2001 MCM A: Choosing a Bicycle Wheel
Cyclists have different types of wheels they can use on their bicycles. The two basic types of wheels are those constructed using wire spokes and those constructed of a solid disk (see Figure 1) The spoked wheels are lighter, but the solid wheels are more aerodynamic. A solid wheel is never used on the front for a road race but can be used on the rear of the bike.
Professional cyclists look at a racecourse and make an educated guess as to what kind of wheels should be used. The decision is based on the number and steepness of the hills, the weather, wind speed, the competition, and other considerations. The director sportif of your favorite team would like to have a better system in place and has asked your team for information to help determine what kind of wheel should be used for a given course.
Figure 1: A solid wheel is shown on the left and a spoked wheel is shown on the right.
The director sportif needs specific information to help make a decision and has asked your team to accomplish the tasks listed below. For each of the tasks assume that the same spoked wheel will always be used on the front but there is a choice of wheels for the rear.
Task 1. Provide a table giving the wind speed at which the power required for a solid rear wheel is less than for a spoked rear wheel.
The table should include the wind speeds for different road grades starting from zero percent to ten percent in one percent increments.
(Road grade is defined to be the ratio of the total rise of a hill divided by the length of the road. If the hill is viewed as a triangle, the grade is the sine of the angle at the bottom of the hill.) A rider starts at the bottom of the hill at a speed of 45 kph, and the deceleration of the rider is proportional to the road grade.
A rider will lose about 8 kph for a five percent grade over 100
meters.
?Task 2. Provide an example of how the table could be used for a specific time trial course.
?Task 3. Determine if the table is an adequate means for deciding on the wheel configuration and offer other suggestions as to how to make this decision.
2001 MCM B: Escaping a Hurricane's Wrath (An Ill Wind...)
Evacuating the coast of South Carolina ahead of the predicted landfall of Hurricane Floyd in 1999 led to a monumental traffic jam. Traffic slowed to a standstill on Interstate I-26, which is the principal route going inland from Charleston to the relatively safe haven of Columbia in the center of the state. What is normally an easy two-hour drive took up to 18 hours to complete. Many cars simply ran out of gas along the way. Fortunately, Floyd turned north and spared the state this time, but the public outcry is forcing state officials to find ways to avoid a repeat of this traffic nightmare.
The principal proposal put forth to deal with this problem is the reversal of traffic on I-26, so that both sides, including the coastal-bound lanes, have traffic headed inland from Charleston to Columbia. Plans to carry this out have been prepared (and posted on the Web) by the South Carolina Emergency Preparedness Division. Traffic reversal on principal roads leading inland from Myrtle Beach and Hilton Head is also planned.
A simplified map of South Carolina is shown. Charleston has approximately 500,000 people, Myrtle Beach has about 200,000 people, and another 250,000 people are spread out along the rest of the coastal strip. (More accurate data, if sought, are widely available.)
The interstates have two lanes of traffic in each direction except in the metropolitan areas where they have three. Columbia, another metro area of around 500,000 people, does not have sufficient hotel space to accommodate the evacuees (including some coming from farther north by other routes), so some traffic continues outbound on I-26 towards Spartanburg; on I-77 north to Charlotte; and on I-20 east to Atlanta. In 1999, traffic leaving Columbia going northwest was moving only very slowly. Construct a model for the problem to investigate what strategies may reduce the congestion observed in 1999. Here are the questions that need to be addressed:
1.Under what conditions does the plan for turning the two
coastal-bound lanes of I-26 into two lanes of Columbia-bound
traffic, essentially turning the entire I-26 into one-way traffic, significantly improve evacuation traffic flow?
2.In 1999, the simultaneous evacuation of the state's entire coastal
region was ordered. Would the evacuation traffic flow improve under an alternative strategy that staggers the evacuation, perhaps
county-by-county over some time period consistent with the pattern of how hurricanes affect the coast?
3.Several smaller highways besides I-26 extend inland from the coast.
Under what conditions would it improve evacuation flow to turn
around traffic on these?
4.What effect would it have on evacuation flow to establish more
temporary shelters in Columbia, to reduce the traffic leaving
Columbia?
5.In 1999, many families leaving the coast brought along their boats,
campers, and motor homes. Many drove all of their cars. Under what conditions should there be restrictions on vehicle types or numbers of vehicles brought in order to guarantee timely evacuation?
6.It has been suggested that in 1999 some of the coastal residents
of Georgia and Florida, who were fleeing the earlier predicted
landfalls of Hurricane Floyd to the south, came up I-95 and
compounded the traffic problems. How big an impact can they have on the evacuation traffic flow? Clearly identify what measures of performance are used to compare strategies. Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.
Clearly identify what measures of performance are used to compare strategies.
Required: Prepare a short newspaper article, not to exceed two pages, explaining the results and conclusions of your study to the public.
2002 MCM A: Wind and Waterspray
An ornamental fountain in a large open plaza surrounded by buildings squirts water high into the air. On gusty days, the wind blows spray from the fountain onto passersby. The water-flow from the fountain is controlled by a mechanism linked to an anemometer (which measures wind speed and direction) located on top of an adjacent building. The objective of this control is to provide passersby with an acceptable balance between an attractive spectacle and a soaking: The harder the wind blows, the lower the water volume and height to which the water is squirted, hence the less spray falls outside the pool area.
Your task is to devise an algorithm which uses data provided by the anemometer to adjust the water-flow from the fountain as the wind conditions change.
2002 MCM B: Airline Overbooking
You're all packed and ready to go on a trip to visit your best friend in New York City. After you check in at the ticket counter, the airline clerk announces that your flight has been overbooked. Passengers need to check in immediately to determine if they still have a seat.
Historically, airlines know that only a certain percentage of passengers who have made reservations on a particular flight will actually take that flight. Consequently, most airlines overbook-that is, they take more reservations than the capacity of the aircraft. Occasionally, more passengers will want to take a flight than the capacity of the plane leading to one or more passengers being bumped and thus unable to take the flight for which they had reservations.
