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每个人的心灵历程都是一首歌,我唱出我的所以我快乐。

 
 
 

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爱好广泛,一事无成,平生喜欢很多,至爱较少。喜欢书法,欧颜柳赵,也曾临过,但缺乏坚持,喜欢绘画,国画工写,西画彩描,也曾摹过,但缺乏深入,喜欢诗歌,诗词歌赋,也曾填过,但缺乏含蓄,喜欢舞蹈,单双多人,也曾迷过,但缺乏精巧,喜欢武术,刀枪棍棒,也曾练过,但缺乏功力,喜欢棋艺,军象跳围,也曾恋过,但缺乏心计,喜欢音乐,吹拉弹唱,也曾试过,但缺乏细胞。 不喜欢数学却上了贼船,不想当教师最终却以之为生。干一件事时间久了,可能会厌倦,也可能会喜欢。兴趣是靠自己培养的。若一个人愿意学习,相信久了会取得成绩。

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2013年美国大学生数学建模赛题原题与适当的翻译  

2013-02-01 14:22:49|  分类: 数学建模赛题 |  标签: |举报 |字号 订阅

  下载LOFTER 我的照片书  |

2013 Contest Problems MCM PROBLEMS   2013数学建模(MCM)赛题

PROBLEM A: The Ultimate Brownie Pan 问题A  终极的布朗尼锅

When baking in a rectangular pan heat is concentrated in the 4 corners and the product gets overcooked at the corners (and to a lesser extent at the edges). In a round pan the heat is distributed evenly over the entire outer edge and the product is not overcooked at the edges. However, since most ovens are rectangular in shape using round pans is not efficient with respect to using the space in an oven.
Develop a model to show the distribution of heat across the outer edge of a pan for pans of different shapes - rectangular to circular and other shapes in between.

Assume
1. A width to length ratio of W/L for the oven which is rectangular in shape.
2. Each pan must have an area of A.
3. Initially two racks in the oven, evenly spaced.
Develop a model that can be used to select the best type of pan (shape) under the following conditions:
1. Maximize number of pans that can fit in the oven (N)
2. Maximize even distribution of heat (H) for the pan
3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different values of W/L and p.
In addition to your MCM formatted solution, prepare a one to two page advertising sheet for the new Brownie Gourmet Magazine highlighting your design and results.

 当用方形的平底锅烤饼时,热量会集中在四角,食物就在四角(甚至还有边缘)烤焦了。在一个圆形的平底锅热量会均匀分布在整个外缘,食物就不会被边缘烤焦。但是,因为大多数烤箱是矩形的,使用圆形的平底锅不那么有效率。建立一个模型来表现热量在不同形状的平底锅的外缘的分布——包括从矩形到圆形以及中间的形状。

假定: 

1. 方形烤箱宽长比为W/L;

2. 所有参考锅的面积必须为A;

3. 最初烤箱的两个支架均衡放置。

构建一个模型用于在如下情境下筛选最佳锅型:

1. 适合该烤炉(N)的最大锅型数;

2. 最大化均匀热度分布(H)的锅型;

3. 最优化条件(1)和(2),各自占有比率为p和(1- p)用以描述W/L与p的差异性。

 除了提供标准的MCM格式解答之外,为布朗尼美食杂志提供一份1-2页的广告宣传,你需要突出你的设计和结果。

PROBLEM B: Water, Water, Everywhere  问题B  水,水,无处不在

Fresh water is the limiting constraint for development in much of the world. Build a mathematical model for determining an effective, feasible, and cost-efficient water strategy for 2013 to meet the projected water needs of [pick one country from the list below] in 2025, and identify the best water strategy. In particular, your mathematical model must address storage and movement; de-salinization; and conservation. If possible, use your model to discuss the economic, physical, and environmental implications of your strategy. Provide a non-technical position paper to governmental leadership outlining your approach, its feasibility and costs, and why it is the “best water strategy choice.”

