07年全国大学生数学建模竞赛特等奖论文
2017年全国大学生数学建模竞赛优秀论文
2017年全国大学生数学建模竞赛优秀论文数学是知识的工具，亦是其它知识工具的泉源。
所有研究顺序和度量的科学均和数学有关，数学建模是培养学生运用数学工具解决实际问题的最好表现。
下文是店铺为大家搜集整理的关于2017年全国大学生数学建模竞赛优秀论文的内容，欢迎大家阅读参考!2017年全国大学生数学建模竞赛优秀论文篇1浅析数学建模课程改革及其教学方法论文关键词:数学课程;数学建模;课程设置;课程改革论文摘要:数学建模教学和竞赛的开展,是培养学生创新能力的重要途径。
对数学建模竞赛中出现的问题进行分析,找出问题产生的根源与必修课和专业课设置不合理有关,应对高校数学课程的设置、教学方式等进行改革,并提出具体改革建议。
1. 前言数学建模,从宏观上讲是人们借助数学改造自然、征服自然的过程,从微观上讲是把数学作为一种工具并应用它解决实际问题的教学活动方式。
数学建模教育本身是一种素质教育,数学建模的教学与竞赛是实施素质教育的有效途径,它既增强了学生的数学应用意识,又提高了学生运用数学知识和计算机技术分析和解决问题的能力。
因而加强数学建模教育,培养学生的数学应用意识与能力已成为我国高校数学建模课程改革的重要目标之一。
虽然目前我国许多高校在数学建模方面取得了一些成绩,但大学生们在竞赛中也暴露出了许多问题,引发出对传统的课程设置和教学方法的思考。
2. 数学建模的现状和所存在问题与原因分析2.1 建模竞赛的现状根据竞赛时间(九月中下旬),我国大部分高校每年一般在七月中旬便开始组织学生的报名培训工作。
培训内容分为两个部分:首先集中讲解一些基础知识,主要包括常微分方程、概率与数理统计、运筹学、数学实验、建模基础等课程;然后进行建模的模拟训练,以往届国内外普通组和大专组的部分竞赛题为选题,让学生自愿结组,在规定时间内完成,并自愿为同学讲解各自的解题思路和方法。
参赛学生首先要参加培训,他们一般是先关注校园网上的通知,再到各院系自愿报名而组成,经培训后选拔出参赛队员。
2007美国大学生数学建模竞赛B题特等奖论文
American Airlines' Next Top ModelSara J. BeckSpencer D. K'BurgAlex B. TwistUniversity of Puget SoundTacoma, WAAdvisor: Michael Z. SpiveySummaryWe design a simulation that replicates the behavior of passengers boarding airplanes of different sizes according to procedures currently implemented, as well as a plan not currently in use. Variables in our model are deterministic or stochastic and include walking time, stowage time, and seating time. Boarding delays are measured as the sum of these variables. We physically model and observe common interactions to accurately reflect boarding time.We run 500 simulations for various combinations of airplane sizes and boarding plans. We analyze the sensitivity of each boarding algorithm, as well as the passenger movement algorithm, for a wide range of plane sizes and configurations. We use the simulation results to compare the effectiveness of the boarding plans. We find that for all plane sizes, the novel boarding plan Roller Coaster is the most efficient. The Roller Coaster algorithm essentially modifies the outside-in boarding method. The passengers line up before they board the plane and then board the plane by letter group. This allows most interferences to be avoided. It loads a small plane 67% faster than the next best option, a midsize plane 37% faster than the next best option, and a large plane 35% faster than the next best option.IntroductionThe objectives in our study are:To board (and deboard) various sizes of plane as quickly as possible."* To find a boarding plan that is both efficient (fast) and simple for the passengers.With this in mind:"* We investigate the time for a passenger to stow their luggage and clear the aisle."* We investigate the time for a passenger to clear the aisle when another passenger is seated between them and their seat.* We review the current boarding techniques used by airlines.* We study the floor layout of planes of three different sizes to compare any difference between the efficiency of a given boarding plan as plane size increases and layouts vary."* We construct a simulator that mimics typical passenger behavior during the boarding processes under different techniques."* We realize that there is not very much time savings possible in deboarding while maintaining customer satisfaction."* We calculate the time elapsed for a given plane to load under a given boarding plan by tracking and penalizing the different types of interferences that occur during the simulations."* As an alternative to the boarding techniques currently employed, we suggest an alternative plan andassess it using our simulator."* We make recommendations regarding the algorithms that proved most efficient for small, midsize, and large planes.Interferences and Delays for BoardingThere are two basic causes for interference-someone blocking a passenger,in an aisle and someone blocking a passenger in a row. Aisle interference is caused when the passenger ahead of you has stopped moving and is preventing you from continuing down the aisle towards the row with your seat. Row interference is caused when you have reached the correct row but already-seated passengers between the aisle and your seat are preventing you from immediately taking your seat. A major cause of aisle interference is a passenger experiencing rowinterference.We conducted experiments, using lined-up rows of chairs to simulate rows in an airplane and a team member with outstretched arms to act as an overhead compartment, to estimate parameters for the delays cause by these actions. The times that we found through our experimentation are given in Table 1.We use these times in our simulation to model the speed at which a plane can be boarded. We