define the average heat(H )as the ratio of total heat and total area of the pans.Aiming to get the most average heat,we set the width-length ratio of the oven λ.Space utilization is not considered here.A conclusion is easy to draw from Figure 8that a square area in the oven from 150mm to 350mm in length shares the most heat evenly.So the pans should beplaced mainly in this area.From model1we know that the corners of the oven are apt to gather heat.Besides,four more pans are added in the corners to absorb more heat. Because heat absorbing is the only aim,there is no need to consider space utilization. Circular pans can distribute heat more evenly than any other shape due to model1.So circular pans are used in Figure17.Figure8.Figure17.We set the heat of the pans in the most heated area(the middle row)as Q.Pans in the corners receive more heat but uneven theoretically.And the square of the four pans in the corners is so small compared with the total square that we set the heat of the four as Q too.When the length of oven(L)increases,the number of pans increases too. It makes the square of the gaps between pans bigger,meanwhile.If each pan has a same radius(r)and square(A),the equation about average heat,length-width ratio and number of pans would be(7).⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎧=+=⎥⎦⎤⎢⎣⎡⋅−====∆⋅+<⎦⎤⎢⎣⎡∆⋅+−∆⋅+≤⋅=∆∆⋅+=<<⋅=⋅⋅=...3,2,12;71021053410002k nN N r W L n W L N L k L W W L k L W L k L r L L k L L L W r A W r λπ(7)Here we get the most average heat (H ):29400WQ H ⋅=πThe third part.We discussed two different plans in the previous parts of the paper.One is aimed to get the most average heat,while the other aimed to place the most pans.The two plans are contradictory with each other,and can not be achieved together.Firstly,the weight of plan 1is P and the weight of plan 2is P −1.Obviously,this kind optimization has difficulty in solving and understanding.So we turn to another way to make it a easier and linear question.It has been set that the width of the oven is a constant W and there should be three pans at most in vertical direction.We make the weight P a proportion of the two plans.Thus the two plans could be achieved together due to proportion P and P −1,as shown in Figure18.Figure 18.As been told in model 1,the corners have a higher temperature than other parts of the oven.So plan 1is used in district 1(in Figure 10)and plan 2is used in district 2(in Figure 10).A better compromise could be reached in this way,as shown in Figure 19.Figure 19.Every pan has a square of A .Radius of circular ones is r .Side length of regular hexagon is a .1.1:23322=⇒⋅=⋅r a a r π(8)Based on the equation (8),if the pans are placed as shown in Figure 19,regular hexagons are placed full of district 1,the circular ones will be placed beyond the border line.If the circular ones are placed full of district 2,there will be more gaps in district 1,which will be wasted.So we change our plan of placing pans as Figure 20.Figure 20.The number of circular ones decreases by two,but the space in district 1is fully used,and no pan will be placed beyond the borderline.We assume that P is bigger than P −1,so that,the heat in district 1will be fully used.By simple calculating,we know that the ratio of the heat absorbed in circular pan (1H )and in regular