Countries: United States, China, Russia, Egypt, or Saudi Arabia

 译文1: 淡水是世界上许多地方发展的限制因素。建立一个数学模型,来确定一个有效的、可行的、低成本的2013的用水计划,来满足某国(从下方的列表中选择一个国家)未来(2025年)的用水需求,并确定最优的用水计划。特别的,你的数学模型必须满足储存、运输、去盐渍化、和环保。如果可能的话,用你的模型来讨论你的计划对经济,自然和环境的影响。提供一个非技术性的意见书给政府领导概述你的方法,以及方法的可行性和成本,以及它为什么是“最好的用水计划的选择”国家:美国,中国,俄罗斯,埃及,或者沙特阿拉伯。

译文2: 淡水资源匮乏已经成了世界很多国家发展的瓶颈。建立某一国2013年的水资源战略数学模式,确定一个高效的、实际可行的、高效率利用成本的水资源战略来满足该国(美国,中国,俄罗斯,埃及或沙特阿拉伯,任选一个)2025年的预期水资源需求,并且确定最佳的水资源战略。尤其要注意的是,你所建立的数学模式必须考虑该国水资源储量和流动规律、海水淡水处理发展状况和水资源保护状况。可能的话,应用你所建立的模式讨论该模式可能产生的对经济、地理和环境方面的影响,为该国领导层提供一份非技术性的政府立场报告,并在该报告中概略介绍你的方法、该方法的可行性和成本核算,以及为什么该方法是“最佳的战略选择”。

可选择的国家:美国,中国,俄罗斯,埃及或沙特阿拉伯

2013年美国大学生数学建模赛题原题与适当的翻译 - 斜沟沿竹子 - 我快乐所以我博客

2013   ICM PROBLEM  交叉学科建模赛题

PROBLEM C: Network Modeling of Earth's Health   

 ICM问题 地球健康的网络建模

Click the title below to download a PDF of the 2013 ICM Problem.

Your ICM submission should consist of a 1 page Summary Sheet and your solution cannot exceed 20 pages for a maximum of 21 pages.

Network Modeling of Earth's Health

Background: Society is interested in developing and using models to forecast the biological and environmental health conditions of our planet. Many scientific studies have concluded that there is growing stress on Earth's environmental and biological systems, but there are very few global models to test those claims. The UN-backed Millennium Ecosystem Assessment Synthesis Report found that nearly two-thirds of Earth's life-supporting ecosystems— including clean water, pure air, and stable climate— are being degraded by unsustainable use. Humans are blamed for much of this damage. Soaring demands for food, fresh water, fuel, and timber have contributed to dramatic environmental changes; from deforestation to air, land, and water pollution. Despite the considerable research being conducted on local habitats and regional factors, current models do not adequately inform decision makers how their provincial polices may impact the overall health of the planet. Many models ignore complex global factors and are unable to determine the long-range impacts of potential policies. While scientists realize that the complex relationships and cross-effects in myriad environmental and biological systems impact Earth's biosphere, current models often ignore these relationships or limit the systems' connections. The system complexities manifest in multiple interactions, feedback loops, emergent behaviors, and impending state changes or tipping points. The recent Nature article written by 22 internationally known scientists entitled "Approaching a state shift in Earth's biosphere" outlines many of the issues associated with the need for scientific models and the importance of predicting potential state changes of the planetary health systems. The article provides two specific quantitative modeling challenges in their call for better predictive models:

1) To improve bio-forecasting through global models that embrace the complexity of Earth's interrelated systems and include the effects of local conditions on the global system and vice versa.

2) To identify factors that could produce unhealthy global state-shifts and to show how to use effective ecosystem management to prevent or limit these impending state changes. The resulting research question is whether we can build global models using local or regional components of the Earth's health that predict potential state changes and help decision makers design effective policies based on their potential impact on Earth's health. Although many warning signs are appearing, no one knows if Planet Earth is truly nearing a global tipping point or if such an extreme state is inevitable. The Nature article and many others point out that there are several important elements at work in the Earth's ecosystem (e.g., local factors, global impacts, multi-dimensional factors and relationships, varying time and spatial scales). There are also many other factors that can be included in a predictive model — human population, resource and habitat stress, habitat transformation, energy consumption, climate change, land use patterns, pollution, atmospheric chemistry, ocean chemistry, bio diversity, and political patterns such as social unrest and economic instability. Paleontologists have studied and modeled ecosystem behavior and response during previous cataclysmic state shifts and thus historic-based qualitative and quantitative information can provide background for future predictive models. However, it should be noted that human effects have increased significantly in our current biosphere situation.