model separately the delays caused by aisle interference and row interference. Both are simulated using a mixed distribution definedas follows:Y = min{2, X},where X is a normally distributed random variable whose mean and standard deviation are fixed in our experiments. We opt for the distribution being partially normal with a minimum of 2 after reasoning that other alternative and common distributions (such as the exponential) are too prone to throw a small value, which is unrealistic. We find that the average row interference time is approximately 4 s with a standard deviation of 2 s, while the average aisle interference time is approximately 7 s with a standard deviation of 4 s. These values are slightly adjusted based on our team's cumulative experience on airplanes.Typical Plane ConfigurationsEssential to our model are industry standards regarding common layouts of passenger aircraft of varied sizes. We use an Airbus 320 plane to model a small plane (85-210 passengers) and the Boeing 747 for a midsize plane (210-330 passengers). Because of the lack of large planes available on the market, we modify the Boeing 747 by eliminating the first-class section and extending the coach section to fill the entire plane. This puts the Boeing 747 close to its maximum capacity. This modified Boeing 747 has 55 rows, all with the same dimensions as the coach section in the standard Boeing 747. Airbus is in the process of designing planes that can hold up to 800 passengers. The Airbus A380 is a double-decker with occupancy of 555 people in three different classes; but we exclude double-decker models from our simulation because it is the larger, bottom deck that is the limiting factor, not the smaller upper deck.Current Boarding TechniquesWe examine the following industry boarding procedures:* random-order* outside-in* back-to-front (for several group sizes)Additionally, we explore this innovative technique not currently used by airlines:* "Roller Coaster" boarding: Passengers are put in order before they board the plane in a style much like those used by theme parks in filling roller coasters.Passengers are ordered from back of the plane to front, and they board in seatletter groups. This is a modified outside-in technique, the difference being that passengers in the same group are ordered before boarding. Figure 1 shows how this ordering could take place. By doing this, most interferencesare avoided.Current Deboarding TechniquesPlanes are currently deboarded in an aisle-to-window and front-to-back order. This deboarding method comes out of the passengers' desire to be off the plane as quickly as possible. Any modification of this technique could leadto customer dissatisfaction, since passengers may be forced to wait while others seated behind them on theplane are deboarding.Boarding SimulationWe search for the optimal boarding technique by designing a simulation that models the boarding process and running the simulation under different plane configurations and sizes along with different boarding algorithms. We then compare which algorithms yielded the most efficient boarding process.AssumptionsThe environment within a plane during the boarding process is far too unpredictable to be modeled accurately. To make our model more tractable,we make the following simplifying assumptions:"* There is no first-class or special-needs seating. Because the standard industry practice is to board these passengers first, and because they generally make up a small portion of the overall plane capacity, any changes in the overall boarding technique will not apply to these passengers."* All passengers board when their boarding group is called. No passengers arrive late or try to board the plane early."* Passengers do not pass each other in the aisles; the aisles are too narrow."* There are no gaps between boarding groups. Airline staff call a new boarding group before the previous boarding group has finished boarding the plane."* Passengers do not travel in groups. Often, airlines allow passengers boarding with groups, especially with younger children, to board in a manner convenient for them rather than in accordance with the boarding plan. These events are too unpredictable to model precisely."* The plane is full. A full plane would typically cause the most passenger interferences, allowing us to view the worst-case scenario in our model."