Airlines deal with bumped passengers in various ways. Some are given nothing, some are booked on later flights on other airlines, and some are given some kind of cash or airline ticket incentive.
Consider the overbooking issue in light of the current situation: Less flights by airlines from point A to point B Heightened security at and around airports Passengers' fear Loss of billions of dollars in revenue by airlines to date
Build a mathematical model that examines the effects that different overbooking schemes have on the revenue received by an airline company in order to find an optimal overbooking strategy, i.e., the number of people by which an airline should overbook a particular flight so that the company's revenue is maximized. Insure that your model reflects the issues above, and consider alternatives for handling “bumped”passengers. Additionally, write a short memorandum to the airline's CEO summarizing your findings and analysis.
2003 MCM A: The Stunt Person
An exciting action scene in a movie is going to be filmed, and you are the stunt coordinator! A stunt person on a motorcycle will jump over an elephant and land in a pile of cardboard boxes to cushion their fall. You need to protect the stunt person, and also use relatively few cardboard boxes (lower cost, not seen by camera, etc.).
Your job is to:
?determine what size boxes to use
?determine how many boxes to use
?determine how the boxes will be stacked
?determine if any modifications to the boxes would help
?generalize to different combined weights (stunt person & motorcycle) and different jump heights
Note that, in “Tomorrow Never Dies”, the James Bond character on a motorcycle jumps over a helicopter.
2003 MCM B: Gamma Knife Treatment Planning
Stereotactic radiosurgery delivers a single high dose of ionizing radiation to a radiographically well-defined, small intracranial 3D brain tumor without delivering any significant fraction of the prescribed dose to the surrounding brain tissue. Three modalities are commonly used in this area; they are the gamma knife unit, heavy charged particle beams, and external high-energy photon beams from linear accelerators.
The gamma knife unit delivers a single high dose of ionizing radiation emanating from 201 cobalt-60 unit sources through a heavy helmet. All 201 beams simultaneously intersect at the isocenter, resulting in a spherical (approximately) dose distribution at the effective dose levels. Irradiating the isocenter to deliver dose is termed a “shot.” Shots can be represented as different spheres. Four interchangeable outer collimator helmets with beam channel diameters of 4, 8, 14, and 18 mm are available for irradiating different size volumes. For a target volume larger than one shot, multiple shots can be used to cover the entire target. In practice, most target volumes are treated with 1 to 15 shots. The target volume is a bounded, three-dimensional digital image that usually consists of millions of points.
The goal of radiosurgery is to deplete tumor cells while preserving normal structures. Since there are physical limitations and biological uncertainties involved in this therapy process, a treatment plan needs to account for all those limitations and uncertainties. In general, an optimal treatment plan is designed to meet the following requirements.
1.Minimize the dose gradient across the target volume.
2.Match specified isodose contours to the target volumes.
3.Match specified dose-volume constraints of the target and critical
organ.
4.Minimize the integral dose to the entire volume of normal tissues
or organs.
5.Constrain dose to specified normal tissue points below tolerance
doses.
6.Minimize the maximum dose to critical volumes.
In gamma unit treatment planning, we have the following constraints:
1.Prohibit shots from protruding outside the target.
2.Prohibit shots from overlapping (to avoid hot spots).
3.Cover the target volume with effective dosage as much as possible.
But at least 90% of the target volume must be covered by shots.
https://www.doczj.com/doc/4e6738619.html,e as few shots as possible.
Your tasks are to formulate the optimal treatment planning for a gamma knife unit as a sphere-packing problem, and propose an algorithm to find a solution. While designing your algorithm, you must keep in mind that your algorithm must be reasonably efficient.
2004 MCM A: Are Fingerprints Unique?
It is a commonplace belief that the thumbprint of every human who has ever lived is different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.
2004 MCM B: A Faster QuickPass System
“QuickPass” systems are increasingly appearing to reduce people's time waiting in line, whether it is at tollbooths, amusement parks, or elsewhere. Consider the design of a QuickPass system for an amusement park. The amusement park has experimented by offering QuickPasses for several popular rides as a test. The idea is that for certain popular rides you can go to a kiosk near that ride and insert your daily park entrance ticket, and out will come a slip that states that you can return to that ride at a specific time later. For example, you insert your daily park entrance ticket at 1:15 pm, and the QuickPass states that you can come back between 3:30 and 4:30 pm when you can use your slip to enter a second, and presumably much shorter, line that will get you to the ride faster. To prevent people from obtaining QuickPasses for several rides at once, the QuickPass machines allow you to have only one active QuickPass at a time. You have been hired as one of several competing consultants to improve the operation of QuickPass. Customers have been complaining about some anomalies in the test system. For example, customers observed that in one instance QuickPasses were being offered for a return time as long as 4 hours later. A short time later on the same ride, the QuickPasses were given for times only an hour or so later. In some instances, the lines for people with Quickpasses are nearly as long and slow as the regular lines.
The problem then is to propose and test schemes for issuing QuickPasses in order to increase people's enjoyment of the amusement park. Part of the problem is to determine what criteria to use in evaluating alternative schemes. Include in your report a non-technical summary for amusement park executives who must choose between alternatives from competing consultants.
2005 MCM A: Flood Planning
Lake Murray in central South Carolina is formed by a large earthen dam, which was completed in 1930 for power production. Model the flooding downstream in the event there is a catastrophic earthquake that breaches the dam.
Two particular questions:
Rawls Creek is a year-round stream that flows into the Saluda River a short distance downriver from the dam. How much flooding will occur in Rawls Creek from a dam failure, and how far back will it extend?
Could the flood be so massive downstream that water would reach up to the S.C. State Capitol Building, which is on a hill overlooking the Congaree River?
