2013美赛ABC试题及翻译
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2013 Contest ProblemsMCM PROBLEMSPROBLEM A: The Ultimate Brownie PanWhen 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.当在一个矩形的锅中烘烤时热量集中在烤箱的4个角落中，并在角落处的食物烤的过了（在某种程度上边缘也是这样）。
在一个圆形盘的热量被均匀地分布在整个外缘，在边缘处的食物烤的不会过头。
然而，因为大多数烤箱是方形的，使用原型的平底锅效率是不高的相对于烤箱中的空间。
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.建立一个模型来说明不同形状的锅(圆形方形或其他形状)的外边缘热量的不同分布。
Assume1. 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.假设1.矩形烤箱的的宽度与长度之比是W / L。
2.每个盘子的面积都是A3.最初，两个机架在烤箱，间隔均匀。
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 pan3. Optimize a combination of conditions (1) and (2) where weights p and (1- p) are assigned to illustrate how the results vary with different valuesof W/L and p.建立一个模型，在下列情况下，可用于选择最佳的锅（形状）：1.可以放到烤箱中的锅的最大数量是（N）2.烤箱里最大限度地均匀分布热量为（H），3.优化的组合的条件（1）和（2）式的权重p和(1 – p)，用来说明如何随不同的值的W/L和P的变化而影响最终结果。
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.除了你的格式化的解决方案,准备一个一到两页的广告页为新布朗尼美食杂志突出自己的设计和结果。
PROBLEM B: Water, Water, EverywhereFresh 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问题B:水,水,到处都是淡水已经是约束世界上大部分国家发展的一个限制条件。
建立一个数学模型来确定一个有效的、可行的,和有成本效益的水侧罗,以满足从2013年开始[选择一个国家从下面的列表]到2025年的水需求,和确定最佳水策略。
特别是,你的数学模型必须解决水的存储和移动;去盐碱化;环保等问题。
如果可能的话,用你的模型来讨论经济、物理和环境影响的战略。
提供一个非技术意见书给政府领导概述你的方法,其可行性和成本,以及为什么它是“最好的水策略选择。
”国家:美国、中国、俄罗斯、埃及或沙特阿拉伯ICM PROBLEMPROBLEM C: Network Modeling of Earth's HealthClick 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 Health2013 ICM ProblemNetwork Modeling of Earth's HealthBackground: 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 thelong-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:背景：建立并使用模型去预测我们星球的生态环境条件是现在社会最感兴趣的话题。