* Every row contains the same number of seats. In reality, the number of seats in a row varies due to engineering reasons or to accommodate luxury-class passengers.ImplementationWe formulate the boarding process as follows:"* The layout of a plane is represented by a matrix, with the rows representing rows of seats, and each column describing whether a row is next to the window, aisle, etc. The specific dimensions vary with each plane type. Integer parameters track which columns are aisles."* The line of passengers waiting to board is represented by an ordered array of integers that shrinks appropriately as they board the plane."* The boarding technique is modeled in a matrix identical in size to the matrix representing the layout of the plane. This matrix is full of positive integers, one for each passenger, assigned to a specific submatrix, representing each passenger's boarding group location. Within each of these submatrices, seating is assigned randomly torepresent the random order in which passengers line up when their boarding groups are called."* Interferences are counted in every location where they occur within the matrix representing the plane layout. These interferences are then cast into our probability distribution defined above, which gives ameasurement of time delay."* Passengers wait for interferences around them before moving closer to their assigned seats; if an interference is found, the passenger will wait until the time delay has finished counting down to 0."* The simulation ends when all delays caused by interferences have counted down to 0 and all passengers have taken their assigned seats.Strengths and Weaknesses of the ModelStrengths"* It is robust for all plane configurations and sizes. The boarding algorithms that we design can be implemented on a wide variety of planes with minimal effort. Furthermore, the model yields reasonable results as we adjust theparameters of the plane; for example, larger planes require more time to board, while planes with more aisles can load more quickly than similarlysized planes with fewer aisles."* It allows for reasonable amounts of variance in passenger behavior. While with more thorough experimentation a superior stochastic distribution describing the delays associated with interferences could be found, our simulationcan be readily altered to incorporate such advances."* It is simple. We made an effort to minimize the complexity of our simulation, allowing us to run more simulations during a greater time period and mini mizing the risk of exceptions and errors occurring."* It is fairly realistic. Watching the model execute, we can observe passengers boarding the plane, bumping into each other, taking time to load their baggage, and waiting around as passengers in front of them move out of theway. Its ability to incorporate such complex behavior and reduce it are key to completing our objective. Weaknesses"* It does not account for passengers other than economy-class passengers."* It cannot simulate structural differences in the boarding gates which couldpossibly speed up the boarding process. For instance, some airlines in Europeboard planes from two different entrances at once."* It cannot account for people being late to the boarding gate."* It does not account for passenger preferences or satisfaction.Results and Data AnalysisFor each plane layout and boarding algorithm, we ran 500 boarding simulations,calculating mean time and standard deviation. The latter is important because the reliability of plane loading is important for scheduling flights.We simulated the back-to-front method for several possible group sizes.Because of the difference in thenumber of rows in the planes, not all group size possibilities could be implemented on all planes.Small PlaneFor the small plane, Figure 2 shows that all boarding techniques except for the Roller Coaster slowed the boarding process compared to the random boarding process. As more and more structure is added to the boarding process, while passenger seat assignments continue to be random within each of the boarding groups, passenger interference backs up more and more. When passengers board randomly, gaps are created between passengers as some move to the back while others seat themselves immediately upon entering the plane, preventing any more from stepping off of the gate and onto the plane. These gaps prevent passengers who board early and must travel to the back of the plane from causing interference with many passengers behind them. However, when we implement the Roller Coaster algorithm, seat interference is eliminated, with the only passenger causing aisle interference being the very last one to boardfrom each group.Interestingly, the small plane's boarding times for all algorithms are greater than their respective boarding time for the midsize plane! This is