2005 MCM B: Tollbooths
Heavily-traveled toll roads such as the Garden State Parkway, Interstate 95, and so forth, are multi-lane divided highways that are interrupted at intervals by toll plazas. Because collecting tolls is usually unpopular, it is desirable to minimize motorist annoyance by limiting the amount of traffic disruption caused by the toll plazas. Commonly, a much larger number of tollbooths is provided than the number of travel lanes entering the toll plaza. Upon entering the toll plaza, the flow of vehicles fans out to the larger number of tollbooths, and when leaving the toll plaza, the flow of vehicles is required to squeeze back down to a number of travel lanes equal to the number of travel lanes before the toll plaza. Consequently, when traffic is heavy, congestion increases upon departure from the toll plaza. When traffic is very heavy, congestion also builds at the entry to the toll plaza because of the time required for each vehicle to pay the toll.
Make a model to help you determine the optimal number of tollbooths to deploy in a barrier-toll plaza. Explicitly consider the scenario where
there is exactly one tollbooth per incoming travel lane. Under what conditions is this more or less effective than the current practice? Note that the definition of “optimal” is up to you to determine.
2006 MCM A: Positioning and Moving Sprinkler Systems for Irrigation
There are a wide variety of techniques available for irrigating a field. The technologies range from advanced drip systems to periodic flooding. One of the systems that is used on smaller ranches is the use of “hand move” irrigation systems. Lightweight aluminum pipes with sprinkler heads are put in place across fields, and they are moved by hand at periodic intervals to insure that the whole field receives an adequate amount of water. This type of irrigation system is cheaper and easier to maintain than other systems. It is also flexible, allowing for use on a wide variety of fields and crops. The disadvantage is that it requires a great deal of time and effort to move and set up the equipment at regular intervals.
Given that this type of irrigation system is to be used, how can it be configured to minimize the amount of time required to irrigate a field that is 80 meters by 30 meters? For this task you are asked to find an algorithm to determine how to irrigate the rectangular field that minimizes the amount of time required by a rancher to maintain the irrigation system. One pipe set is used in the field. You should determine the number of sprinklers and the spacing between sprinklers, and you should find a schedule to move the pipes, including where to move them.
A pipe set consists of a number of pipes that can be connected together in a straight line. Each pipe has a 10 cm inner diameter with rotating spray nozzles that have a 0.6 cm inner diameter. When put together the resulting pipe is 20 meters long. At the water source, the pressure is 420 Kilo- Pascal’s and has a flow rate of 150 liters per minute. No part of the field should receive more than 0.75 cm per hour of water, and each part of the field should receive at least 2 centimeters of water every 4 days. The total amount of water should be applied as uniformly as possible.
2006 MCM B: Wheel Chair Access at Airports
One of the frustrations with air travel is the need to fly through multiple airports, and each stop generally requires each traveler to change to a different airplane. This can be especially difficult for people who are
not able to easily walk to a different flight's waiting area. One of the ways that an airline can make the transition easier is to provide a wheel chair and an escort to those people who ask for help. It is generally known well in advance which passengers require help, but it is not uncommon to receive notice when a passenger first registers at the airport. In rare instances an airline may not receive notice from a passenger until just prior to landing.
Airlines are under constant pressure to keep their costs down. Wheel chairs wear out and are expensive and require maintenance. There is also a cost for making the escorts available. Moreover, wheel chairs and their escorts must be constantly moved around the airport so that they are available to people when their flight lands. In some large airports the time required to move across the airport is nontrivial. The wheel chairs must be stored somewhere, but space is expensive and severely limited in an airport terminal. Also, wheel chairs left in high traffic areas represent a liability risk as people try to move around them. Finally, one of the biggest costs is the cost of holding a plane if someone must wait for an escort and becomes late for their flight. The latter cost is especially troubling because it can affect the airline's average flight delay which can lead to fewer ticket sales as potential customers may choose to avoid an airline.
Epsilon Airlines has decided to ask a third party to help them obtain a detailed analysis of the issues and costs of keeping and maintaining wheel chairs and escorts available for passengers. The airline needs to find a way to schedule the movement of wheel chairs throughout each day in a cost effective way. They also need to find and define the costs for budget planning in both the short and long term.
Epsilon Airlines has asked your consultant group to put together a bid to help them solve their problem. Your bid should include an overview and analysis of the situation to help them decide if you fully understand their problem. They require a detailed description of an algorithm that you would like to implement which can determine where the escorts and wheel chairs should be and how they should move throughout each day. The goal is to keep the total costs as low as possible. Your bid is one of many that the airline will consider. You must make a strong case as to why your solution is the best and show that it will be able to handle a wide range of airports under a variety of circumstances.
Your bid should also include examples of how the algorithm would work for a large (at least 4 concourses), a medium (at least two concourses), and a small airport (one concourse) under high and low traffic loads. You should determine all potential costs and balance their respective weights.
Finally, as populations begin to include a higher percentage of older people who have more time to travel but may require more aid, your report should include projections of potential costs and needs in the future with recommendations to meet future needs.
2007 MCM A: Gerrymandering
Gerrymandering The United States Constitution provides that the House of Representatives shall be composed of some number (currently 435) of individuals who are elected from each state in proportion to the state’s population relative to that of the country as a whole. While this provides a way of determining how many representatives each state will have, it says nothing about how the district represented by a particular representative shall be determined geographically. This oversight has led to egregious (at least some people think so, usually not the incumbent) district shapes that look “unnatural” by some standards.
Hence the following question: Suppose you were given the opportunity to draw congressional districts for a state. How would you do so as a purely “baseline” exercise to create the “simplest” shapes for all the districts in a state? The rules include only that each district in the state must contain the same population. The definition of “simple” is up to you; but you need to make a convincing argument to voters in the state that your solution is fair. As an application of your method, draw geographically simple congressional districts for the state of New York.
2007 MCM B: The Airplane Seating Problem
Airlines are free to seat passengers waiting to board an aircraft in any order whatsoever. It has become customary to seat passengers with special needs first, followed by first-class passengers (who sit at the front of the plane). Then coach and business-class passengers are seated by groups of rows, beginning with the row at the back of the plane and proceeding forward.
Apart from consideration of the passengers’ wait time, from the airline’s point of view, time is money, and boarding time is best minimized. The plane makes money for the airline only when it is in motion, and long boarding times limit the number of trips that a plane can make in a day.