hexagon (2H )is 1.2:1.Figure21.So,based on the pans placing plan,a equation on heat can be got as follow:⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎧=⎥⎦⎤⎢⎣⎡−⋅−=⎥⎦⎤⎢⎣⎡−⋅====∆⋅+<⎥⎦⎤⎢⎣⎡∆⋅+−∆⋅+≤=∆∆⋅+=<<⋅=⋅==≈...3,2,1)1(,911233;23212kxWLPnxWLPnWLNLkLWWLkLWLkLxLLkLLLWraAxraλπ(9)Resolution:⎪⎪⎪⎪⎪⎪⎪⎩⎪⎪⎪⎪⎪⎪⎪⎨⎧=⋅⋅+⋅+⋅⋅+=⋅⋅+⋅+⋅⋅−+==⋅+⋅+=−=+−⋅+⋅+=...3,2,1)24(2.1)325()24(2.1)3215()2(232)12(12132221212111121211201k A N n Q Q n H A N n Q Q n H k n n n N N k n n n N N (10)1N and 1H means the number of pans and average heat absorbed when n is odd.2N and 2H means the number of pans and average heat absorbed when n is even.For example:(1)When 37.0=λ,6.0=P :16=N ,AQ H 075.1=.The best placing plan is:(2)When 37.0=λ,7.0=P :18=N ,AQ H ⋅=044.1.The best placing planis:(3)When 58.0=λ,6.0=P ：12=N ,AQ H ⋅=067.1.The best placing plan is:A conclusion is easy to draw that when the ratio of width and length of the oven (λ)is a constant,the number of pans increases with an increasing P,but the average heat decreases (example (1)and (2)).When the weight P is a constant,the number of pans decreases with an increasing λ,and the average heat decreases also.So,the actual plan should be base on your specific needs.ConclusionIn conclusion,our team is very certain that the method we came up with is effective in heat distribution analysis.Based on our model,the more edges the pan has,the more evenly the heat distribute on.With the discretize-convert approach,we know that when the ratio of width and length of the oven (γ)is a constant,the number of pans increases with an increasing P ,but the average heat decreases.When the weight P is a constant,the number of pans decreases with an increasing γ,and the average heat decreases also.So,the actual plan should be base on your specific needs.Strengths &WeaknessesStrengths•Difficulties Avoided Avoided..In model 1,we turn to another way to work simulate the heat distribution instead of work on heat conduction directly.Firstly,we simulate heat radiation not heat conduction to keep away from the sophisticated partial differential equations.Then,we create a unique method to convert every variable from the whole space to section.In other words,we work everything out in heat radiation and convert them into heat contradiction.•Close to Reality.Our model considers both the thermal radiation and surface reflection,which is relatively close to the actual situation.•Flexibility Provided.Our algorithm does a great job in flexibility.The heat distribution map on sections are intercepted from the heat distribution maps of the entire space.All shapes of sections can be used in the algorithm.The heat distribution in the whole space is generated based on the location of the electrical heating tubes and the decay curve of the heat, which can be modified at any time.•Innovation.Based on our model,the space of an oven can be divided into six parts with different hear distribution.In order to make full use of the inner space,we invent a new pan which allows users to cook six different kinds of food at same time.An advertisement is published in the end of the paper.WeaknessesPan’’s Thermal Conductivity Ignored.•PanThe heat comes from not only the electrical heating tubes,but also heat conduction of the pans themselves.But the pan’s thermal conduction is ignored in the model,which may cause little inaccuracy.