because the number of seats per row per aisle is greater in the small plane than in the midsize plane.Midsize PlaneThe results experienced from the simulations of the mid-sized plane areshown in Figure 3 and are comparable to those experienced by the small plane.Again, the Roller Coaster method proved the most effective.Large PlaneFigure 4 shows that the boarding time for a large aircraft, unlike the other plane configurations, drops off when moving from the random boarding algorithm to the outside-in boarding algorithm. Observing the movements by the passengers in the simulation, it is clear that because of the greater number of passengers in this plane, gaps are more likely to form between passengers in the aisles, allowing passengers to move unimpeded by those already on board.However, both instances of back-to-front boarding created too much structure to allow these gaps to form again. Again, because of the elimination of row interference it provides for, Roller Coaster proved to be the most effective boarding method.OverallThe Roller Coaster boarding algorithm is the fastest algorithm for any plane pared to the next fastest boarding procedure, it is 35% faster for a large plane, 37% faster for a midsize plane, and 67% faster for a small plane. The Roller Coaster boarding procedure also has the added benefit of very low standard deviation, thus allowing airlines a more reliable boarding time. The boarding time for the back-to-front algorithms increases with the number of boarding groups and is always slower than a random boarding procedure.The idea behind a back-to-front boarding algorithm is that interference at the front of the plane is avoided until passengers in the back sections are already on the plane. A flaw in this procedure is that having everyone line up in the plane can cause a bottleneck that actually increases the loading time. The outside-in ("Wilma," or window, middle, aisle) algorithm performs better than the random boarding procedure only for the large plane. The benefit of the random procedure is that it evenly distributes interferences throughout theplane, so that they are less likely to impact very many passengers.Validation and Sensitivity AnalysisWe developed a test plane configuration with the sole purpose of implementing our boarding algorithms on planes of all sizes, varying from 24 to 600 passengers with both one or two aisles.We also examined capacities as low as 70%; the trends that we see at full capacity are reflected at these lower capacities. The back-to-front and outside-in algorithms do start to perform better; but this increase inperformance is relatively small, and the Roller Coaster algorithm still substantially outperforms them. Underall circumstances, the algorithms we test are robust. That is, they assign passenger to seats in accordance with the intention of the boarding plans used by airlines and move passengers in a realistic manner.RecommendationsWe recommend that the Roller Coaster boarding plan be implemented for planes of all sizes and configurations for boarding non-luxury-class and nonspecial needs passengers. As planes increase in size, its margin of success in comparison to the next best method decreases; but we are confident that the Roller Coaster method will prove robust. We recommend boarding groups that are traveling together before boarding the rest of the plane, as such groups would cause interferences that slow the boarding. Ideally, such groups would be ordered before boarding.Future WorkIt is inevitable that some passengers will arrive late and not board the plane at their scheduled time. Additionally, we believe that the amount of carry-on baggage permitted would have a larger effect on the boarding time than the specific boarding plan implemented-modeling this would prove insightful.We also recommend modifying the simulation to reflect groups of people traveling (and boarding) together; this is especially important to the Roller Coaster boarding procedure, and why we recommend boarding groups before boarding the rest of the plane.。
数学建模竞赛特等奖论文摘要
d y − r 2 − x 2 sin θ = z d cos θ + w − r 2 − x 2 .
令 u = L / 2 ，就可得到桌脚边缘线的方程(5-12)或(5-13). 进一步可以确定设计加工参数， 如从中间到两边的木条空槽长度分别为 20.09，19.60，18.77，17.59，16.06，14.14，11.81，9.00，
5.53(cm).
(
)
(
)
针对问题二，以用料最省(板材最短)、加工方便(总开槽长度最短)为目标，各木条 开槽下界不能超出木条、 桌子状态下桌腿边缘不能相交、 中间所有木条的桌腿不能沾地， 以及桌子的稳固性作为约束条件，建立多目标优化模型. 利用 Matlab 编程,求得最优结 钢筋的初始位置到桌腿底端的距离 s 为 43.80cm， 果为： 折叠桌弯折角 θ 为 1.0605(弧度)， 木板的长度 L 为 158.56cm. 针对问题三， 先将圆形折叠桌的侧面直纹曲面和桌脚边缘线的方程推广到一般形状 桌面和一般形状板材，然后利用多目标优化模型设计了两种特殊形状的折叠桌：非长方 形板材的正方形折叠桌和 8 字形折叠桌. 通过改变木条的旋转角度分别画出了这两种形 状折叠桌的动态变化示意图，并给出了具体的设计加工参数.