The development of larger planes, such as the Airbus A380 (800 passengers), accentuate the problem of minimizing boarding (and deboarding) time.
Devise and compare procedures for boarding and deboarding planes with varying numbers of passengers: small (85–210), midsize (210–330), and large (450–800).
Prepare an executive summary, not to exceed two single-spaced pages, in which you set out your conclusions to an audience of airline executives, gate agents, and flight crews.
An article appeared in the NY Times Nov 14, 2006 addressing procedures currently being followed and the importance to the airline of finding better solutions. The article can be seen at:
https://www.doczj.com/doc/4e6738619.html,/2006/11/14/business/14boarding.html
2008 MCM A: Take a Bath
Consider the effects on land from the melting of the north polar ice cap due to the predicted increase in global temperatures. Specifically, model the effects on the coast of Florida every ten years for the next 50 years due to the melting, with particular attention given to large metropolitan areas. Propose appropriate responses to deal with this. A careful discussion of the data used is an important part of the answer.
2008 MCM B: Creating Sudoku Puzzles
Develop an algorithm to construct Sudoku puzzles of varying difficulty. Develop metrics to define a difficulty level. The algorithm and metrics should be extensible to a varying number of difficulty levels. You should illustrate the algorithm with at least 4 difficulty levels. Your algorithm should guarantee a unique solution. Analyze the complexity of your algorithm. Your objective should be to minimize the complexity of the algorithm and meet the above requirements.
2009 MCM A: Designing a Traffic Circle
Many cities and communities have traffic circles—from large ones with many lanes in the circle (such as at the Arc de Triomphe in Paris and the Victory Monument in Bangkok) to small ones with one or two lanes in the circle. Some of these traffic circles position a stop sign or a yield sign on every incoming road that gives priority to traffic already in the circle; some position a yield sign in the circle at each incoming road to give priority to incoming traffic; and some position a traffic light on each
incoming road (with no right turn allowed on a red light). Other designs may also be possible.
The goal of this problem is to use a model to determine how best to control traffic flow in, around, and out of a circle. State clearly the objective(s) you use in your model for making the optimal choice as well as the factors that affect this choice. Include a Technical Summary of not more than two double-spaced pages that explains to a Traffic Engineer how to use your model to help choose the appropriate flow-control method for any specific traffic circle. That is, summarize the conditions under which each type of traffic-control method should be used. When traffic lights are recommended, explain a method for determining how many seconds each light should remain green (which may vary according to the time of day and other factors). Illustrate how your model works with specific examples.
2009 MCM B: Energy and the Cell Phone
This question involves the “energy” consequences of the cell phone revolution. Cell phone usage is mushrooming, and many people are using cell phones and giving up their landline telephones. What is the consequence of this in terms of electricity use? Every cell phone comes with a battery and a recharger.
Requirement 1
Consider the current US, a country of about 300 million people. Estimate from available data the number H of households, with m members each, that in the past were serviced by landlines. Now, suppose that all the landlines are replaced by cell phones; that is, each of the m members of the household has a cell phone. Model the consequences of this change for electricity utilization in the current US, both during the transition and during the steady state. The analysis should take into account the need for charging the batteries of the cell phones, as well as the fact that cell phones do not last as long as landline phones (for example, the cell phones get lost and break).
Requirement 2
Consider a second “Pseudo US”—a country of about 300 million people with about the same economic status as the current US. However, this emerging country has neither landlines nor cell phones. What is the optimal way of providing phone service to this country from an energy perspective? Of course, cell phones have many social consequences and uses that landline phones do not allow. A discussion of the broad and hidden
consequences of having only landlines, only cell phones, or a mixture of the two is welcomed.
Requirement 3
Cell phones periodically need to be recharged. However, many people always keep their recharger plugged in. Additionally, many people charge their phones every night, whether they need to be recharged or not. Model the energy costs of this wasteful practice for a Pseudo US based upon your answer to Requirement 2. Assume that the Pseudo US supplies electricity from oil. Interpret your results in terms of barrels of oil.
Requirement 4
Estimates vary on the amount of energy that is used by various recharger types (TV, DVR, computer peripherals, and so forth) when left plugged in but not charging the device. Use accurate data to model the energy wasted by the current US in terms of barrels of oil per day.
Requirement 5
Now consider population and economic growth over the next 50 years. How might a typical Pseudo US grow? For each 10 years for the next 50 years, predict the energy needs for providing phone service based upon your analysis in the first three requirements. Again, assume electricity is provided from oil. Interpret your predictions in term of barrels of oil.