•Thermal Conductivity of Electrical Heating Tubes IgnoredIgnored..it is assumed that there are two electrical heating tubes in the oven and placed in a specific location.The initial temperature of the tubes is a desired constant temperature. In other words,the time electrical heating tubes spend to heating themselves is ignored.The simplification can cause some inaccuracy.simplification..•Linear simplificationIn model2,the length of the oven is discretized,so that the number of pans will changes linearly.calculating through simple integer linear method.This will lead to the result of our model is not accurate enough.ApplicationWe have discussed the heat distribution in the oven in model1.The heat distributionis shown in figure1and figure2.Figure1Figure2As shown,the edges of the oven are distributed the most heat.Areas on both sides of the,is distributed the least heat.While the middle area absorbs little less than theedges.So,we can separate the oven area into six parts,as shown bellow.Part1and part2are distributed the least heat and located the furthest from the heat source(the electrical heating tubes locate on the bottom of the oven).So these two parts absorb the least heat.Part3and part4are distributed the least heat but locating the nearest to the heat source.Part5located far from the bottom but distributed the most heat.So simply,we regard the heat of part3,part4and part5as the same.Part6 is distributed the most heat,and locating nearest to the bottom.So,the heat part6 absorbs is the most in the oven.Based on our conclusion above,we invent the iPan,a new combined pan,which can bake three kinds of food at the same time.For example,one wants to have a little bread,pieces of sausage,a chicken wing and a pizza for lunch.He will have to wait 30minutes at least for his lunch,if he just has one oven.As the Chinese saying goes,‘Bear paws and fish never come together’.By using iPan can solve the issue for him,he could put the bread in pan1,pizza in pan2,sausage in pan5and chicken wing in pan6,and power on.Thus,he can have his delicious lunch in at least10minutes.So,bear paws and fish come together.We make an advertisement for Brownie Gourmet Magazine in the end of the paper.Advertising SheetsReferences[1]Heat Radiation,/view/f5ed1619cc7931b765ce1599.html, Page.4[2]G.S.Ranganath,Black-body Radiation,/article/10.1007%2Fs12045-008-0028-7?LI=true#,February, 2013[3]Kaiqing Lu,The Chemical Basis of Heat Transfer,Journal of Higher Correspondence Education(Natural Sciences Edition),Vol.3:p.33,1996[4]Mark M.Meerschaert,Mathematical Modeling(Third Edition),China:China Machine Press,May.2009[5]Jianzhong Zhang,Monte Carlo Method,Mathematics in Practice and Theory,Vol.1p.28,1974[6]Shallow water equations,/wiki/Shallow_water_equations。
美赛6种题型及通关详解
所谓6种题型，提示了部分题目的内容，但如果作为选题依据，作用非常有限。
如果是为了更好的选题，搞清楚MCM与ICM的区别，可能更有帮助。
选哪道题不是特别重要，重要的是应该“尽快”选题。
竞赛时间是固定的，选题的时间越长，做题的时间越少。
选题多花1小时，意味着建模和写论文的时间就少了1小时。
能获什么奖主要看实力，其次看运气。
准备越充分，胜算越大。
如果不想碰运气的话，早点动手准备吧。
六种题型怎么理解首先，MCM/ICM（2016年起）每年共有6道题，不是6种题，MCM是ABC三题，ICM是DEF三题。
对6道题目类型的描述，不是严格的划分，角度和依据都不相同。
continuous和discrete是指模型的类型，data insights是指问题数据的特征，operations research/network science和environmental science是指问题涉及到的学科，而environmental science和policy又是指问题本身的背景。
这不是按照同一标准对题目进行划分，之间有重叠。