Requirements:

You are members of the International Coalition of Modelers (ICM) which will soon be hosting a workshop entitled "Networks and Health of Planet Earth" and your research leader has asked you to perform modeling and analysis in advance of the workshop. He requires your team to do the following:

Requirement 1: Build a dynamic global network model of some aspect of Earth's health (you develop the measure) by identifying local elements of this condition (network nodes) and appropriately connecting them (network links) to track relationship and attribute effects. Since the dynamic nature of these effects is important, this network model must include a dynamic time element that allows the model to predict future states of this health measure. For example, your nodes could be nations, continents, oceans, habitats, or any combination of these or other elements which together constitute a global model. Your links could represent nodal or environmental influences, or the flow or propagation of physical elements (such as pollution) over time. Your health measure could be any element of Earth's condition to include demographic, biological, environmental, social, political, physical, and/or chemical conditions. Be sure to define all the elements of your model and explain the scientific bases for your modeling decisions about network measures, nodal entities, and link properties. Determine a methodology to set any parameters and explain how you could test your model if sufficient data were available. What kinds of data could be used to validate or verify the efficacy of your model? (Note: If you do not have the necessary data to determine parameters or perform verification, do not throw out the model. Your supervisor realizes that, at this stage, good creative ideas and theories are as important as verified data-based models.) Make sure you include the human element in your model and explain where human behavior and government policies could affect the results of your model.

The Nature article and many others point out that there are several important elements at work in the Earth's ecosystem (e.g., local factors, global impacts, multi-dimensional factors and relationships, varying time and spatial scales). There are also many other factors that can be included in a predictive model — human population, resource and habitat stress, habitat transformation, energy consumption, climate change, land use patterns, pollution, atmospheric chemistry, ocean chemistry, bio diversity, and political patterns such as social unrest and economic instability. Paleontologists have studied and modeled ecosystem behavior and response during previous cataclysmic state shifts and thus historic-based qualitative and quantitative information can provide background for future predictive models. However, it should be noted that human effects have increased significantly in our current biosphere situation.

Requirements:

You are members of the International Coalition of Modelers (ICM) which will soon be hosting a workshop entitled "Networks and Health of Planet Earth" and your research leader has asked you to perform modeling and analysis in advance of the workshop. He requires your team to do the following:

Requirement 1: Build a dynamic global network model of some aspect of Earth's health (you develop the measure) by identifying local elements of this condition (network nodes) and appropriately connecting them (network links) to track relationship and attribute effects. Since the dynamic nature of these effects is important, this network model must include a dynamic time element that allows the model to predict future states of this health measure. For example, your nodes could be nations, continents, oceans, habitats, or any combination of these or other elements which together constitute a global model. Your links could represent nodal or environmental influences, or the flow or propagation of physical elements (such as pollution) over time.

Your health measure could be any element of Earth's condition to include demographic, biological, environmental, social, political, physical, and/or chemical conditions. Be sure to define all the elements of your model and explain the scientific bases for your modeling decisions about network measures, nodal entities, and link properties. Determine a methodology to set any parameters and explain how you could test your model if sufficient data were available. What kinds of data could be used to validate or verify the efficacy of your model? (Note: If you do not have the necessary data to determine parameters or perform verification, do not throw out the model. Your supervisor realizes that, at this stage, good creative ideas and theories are as important as verified data-based models.) Make sure you include the human element in your model and explain where human behavior and government policies could affect the results of your model.

点击标题下面的2013年ICM问题,以PDF格式下载。

您的ICM提交应包括一个第1页汇总表和您的解决方案不能超过20页,最多21页。地球健康的网络建模

 背景:

社会是有兴趣在开发和使用模型来预测我们的星球的生物和环境健康状况。许多科学研究得出的结论是对地球环境和生物系统的越来越大的压力,但也有极少数的全球模型,以测试这些要求。联合国支持的千年生态系统评估综合报告发现,近三分之二的地球上的生命支持,包括干净的水,纯净的空气,稳定的气候不可持续的利用正在退化的生态系统。人类被指责为多,这种损害。飞涨的食品,淡水,燃料和木材的需求环境急剧变化,从毁林空气,土地,和水的污染作出了贡献。

尽管本地生境和区域因素进行了大量的研究,目前的模型没有充分告知决策者如何省。政策可能会影响到整个地球健康的。许多模型忽略了复杂的全球性因素,是无法确定远程的潜在政策的影响。