经典广告词中英文翻译 2． Obey your thirst．服从你的渴望。（雪碧） 3． The new digital era．数码新时代。（索尼影碟机） 4． We lead． Others copy．我们领先，他人仿效。（理光复印机） 5． Impossible made possible．使不可能变为可能。（佳能打印机） 6． Take time to indulge．尽情享受吧！（雀巢冰激凌） 7． The relentless pursuit of perfection．不懈追求完美。（凌志轿车） 8． Poetry in motion， dancing close to me．动态的诗，向我舞近。（丰田汽车）9． Come to where the flavor is． Marlboro Country． 光临风韵之境——万宝路世界。（万宝路香烟） 10．To me， the past is black and white， but the future is always color．对我而言，过去平淡无奇；而未来，却是绚烂缤纷。（轩尼诗酒） 11. Just do it. 只管去做。（耐克运动鞋） 12. Ask for more. 渴望无限。（百事流行鞋） 13. The taste is great. 味道好极了。（雀巢咖啡） 14. Feel the new space. 感受新境界。（三星电子） 15. Intelligence everywhere. 智慧演绎，无处不在。（摩托罗拉手机） 16. The choice of a new generation. 新一代的选择。（百事可乐） 17. We integrate, you communicate. 我们集大成，您超越自我。（三菱电工） 18. Take TOSHIBA, take the world. 拥有东芝，拥有世界。（东芝电子） 19. Let’s make things better. 让我们做得更好。（飞利浦电子） 20. No business too small, no problem too big. 没有不做的小生意，没有解决不了的大问题。（IBM公司） 1 Good to the last drop? ?滴滴香浓，意犹未尽??麦式咖啡Maxwell 2 Time is what you make of it? ?天长地久? ?斯沃奇手表Swatch 3Make yourself heard? ?理解就是沟通? ???爱立信Ericsson 4Start ahead? ? 成功之路从头开始? ? 飘柔rejoice 5Diamond lasts forever 钻石恒久远，一颗永流传第比尔斯De Bieeres 6Things go better with Coca-cola? ? 饮可口可乐万事如意 7Connecting people Nokia? ? 科技以人为本? ?诺基亚Nokia 9A Kodak moment? ?? ?就在柯达一刻? ?? ?柯达Kodak 10Mosquito Bye Bye Bye，蚊子杀杀杀雷达牌驱蚊虫剂RADAR
数学中国MCM/ICM参赛指南翻译（2014版） MCM:The Mathematical Contest in Modeling MCM：数学建模竞赛 ICM:The InterdisciplinaryContest in Modeling ICM：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
经典广告词中英文翻译2．Obey your thirst．服从你的渴望。（雪碧） 3．The new digital era．数码新时代。（索尼影碟机） 4．We lead．Others copy．我们领先，他人仿效。（理光复印机）5．Impossible made possible．使不可能变为可能。（佳能打印机） 6．Take time to indulge．尽情享受吧！（雀巢冰激凌） 7．The relentless pursuit of perfection．不懈追求完美。（凌志轿车）8．Poetry in motion，dancing close to me．动态的诗，向我舞近。（丰田汽车）9．Come to where the flavor is．Marlboro Country． 光临风韵之境——万宝路世界。（万宝路香烟） 10．To me，the past is black and white，but the future is always color．对我而言，过去平淡无奇；而未来，却是绚烂缤纷。（轩尼诗酒） 11. Just do it.只管去做。（耐克运动鞋） 12. Ask for more.渴望无限。（百事流行鞋） 13. The taste is great.味道好极了。（雀巢咖啡） 14. Feel the new space.感受新境界。（三星电子） 15. Intelligence everywhere.智慧演绎，无处不在。（摩托罗拉手机） 16. The choice of a new generation. 新一代的选择。（百事可乐） 17. We integrate, you communicate. 我们集大成，您超越自我。（三菱电工） 18. Take TOSHIBA, take the world. 拥有东芝，拥有世界。（东芝电子） 19. Let’s make things better.让我们做得更好。（飞利浦电子） 20. No business too small, no problem too big. 没有不做的小生意，没有解决不了的大问题。（IBM公司） 1 Good to the last drop 滴滴香浓，意犹未尽麦式咖啡Maxwell 2 Time is what you make of it 天长地久斯沃奇手表Swatch 3Make yourself heard 理解就是沟通爱立信Ericsson 4Start ahead 成功之路从头开始飘柔rejoice 5Diamond lasts forever 钻石恒久远，一颗永流传第比尔斯De Bieeres 6Things go better with Coca-cola 饮可口可乐万事如意 7Connecting people Nokia 科技以人为本诺基亚Nokia 9A Kodak moment 就在柯达一刻柯达Kodak 10Mosquito Bye Bye Bye，蚊子杀杀杀雷达牌驱蚊虫剂RADAR
数学建模知识竞赛题库 1.请问计算机中的二进制源于我国古代的哪部经典? D A.《墨经》 B.《诗经》 C.《周书》 D.《周易》 2.世界上面积最大的高原是？D A.青藏高原 B.帕米尔高原 C.黄土高原 D.巴西高原 3.我国海洋国土面积约有多少万平方公里? B A.200 B.300 C.280 D.340 4.世界上面值最高的邮票是匈牙利五百亿彭哥，它的图案是B A.猫 B.飞鸽 C.海鸥 D.鹰 5. 龙虾是我们的一种美食、你知道它体内的血是什么颜色的吗？B A.红色 B.蓝色 C.灰色 D.绿色 6.MATLAB使用三维向量[R G B]来表示一种颜色，则黑色为（D ） A. [1 0 1] B. [1 1 1] C. [0 0 1] D. [0 0 0] 7.秦始皇之后，有几个朝代对长城进行了修葺？ A A.7个 B.8个 C.9个 D.10个 8.中国历史上历时最长的朝代是？A A.周朝 B.汉朝 C.唐朝 D.宋朝 9我国第一个获得世界冠军的是谁？C A 吴传玉 B 郑凤荣 C 荣国团 D 陈镜开 10.我国最早在奥运会上获得金牌的是哪位运动员？B A.李宁 B.许海峰 C.高凤莲 D.吴佳怩
11.围棋共有多少个棋子？B A.360 B.361 C.362 D.365 12下列属于物理模型的是:A A水箱中的舰艇 B分子结构图 C火箭模型 D电路图 13名言：生命在于运动是谁说的？C A.车尔尼夫斯基 B.普希金 C.伏尔泰 D.契诃夫 14.饱食后不宜剧烈运动是因为B A.会得阑尾炎 B.有障消化 C.导致神经衰弱 D.呕吐 15、MATLAB软件中，把二维矩阵按一维方式寻址时的寻址访问是按（B）优先的。 A.行 B.列 C.对角线 D.左上角16红军长征中，哪次战役最突出反应毛泽东的军事思想和指挥才?A A.四渡赤水B.抢渡大渡河C.飞夺泸定桥D.直罗镇战役 17色盲患者最普遍的不易分辨的颜色是什么？A A.红绿 B.蓝绿 C.红蓝 D.绿蓝 18下列哪种症状是没有理由遗传的？ A.精神分裂症 B.近视 C.糖尿病 D.口吃 19下面哪个变量是正无穷大变量？（A ）
经典英文广告语20条 经典英文广告语20条 1． Good to the last drop． 滴滴香浓，意犹未尽。（麦斯威尔咖啡) 2． Obey your thirst． 服从你的渴望。（雪碧） 3． The new digital era． 数码新时代。（索尼影碟机） 4． We lead． Others copy． 我们领先，他人仿效。（理光复印机） 5． Impossible made possible． 使不可能变为可能。（佳能打印机） 6． Take time to indulge． 尽情享受吧！（雀巢冰激凌） 7． The relentless pursuit of perfection． 不懈追求完美。（凌志轿车） 8． Poetry in motion， dancing close to me． 动态的诗，向我舞近。（丰田汽车） 9． Come to where the flavor is． Marlboro Country． 光临风韵之境——万宝路世界。（万宝路香烟） 10．To me， the past is black and white， but the future is always color．对我而言，过去平淡无奇；而未来，却是绚烂缤纷。（轩尼诗酒） 11. Just do it. 只管去做。（耐克运动鞋） 12. Ask for more. 渴望无限。（百事流行鞋） 13. The taste is great. 味道好极了。（雀巢咖啡） 14. Feel the new space. 感受新境界。（三星电子） 15. Intelligence everywhere. 智慧演绎，无处不在。（摩托罗拉手机） 16. The choice of a new generation. 新一代的选择。（百事可乐） 17. We integrate, you communicate. 我们集大成，您超越自我。（三菱电工） 18. Take TOSHIBA, take the world. 拥有东芝，拥有世界。（东芝电子） 19. Let’s make things better. 让我们做得更好。（飞利浦电子） 20. No business too small, no problem too big.