最显然的，如果认为continuous和discrete是互补的，那么其他4道题目应该可以分别归入其中某一类。
其次，这些一两个词的描述过于笼统、宽泛，无法体现题目的具体特征，特别是A、B、F 题的描述，提供的信息非常少，说了几乎等于没说。
continuous、discrete把所有的模型全包括了。
policy范围也太广，人类主宰世界，方方面面都可能涉及政策问题。
而且F题也是2016年新增加的，只有2016年一年的题目（难民问题），暂时还看不出来什么规律。
而C题和D题的特征相对具体一些。
比如，针对2016年起MCM新增加的C题，COMAP （Consortium for Mathematics and Its Applications）专门发布了一份文档（中文简介）说明其特征。
概括起来，MCM的C题与数据有关，虽然称不上大数据，但压缩包也在100MB 以上，与MCM/ICM其他题目相比，数据量算是大的（实际上以往MCM/ICM的题目很少给数据），这就要求选这一题的参赛队要熟悉数据处理的基本方法，包括预处理、后处理等，并掌握相应的编程技能或是相关软件的使用方法。
美国数学建模题目2017至2017翻译
美国数学建模题目2017至2017翻译各位读友大家好，此文档由网络收集而来，欢迎您下载，谢谢篇一：2017年建模美赛C题带翻译Problem C: “Cooperate and navigate”Traffic capacity is limited in many regions of the United States due to the number of lanes of example, in the Greater Seattle area drivers experience long delays during peak traffic hoursbecause the volume of traffic exceeds the designed capacity of the road networks. This is particularlypronounced on Interstates 5, 90, and 405, as well as State Route 520, the roads of particular interestfor this problem.Self-driving, cooperating cars have been proposed as a solution to increase capacity of highwayswithout increasing number of lanes or roads. The behavior ofthese cars interacting with the existingtraffic flow and each other is not well understood at this point.The Governor of the state of Washington has asked for analysis of the effects of allowing self-driving,cooperating cars on the roads listed above in Thurston, Pierce, King, and Snohomish counties. (Seethe provided map and Excel spreadsheet). In particular, how do the effects change as thepercentage of self-driving cars increases from 10% to 50% to 90%? Do equilibria exist? Is there atipping point where performance changes markedly? Under what conditions, if any, should lanes bededicated to these cars? Does your analysis of your model suggest any other policy changes?Your answer should include a model of the effects on traffic flow of the number of lanes, peak and/oraverage trafficvolume, and percentage of vehicles using self-driving, cooperating systems. Yourmodel should address cooperation between self-driving cars as well as the interaction between self-driving and non-self-driving vehicles. Your model should then be applied to the data for the roads ofinterest, provided in the attached Excel spreadsheet.Your MCM submission should consist of a 1 page Summary Sheet, a 1-2 page letter to theGovernor’s office, and your solution (not to exceed 20 pages) for a maximum of 23 pages. Note: Theappendix and references do not count toward the 23 page limit. Some useful background information:On average, 8% of the daily traffic volume occurs during peak travel hours. ? The nominal speed limit for all these roads is 60 miles per hour.? Mileposts are numbered from southto north, and west to east.? Lane widths are the standard 12 feet.? Highway 90 is classified as a state route until it intersects Interstate 5.? In case of any conflict between the data provided in this problem and any other source, use thedata provided in this problem.Definitions:milepost: A marker on the road that measures distance in miles from either the start of the route or astate boundary.average daily traffic: The average number of cars per day driving on the : A limited access highway, part of a national system.state route: A state highway that may or may not be limited access.route ID: The number of the highway.increasing direction: Northbound for N-S roads, Eastbound for E-W roads.decreasing direction: Southbound for N-S roads, Westbound for E-W roads.问题C：“合作和导航”由于道路的数量，美国许多地区的交通容量有限。