基于旅行商规划模型的碎纸片拼接复原问题研究
摘要
本文分别针对 RSSTD(Reconstruction of Strip Shredded Text Document） 、 RCCSTD(Reconstruction of cross-cut Shredded Text Document)和 Two-Sides RCCSTD 三种类型的碎纸片拼接复原问题进行了建模与求解算法设计。首先我 们对于 RSSTD 问题，建立了基于二值匹配度的 TSP 模型，并将其转化为线性规 划模型，利用贪心策略复原了该问题的中文和英文碎片；然后对于 RCCSTD 问 题， 由于中英文字的差别， 我们分别建立了基于改进误差评估的汉字拼接模型和 基于文字基线的误差评估的英文字拼接模型，并利用误差评估匹配算法，复原了 该问题的中文和英文碎片；随后我们针对正反两面的 RCCSTD 问题，利用基线 的概念将正反两面分行，转化为 RCCSTD 问题，并复原了该问题的英文碎片。 最后，我们对模型的算法和结果进行了检验和分析。 ◎问题一：我们针对仅纵切的情况，首先将图像进行数字化处理，转换为了 二值图像， 然后得到各图像的边缘， 并计算所有碎片与其他碎片边缘的匹配程度。 然后，根据两两碎片之间的匹配程度建立了 TSP 模型，并将其划归为线性规划 模型。最终，我们根据左边距的信息确定了左边第一碎片，随后设计了基于匹配 度的贪心算法从左向右得到了所有碎片的拼接复原结果。 结果表明我们的方法对 于中英文两种情况适用性均较好，且该过程不需要人工干预。 ◎问题二：我们针对既纵切又横切的情况，由于中英文的差异性，我们在进 行分行聚类时应采用不同的标准。 首先根据左右边距的信息确定了左边和右边的 碎片， 随后分别利用基于改进误差评估的汉字拼接模型和基于文字基线的误差评 估模型， 将剩余的碎片进行分行聚类，然后再利用基于误差评估的行内匹配算法 对行内进行了拼接， 最终利用行间匹配算法对行间的碎片进行了再拼接，最终得 到了拼接复原结果。对于拼接过程中可能出现误判的情况，我们利用 GUI 编写 了人机交互的人工干预界面，用人的直觉判断提高匹配的成功率和完整性。 ◎问题三：我们针对正反两面的情况，首先根据正反基线信息，分别确定了 左右两边的碎片， 然后利用基线差值将其两两聚类， 聚类以后其正反方向也一并 确定， 随后我们将其与剩余碎片进行分行聚类， 最终又利用行内匹配和行间匹配 算法得到了最终拼接复原结果。其中，对于可能出现的误判情况，我们同样在匹 配算法中使用了基于 GUI 的人机交互干预方式，利用人的直觉提高了结果的可 靠性和完整性。 关键字：碎片复原、TSP、误差评估匹配、基线误差、人工干预
全国大学生数学建模优秀论文(A题
地下储油罐的变位分析与罐容表标定摘要加油站地下储油罐在使用一段时间后，由于地基变形等原因会发生纵向倾斜及横向偏转，导致与之配套的“油位计量管理系统”受到影响，必须重新标定罐容表。
本文即针对储油罐的变位时罐容表标定的问题建立了相应的数学模型。
首先从简单的小椭圆型储油罐入手，研究变位对罐容表的影响。
在无变位、纵向变位的情况下分别建立空间直角坐标系，在忽略罐壁厚度等细微影响下，运用积分的方法求出储油量和测量油位高度的关系。
将计算结果与实际测量数据在同一个坐标系中作图，经计算得误差均保持在3.5%以内。
纵向变位中，要分三种情况来进行求解，然后将三段的结果综合在一起与变位前作比较，可以得到变位对罐容表的影响。
通过计算，具体列表给出了罐体变位后油位高度间隔为1cm 的罐容表标定值。
进一步考虑实际储油罐，两端为球冠体顶。
把储油罐分成中间的圆柱体和两边的球冠体分别求解。
中间的圆柱体求解类似于第一问，要分为三种情况。
在计算球冠内储油量时为简化计算，将其内油面看做垂直于圆柱底面。
根据几何关系，可以得到如下几个变量之间的关系：测量的油位高度0h 实际的油位高度h 计算体积所需的高度H于是得到罐内储油量与油位高度及变位参数（纵向倾斜角度和横向偏转角度 ）之间的一般关系。
再利用附表2中的数据列方程组寻找与最准确的取值。
αβ一、问题重述通常加油站都有若干个储存燃油的地下储油罐，并且一般都有与之配套的“油位计量管理系统”，采用流量计和油位计来测量进/出油量与罐内油位高度等数据，通过预先标定的罐容表（即罐内油位高度与储油量的对应关系）进行实时计算，以得到罐内油位高度和储油量的变化情况。