虽然科学家们知道,无数的环境和生物系统的影响地球的生物圈中的复杂关系和交叉效应,目前的模型往往忽略这些关系或限制系统的连接。该系统的复杂性表现在多个交互,反馈回路,紧急行为,以及即将发生的状态变化或临界点。最近的自然写的文章了22个国际知名科学家题为“接近地球生物圈的状态转变”,列出了很多相关的问题需要科学的模型和预测潜在的行星卫生系统状态的变化的重要性。本文提供了两个具体的量化建模的挑战, 他们要求更好的预测模型:

1)为了提高生物预测,通过全球性的模型,拥抱地球上的相互关联的系统的复杂性,包括当地条件的影响,对全球系统,反之亦然。

2)确定因素,可能会产生不健康的全局状态变化,并显示如何使用有效的生态 系统管理,以防止或限制这些即将发生的状态变化。

研究的问题是,我们是否可以建立全球性的模型,利用当地或地区的地球的健康,预测潜在状态的改变和决策者的潜在影响地球的健康的基础上设计出有效的政策。虽然许多警告标志出现,没有人知道,如果地球是真正的接近一个全球性的 临界点,如果这种极端的状态是不可避免的。

自然的文章和其他许多人指出,有几个重要的元素在地球生态系统中的工作(例如,本地因素的影响,全球性的影响,多维度的因素和关系,不同的时间和空间尺度)。也有许多其他因素的预测模型 - 人口,资源和栖息地的压力,栖息地改造,能源消耗,气候变化,土地利用方式,污染,大气化学,海洋化学,生物多样性,和政治模式可以包含在如社会动荡和经济的不稳定。古生物学家的研究和对未来的预测模型模拟生态系统的行为和反应在以前的灾难性的状态变化,因此,基于历史的定性和定量的信息可以提供背景。然而,应该指出的是,人类的影响已在我们目前生物圈情况显着增加。

 要求:

 你是会员的国际联盟的建模(ICM)。即将举办了一个题为“网络和地球的健康”,研究的领导者,要求你提前车间进行建模和分析。他要求你的团队做到以下几点: 

要求1:建立一个动态的全球网络模型的某些方面的地球的健康(发展的措施),

这种情况下的本地元素(网络节点)和适当连接(网络链接)跟踪关系和属性效果。由于这些影响的动态特性是很重要的,这个网络模型必须包括一个动态的元素,允许模型来预测未来的状态,这卫生措施。例如,节点可以是国家,大陆,海洋,栖息地,或这些的任意组合或其他元素,它们共同构成了全球性的模型。您的链接可以代表节点或环境的影响,或物理元素(如污染),随着时间的推移的流量或传播。你的健康措施可能是地球上的条件,包括人口,生物,环境,社会,政治,物理和或化学条件的任何元素。要确保网络的措施,节点实体和链路属性,你的模型中定义的所有元素,并解释您的建模决策的科学依据。

确定一种方法来设置任何参数,并解释如何,你可以测试你的模型,如果有足够的数据。什么样的数据可以用来验证或验证你的模型的有效性?

 (注:如果你不具备必要的数据,以确定参数进行验证,不扔出去的模型。你的上司意识到,在这个阶

段,好的创意思想和理论是重要的,因为经核实的数据为基础的模型。)确保你包括人的因素在模型中,

解释人类的行为和政府政策可能会影响你的模型的结果。

 

潜在的有用的参考文献包括:

  安东尼·D. Barnosky,霍尔迪Bascompte,伊丽莎白A. Hadly,埃里克·L.伯洛,约翰·哈特,詹姆斯·

H.布朗,MIKAEL Fortelius,韦恩M.盖茨,艾伦·黑斯廷斯,巴勃罗·马尔凯,新D.马丁内斯,阿恩Mooers

彼得Roopnarine,Geerat Vermeij,约翰·威廉姆斯,迷迭香吉莱斯皮,贾斯汀Kitzes,查尔斯·马歇尔,尼古拉斯Matzke,大卫P.明德尔,埃洛伊雷维利亚,亚当·B·史密斯。的“走近状态转变在地球的生物圈”。自然,2012,486(7401):52  DOI:10.1038/nature11018 Donella

草甸,约根兰德,和丹尼斯·梅多斯。“增长的极限:30年更新的,2004年。

 罗伯特·沃森(Robert Watson)和A.Hamid Zakri。联合国千年生态系统评估综合报告,联合国的报告,2005年。

美国加州大学 - 伯克利分校。 “即将引爆点的地球的证据。”   科学日报,2012年6月6日。网络。 2012年10月22日。

 

 

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