2019美赛数学建模题目
2019美赛数学建模题目（实用版）目录1.2019 美赛数学建模题目概述2.题目 A：无人机系统的设计与优化3.题目 B：植物病害检测与分类4.题目 C：非洲地区电力供应网络优化5.题目 D：城市交通信号控制优化6.总结正文【2019 美赛数学建模题目概述】2019 年美国大学生数学建模竞赛（MCM/ICM）共有六道题目，分别为A、B、C、D、E、F，涉及无人机系统设计与优化、植物病害检测与分类、非洲地区电力供应网络优化、城市交通信号控制优化等多个领域。
这些题目旨在考验参赛选手运用数学方法和技术解决实际问题的能力。
【题目 A：无人机系统的设计与优化】题目 A 要求参赛选手设计一种无人机系统，用于在城市和乡村地区进行环境监测、基础设施检查和灾难评估等任务。
选手需要考虑无人机的尺寸、重量、速度、航程、传感器和执行器等因素，通过建立数学模型来优化无人机系统的性能。
【题目 B：植物病害检测与分类】题目 B 要求参赛选手研究植物病害检测与分类的方法。
选手需要利用图像处理、机器学习和数据挖掘等技术，从植物叶片的图像中提取特征，建立分类模型，实现对植物病害的自动检测和分类。
【题目 C：非洲地区电力供应网络优化】题目 C 要求参赛选手研究非洲地区电力供应网络的优化问题。
选手需要分析非洲地区的电力需求和供应现状，建立电力网络模型，通过优化电力供应网络的结构和运行方式，提高电力供应的可靠性和经济性。
【题目 D：城市交通信号控制优化】题目 D 要求参赛选手研究城市交通信号控制的优化问题。
选手需要建立城市交通网络模型，分析交通流量和拥堵状况，设计优化信号控制策略，以提高道路通行能力和减少拥堵。
【总结】2019 美赛数学建模题目涵盖了多个领域，旨在考验参赛选手运用数学方法和技术解决实际问题的能力。
2023年美赛数学建模c题题目
2023年美赛数学建模c题题目摘要：1.2023 年美赛数学建模C 题题目概述2.美赛数学建模竞赛的背景和历史3.2023 年美赛数学建模C 题的题目分析4.2023 年美赛数学建模C 题的解题思路和策略5.总结正文：一、2023 年美赛数学建模C 题题目概述2023 年美国大学生数学建模竞赛（美赛）的C 题题目为：“Wordle 游戏”。
该题目要求参赛者针对这个游戏的特点，运用数学建模的方法，对游戏中的词汇进行分类和排序，并分析游戏中的词汇分布规律。
二、美赛数学建模竞赛的背景和历史美国大学生数学建模竞赛（MCM/ICM）是由美国数学及其应用联合会（American Mathematical Society，简称AMS）主办的一项国际性数学建模竞赛，也是世界范围内最具影响力的数学建模竞赛之一。
该竞赛自1985 年创办以来，已经成功举办了30 多届，吸引了来自世界各地的数千所高校和数万名大学生参赛。
三、2023 年美赛数学建模C 题的题目分析2023 年美赛数学建模C 题的题目是“Wordle 游戏”，要求参赛者通过数学建模的方法，对游戏中的词汇进行分类和排序，并分析游戏中的词汇分布规律。
具体来说，参赛者需要考虑以下几个方面：1.对游戏中的词汇进行分类，包括根据词汇的意义、词性、字母数等方面进行分类；2.对分类后的词汇进行排序，包括根据词汇出现的频率、字母数等方面进行排序；3.分析游戏中的词汇分布规律，包括词汇在游戏中的出现频率、位置分布等方面。
四、2023 年美赛数学建模C 题的解题思路和策略针对2023 年美赛数学建模C 题，参赛者可以采用以下解题思路和策略：1.首先，对游戏中的词汇进行预处理，包括去除重复词汇、转换为小写等操作；2.其次，根据词汇的意义、词性、字母数等方面，对词汇进行分类；3.再次，根据词汇出现的频率、字母数等方面，对分类后的词汇进行排序；4.最后，分析词汇在游戏中的分布规律，包括词汇的出现频率、位置分布等方面。
优秀论文-图论
15
Algorithms in Mathematical Modeling
2015/8/26
Genetic Algorithm
4、模型分析
4.1对于问题一 对于题目所给的数据用MATLAB重新绘制图并求个路段 长度和警车的行驶时间， 再分别以交巡警平台为中心，求出不大于三分钟的最大 路径，然后将路径终点连接起来，再适当考虑发案率， 调整连接的区域，便是交巡警的管辖范围 。当发生重 大事件时，由靠近重要路段的交巡警迅速前往即可。 根据以上模型，A的交巡警平台如若不足，存在盲点， 则，我们需要在盲点处增加交巡警平台。
2015/8/26
Genetic Algorithm
数学建模竞赛常用算法(10)
10. 图象处理算法
赛题中有一类问题与图形有关，即使问题与图形无 关，论文中也会需要图片来说明问题，这些图形如何展 示以及如何处理就是需要解决的问题，通常使用MATLAB 进行处理。 01年A 题中需要你会读BMP 图象 98年美国A 题需要你知道三维插值计算 03年B 题要求更高，不但需要编程计算还要进行处理 数模论文中也有很多图片需要展示，解决这类问题 要熟悉MATLAB图形图像工具箱。
Genetic Algorithm
优秀论文导读
图论
Algorithms in Mathematical Modeling
Genetic Algorithm
数学建模竞赛常用算法(1)
1. 蒙特卡罗方法(Monte-Carlo方法, MC) 2. 数据拟合、参数估计、插值等数据处理算法 3. 规划类问题算法
6
Algorithms in Mathematical Modeling 2015/8/26
2021年美国大学生数学建模竞赛题目A--真菌范文六篇(含Matlab源代码)
do the different fungi interact and decompose ground litter in a fixed patch of land in different
?12122?1142?1???1???11112206?12?2242?2???1???2222110102025wheremoisturetoleranceiswelldeterminedby
2021年美国大学生数学建模竞赛题目A--真菌范文六
篇（含Matlab源代码）
问题A：真菌……………………………………………………………………2
Include predictions about the relative advantages and disadvantages for each species and
combinations of species likely to persist, and do so for different environments including arid,
(difference of each isolate’s competitive ranking and their
moisture niche width, both scaled to [0,1]) of various fungi
and the resulting wood decomposition rate (% mass loss
Your complete solution.