Problem A Warmer Days or Sour Grapes ? The high quality of wines（葡萄酒）produced in the Finger Lakes Region（五指湖区）of upstate （北部）New York is widely known. Proximity（接近）to lakes tempers the climate and makes it more suitable for growing several varieties of premium（独特）grapes: R iesling（雷司令）, G ewürztraminer（琼瑶浆）, C hardonnay（霞多丽）, M erlot（梅洛）, P inot Noir（黑比诺）, and Cabernet F ranc（品丽珠）. (There are many more, but we will restrict（限制）the discussion to these six to simplify（简化）the modeling.) Each variety has its own preferred “average temperature” range but is also different in its susceptibility（感受性）to diseases and ability to withstand（抵抗）short periods of unusually cold temperature. As our local climate changes, the relative suitability of these varieties will be changing as well. A forward-looking winery（酒厂）has hired your team to help with the long-term planning. You will need to recommend a) the proportion（比例）of the total vineyard（葡萄园）to be used for growing each of the above six varieties; b) and when should these changes be implemented （实施）(based on observed temperatures and/or current market prices for each type of wine). Naturally, the winery is interested in maximizing its annual profit. But since the latter （后者）is weather-dependent, it might vary a lot year-to-year. You are also asked to evaluate the trade-offs （权衡）between optimizing the expected/average case versus the worst(-realistic-)scenario（情景）. Things to keep in mind: Climate modeling is complicated（复杂）and predicting the rate of “global warming” is a hotly debated area. For the purposes of this problem, assume that the annual average temperature in Ithaca（伊萨卡）, NY will increase by no more than 4°C by the end of this century. It is not all about the average temperature – a short snap（临时）of sub- zero（零度）temperature in late Ferburay or early March (after the vines already started getting used to warmer weather) is far more damaging than the same low temperature would be in the middle of the winter. It takes at least 3 years for a newly planted vine to start producing grapes suitable for winemaking. Problem B Outlook of Car-to-Car Tech SAN FRANCISCO -- After more than a decade of research into car-to-car communications, U.S. auto safety regulators took a step forward today by unveiling their plan for requiring cars to have wireless gear that will enable them to warn drivers of danger.
The first part, who can be a president? First, the U.S. president must be native American born in the United States. Second, he must be at least 35 years old. Third, he has lived in the United States at least 14 years. Next, I will introduce the process of the election. The U.S. implement Presidential system, the presidential election was hold every four years. It includes five stages. Primary election、Nominating process、Running、General election 、Inauguration. Let's look it one by one. 1. Primary election usually starts in Feb. and ends in June. It has two forms: indirect election system & direct election system. The first form, each county, strict, state host meeting to select electors. The second form, all voters cast ballots in the same day to select electors. Most states adopt the second form. purpose: To select electors for the National Party Conventions. 2.Nominating process from July to Aug. The electors from each state make up the "Electoral College".The major political parties will officially hold its Presidential Nominating Conventions. In this Nominating Conventions, the "Electoral College" cast ballots for the candidates. Normally, the candidate for president receiving the majority(>50%) of the electoral votes is the elected president. 3.Running. The candidates of the major parties will go to many states to win the supporters by means of: campaigning trips to different states, addressing TV speeches, showing on TV debates etc. The candidates deliver countless speeches and shake countless hands. The media tools play an important role in this process. From this picture, we can see this process costs a lot. 4.General election: The first Tuesday after the first Monday in Nov. is called Presidential Election Day. That day, all voters cast ballots for the candidates. V oters can't determine the president directly. The first Monday after the second Wednesday is the real presidential election day. That day, the “Electoral College”represents the wishes of the voters to cast ballots for the candidate. Take California as an example, this state has 55 ballots, if more than a half voters support President Obama, then the electoral college will vote these 55 ballots to Obama. From this picture, we can see, there are 538 ballots altogether. Each state is allocated a number of Electoral College electors equal to the number of its Senators and Representatives in the U.S. Congress. 5.The candidate who gets more than 270 ballots can be the president. In 2012, president Obama got 332 ballots. In Inauguration day, there are nine events, let 's look at together . 1.Morning Worship Service The tradition of attending a morning worship service on Inauguration Day began with Franklin D. Roosevelt in 1933.
PROBLEM A: The Ultimate Brownie Pan 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)
餐厅广告语,英文 篇一：经典英文广告语20条 经典英文广告语20条 经典英文广告语20条1．Goodtothelastdrop． 滴滴香浓，意犹未尽。（麦斯威尔咖啡) 2．obeyyourthirst． 服从你的渴望。（雪碧）3．Thenewdigitalera． 数码新时代。（索尼影碟机）4．welead．otherscopy． 我们领先，他人仿效。（理光复印机）5．impossiblemadepossible． 使不可能变为可能。（佳能打印机）6．Taketimetoindulge． 尽情享受吧！（雀巢冰激凌）7．Therelentlesspursuitofperfection． 不懈追求完美。（凌志轿车）8．Poetryinmotion，dancingclosetome． 动态的诗，向我舞近。（丰田汽车）
9．cometowheretheflavoris．marlborocountry． 光临风韵之境——万宝路世界。（万宝路香烟） 10．Tome，thepastisblackandwhite，butthefutureisalwayscolor．对我而言，过去平淡无奇；而未来，却是绚烂缤纷。（轩尼诗酒） 11.Justdoit. 只管去做。（耐克运动鞋） 12.askformore. 渴望无限。（百事流行鞋） 13.Thetasteisgreat. 味道好极了。（雀巢咖啡） 14.Feelthenewspace. 感受新境界。（三星电子） 15.intelligenceeverywhere. 智慧演绎，无处不在。（摩托罗拉手机） 16.Thechoiceofanewgeneration. 新一代的选择。（百事可乐） 17.weintegrate,youcommunicate. 我们集大成，您超越自我。（三菱电工） 18.TakeToSHiBa,taketheworld. 拥有东芝，拥有世界。（东芝电子） 19.Let’smakethingsbetter. 让我们做得更好。（飞利浦电子）
中国大学生数学建模竞赛： 全国大学生数学建模竞赛创办于1992年，每年一届，已成为全国高校规模最大的基础性学科竞赛，也是世界上规模最大的数学建模竞赛。2018年，来自全国34个省/市/区(包括香港、澳门和台湾)及美国和新加坡的1449所院校/校区、42128个队（本科38573队、专科3555队）、超过12万名大学生报名参加本项竞赛。 赛事设置： 竞赛宗旨 创新意识团队精神重在参与公平竞争。 指导原则 指导原则：扩大受益面，保证公平性，推动教学改革，提高竞赛质量，扩大国际交流，促进科学研究。 规模与数据 全国大学生数学建模竞赛是全国高校规模最大的课外科技活动之一。该竞赛每年9月（一般在上旬某个周末的星期五至下周星期一共3天，72小时）举行，竞赛面向全国大专院校的学生，不分专业（但竞赛分本科、专科两组，本科组竞赛所有大学生均可参加，专科组竞赛只有专科生（包括高职、高专生）可以参加）。同学可以向该校教务部门咨询，如有必要也可直接与全国竞赛组委会或各省（市、自治区）赛区组委会联系。 全国大学生数学建模竞赛创办于1992年，每年一届，成为全国高校规模最大的基础性学科竞赛，也是世界上规模最大的数学建模竞
赛。2014年，来自全国33个省/市/自治区(包括香港和澳门特区)及新加坡、美国的1338所院校、25347个队（其中本科组22233队、专科组3114队）、7万多名大学生报名参加本项竞赛。 比赛时间 2017年比赛时间是9月14号20:00到9月17号24:00，总共76小时，采取通讯方式比赛，比赛地点在各个高校。比赛时间全国统一的，不可以与老师交流，可以在互联网查阅资料。 同学们在比赛期间应该注意安排时间，以免出现时间不够用的情况。 组委名单 注：第五届专家组任期两年（2010-2011）。2011年底任期届满后，组委会对专家组进行了调整，并决定此后不再对外公布专家组成员名单。 第五届组委会成员名单（2010-2013）及下属专家组成员名单 第四届组委会成员名单及下属专家组成员名单 第一、二、三届组委第一、二、三届组委会成员名单及下属专家组成员名单引各赛区组委会各赛区联系方式列表引 [注1] 各赛区联系人请注意：若本赛区联系e-mail地址发生变化，请通知全国组委会进行修改。 [注2] 全国已成立赛区的有28个省、市、自治区，国内尚未成立赛区的区域组成联合赛区，其他（境外参赛学生）组成国际赛区，共30个赛区。
特朗普当选美国总统的演讲稿（英文原文） Thank you. Thank you very much, everyone. Sorry to keep you waiting. Complicated business, complicated. Thank you very much. I've just received a call from Secretary Clinton. She congratulated us. It’s about us. On our victory, and I congratulated her and her family on a very, very hard-fought campaign. I mean she fought very hard. Hillary has worked very long and very hard over a long period of time, and we owe her a major debt of gratitude for her service to our country. I mean that very sincerely. Now it is time for America to bind the wounds of pision, have to get together, to all Republicans and Democrats and independents across this nation I say it is time for us to come together as one united people. It is time. I pledge to every citizen of our land that I will be president for all of Americans, and this is so important to me. For those who have chosen not to support me in the past, of which there were a few people, I'm reaching out to you for your guidance and your help so that we can work together and unify our great country. As I've said from the beginning, ours was not a campaign but rather an incredible and great movement, made up of millions of hard-working men and women who love their country and want a better, brighter future for themselves and for their family. It is a movement comprised of Americans from all races, religions, backgrounds and beliefs, who want and expect our government to serve the people, and serve the people it will. Working together we will begin the urgent task of rebuilding our nation and renewing the American dream. I've spent my entire life in business, looking at the untapped potential in projects and in people all over the world. That is now what I want to do for our country. Tremendous potential. I've gotten to know our country so well. Tremendous potential. It is going to be a beautiful thing. Every single American will have the opportunity to realize his or her fullest potential. The forgotten men and women of our country will be forgotten no longer. We are going to fix our inner cities and rebuild our highways, bridges, tunnels, airports, schools, hospitals. We're going to rebuild our infrastructure, which will become, by the way, second to none, and we will put millions of our people to work as we rebuild it. We will also finally take care of our great veterans who have been so loyal, and I've gotten to know so many over this 18-month journey. The time I've spent with them during this campaign has been among my greatest honors. Our veterans are incredible people. We will embark upon a project of national growth and renewal. I will harness the creative talents of our people and we will call upon the best and brightest to
如何准备美赛 数学模型：数学模型的功能大致有三种：评价、优化、预测。几乎所有模型都是围绕这三种功能来做的。比如，2012年美赛A题树叶分类属于评价模型，B题漂流露营安排则属于优化模型。 对于不同功能的模型有不同的方法，例如 评价模型方法有层次分析、模糊综合评价、熵值法等； 优化模型方法有启发式算法（模拟退火、遗传算法等）、仿真方法（蒙特卡洛、元胞自动机等）； 预测模型方法有灰色预测、神经网络、马尔科夫链等。 在数学中国、数学建模网站上有许多关于这些方法的相关介绍与文献。 软件与书籍： 软件一般三款足够：Matlab、SPSS、Lingo，学好一个即可。 书籍方面，推荐三本，一本入门，一本进级，一本参考，这三本足够： 《数学模型》姜启源谢金星叶俊高等教育出版社 《数学建模方法与分析》Mark M. Meerschaert 机械工业出版社 《数学建模算法与程序》司守奎国防工业出版社 入门的《数学模型》看一遍即可，对数学模型有一个初步的认识与把握，国赛前看完这本再练习几篇文章就差不多了。另外，关于入门，韩中庚的《数学建模方法及其应用》也是不错的，两本书选一本阅读即可。如果参加美赛的话，进级的《数学建模方法与分析》要仔细研究，这本书写的非常好，可以算是所有数模书籍中最好的了，没有之一，建议大家去买一本。这本书中开篇指出的最优化模型五步方法非常不错，后面的方法介绍的动态模型与概率模型也非常到位。参考书目《数学建模算法与程序》详细的介绍了多种建模方法，适合用来理解模型思想，参考自学。 分工合作：数模团队三个人，一般是分别负责建模、编程、写作。当然编程的可以建模，建模的也可以写作。这个要视具体情况来定，但这三样必须要有人擅长，这样才能保证团队最大发挥出潜能。 这三个人中负责建模的人是核心，要起主导作用，因为建模的人决定了整篇论文的思路与结构，尤其是模型的选择直接关系到了论文的结果与质量。 对于建模的人，首先要去大量的阅读文献，要见识尽可能多的模型，这样拿到一道题就能迅速反应到是哪一方面的模型，确定题目的整体思路。 其次是接口的制作，这是体现建模人水平的地方。所谓接口的制作就是把死的方法应用到具体问题上的过程，即用怎样的表达完成程序设计来实现模型。比如说遗传算法的方法步骤大家都知道，但是应用到具体问题上，编码、交换、变异等等怎么去做就是接口的制作。往往对于一道题目大家都能想到某种方法，可就是做不出来，这其实是因为接口不对导致的。做接口的技巧只能从不断地实践中习得，所以说建模的人任重道远。 另外，在平时训练时，团队讨论可以激烈一些，甚至可以吵架，但比赛时，一定要保持心平气和，不必激烈争论，大家各让3分，用最平和的方法讨论问题，往往能取得效果并且不耽误时间。经常有队伍在比赛期间发生不愉快，导致最后的失败，这是不应该发生的，毕竟大家为了一个共同的目标而奋斗，这种经历是很难得的。所以一定要协调好队员们之间的关系，这样才能保证正常发挥，顺利进行比赛。 美赛特点：一般人都认为美赛比国赛要难，这种难在思维上，美赛题目往往很新颖，一时间想不出用什么模型来解。这些题目发散性很强，需要查找大量文献来确定题目的真正意图，美赛更为注重思想，对结果的要求却不是很严格，如果你能做出一个很优秀的模型，也许结果并不理想也可能获得高奖。另外，美赛还难在它的实现，很多东西想到了，但实现起来非常困难，这需要较高的编程水平。 除了以上的差异，在实践过程中，美赛和国赛最大的区别有两点： 第一点区别当然是美赛要用英文写作，而且要阅读很多英文文献。对于文献阅读，可以安装有道词典，
A题炉温曲线 在集成电路板等电子产品生产中，需要将安装有各种电子元件的印刷电路板放置在回焊炉中，通过加热，将电子元件自动焊接到电路板上。在这个生产过程中，让回焊炉的各部分保持工艺要求的温度，对产品质量至关重要。目前，这方面的许多工作是通过实验测试来进行控制和调整的。本题旨在通过机理模型来进行分析研究。 回焊炉内部设置若干个小温区，它们从功能上可分成4个大温区：预热区、恒温区、回流区、冷却区（如图1所示）。电路板两侧搭在传送带上匀速进入炉内进行加热焊接。 图1 回焊炉截面示意图 某回焊炉内有11个小温区及炉前区域和炉后区域（如图1），每个小温区长度为30.5 cm，相邻小温区之间有5 cm的间隙，炉前区域和炉后区域长度均为25 cm。 回焊炉启动后，炉内空气温度会在短时间内达到稳定，此后，回焊炉方可进行焊接工作。炉前区域、炉后区域以及小温区之间的间隙不做特殊的温度控制，其温度与相邻温区的温度有关，各温区边界附近的温度也可能受到相邻温区温度的影响。另外，生产车间的温度保持在25oC。 在设定各温区的温度和传送带的过炉速度后，可以通过温度传感器测试某些位置上焊接区域中心的温度，称之为炉温曲线（即焊接区域中心温度曲线）。附件是某次实验中炉温曲线的数据，各温区设定的温度分别为175oC（小温区1~5）、195oC（小温区6）、235oC（小温区7）、255oC（小温区8~9）及25oC（小温区10~11）；传送带的过炉速度为70 cm/min；焊接区域的厚度为0.15 mm。温度传感器在焊接区域中心的温度达到30oC时开始工作，电路板进入回焊炉开始计时。 实际生产时可以通过调节各温区的设定温度和传送带的过炉速度来控制产品质量。在上述实验设定温度的基础上，各小温区设定温度可以进行oC范围内的调整。调整时要求小温区1~5中的温度保持一致，小温区8~9中的温度保持一致，小温区10~11中的温度保持25oC。传送带的过炉速度调节范围为65~100 cm/min。 在回焊炉电路板焊接生产中，炉温曲线应满足一定的要求，称为制程界限（见表1）。 表1 制程界限 界限名称 最低值 最高值