许多储油罐在使用一段时间后，由于地基变形等原因，使罐体的位置会发生纵向倾斜和横向偏转等变化（以下称为变位），从而导致罐容表发生改变。
按照有关规定，需要定期对罐容表进行重新标定。
题目给出了一种典型的储油罐尺寸及形状示意图，其主体为圆柱体，两端为球冠体。
全国数学建模优秀论文
全国数学建模优秀论文引言数学建模是运用数学方法解决实际问题的过程，具有广泛的应用价值。
每年，全国范围内举办各级数学建模竞赛，以鼓励学生利用数学建模方法解决实际问题并提高数学建模能力。
本文将介绍全国数学建模优秀论文的主要特点及其贡献。
优秀论文的特点1.创新性：全国数学建模优秀论文具有独特的思路和创新的解决方法。
优秀论文能够从原始问题中挖掘出新的问题，提出新颖的数学模型，并给出有效的数学分析和求解方法。
2.实用性：优秀论文通过数学建模方法解决了实际问题，并且解决方案具有实用性和可操作性。
优秀论文所提出的数学模型能够帮助决策者做出科学决策，解决实际的工程和管理问题。
3.论证性：优秀论文能够充分论证所提出的数学模型的合理性和有效性。
论文通过逻辑推理、数学证明和实例分析等方法来验证所提出的数学模型的正确性和准确性。
4.可读性：优秀论文具有良好的文笔和清晰的逻辑结构，能够使读者快速理解所提出的问题、模型和解决方法。
论文应该包括问题的背景介绍、问题的分析与建模过程、模型的数学表述和求解方法等内容。
优秀论文的贡献1.推动学术研究：全国数学建模优秀论文提供了新的问题和方法，推动了数学建模领域的学术研究。
优秀论文通过提出新的问题和解决方法，拓宽了数学建模的研究范围和深度。
2.指导实际应用：优秀论文所提出的数学模型可以指导实际应用。
例如，在环境保护领域，优秀论文提出的数学模型可以帮助相关部门预测大气污染程度，优化排污方案，提高环境监测的效能。
3.培养人才：全国数学建模优秀论文鼓励并培养了一批有创新能力和实践能力的优秀学生。
这些学生通过参与数学建模竞赛，积累了解决实际问题的经验，提高了数学建模能力，为国家培养了一批数学建模人才。
4.促进社会发展：优秀论文所解决的问题通常具有一定的社会影响力和应用价值。
例如，在交通规划领域，优秀论文可以帮助相关部门进行交通流模拟，分析交通拥堵状况，提出改进交通网络的方案，以提高城市交通效率和减少拥堵。
全国数模优秀论文参考
全国数模优秀论文参考数学建模就是通过计算得到的结果来解释实际问题，并接受实际的检验，来建立数学模型的全过程。
本篇文章整理提供了两篇全国数模优秀论文范文供大家参考学习。
全国数模优秀范文一：溜井放矿量与磨损量计算式的数模摘要:在溜井放矿过程中，井筒井壁会随着井筒内矿石移动而同时产生磨损，这种磨损缓慢、渐进式连续发生的，均匀的向四周发展扩大。
提出了连续式的积分方程，推导出溜井井筒的磨损量与放矿量之间关系的数学模型。
用德兴铜矿的相关数据进行了计算，计算结果表明，该数学模型所提供的计算数据与实际井筒磨损情况接近，可为矿山规划、溜井设计与生产管理提供可靠的依据。
关键词:溜井放矿;放矿量;磨损量;数学模型在溜井放矿过程中，井筒必然产生磨损。
若管控不严，措施不当，会引起井筒破坏，影响生产，威胁安全，严重时井筒报废。
研究溜井放矿时的井筒磨损规律，减缓井筒磨损速度，延长服务年限，增加井筒通过矿量，是一个重要的研究课题。
本文就溜井放矿时井筒磨损规律进行探讨。
1、溜井放矿时井筒磨损人们在长期观察中发现，溜井在放矿过程中，井筒的井壁磨损呈现:贮矿段井筒磨损速度较小且均匀，井壁光滑［1］;矿石对井壁的磨损轻微，溜井周边面磨损是均匀的［2］;贮矿段溜井磨损均匀，上下磨损速度非常接近［3］;全溜井的井壁光滑、完整，磨损轻微［4］。
根据以上的观察描述，溜井放矿的井筒磨损规律是:在放矿过程中，贮矿段的溜井井筒是以其中心线为中心，向四周磨损扩大是均匀的、相等的。
2、溜井磨损的计算式2．1、多项式的计算式根据上述井筒磨损规律，按照井筒磨损速度的计算公式U=r－r0Q(其中，U为井筒磨损速度，m/万t;r为经放矿磨损后的井筒半径，m;r0为初始的井筒半径，m;Q为放出的矿石量，万t)，采用多项式推导出的溜井放矿量与井筒磨损量之间的计算公式为［5］:为溜井井筒初始直径，m溜井放矿的井筒磨损量与放矿量之间的关系是一个相互渐进且连续的过程。
上述使用多项式的推导过程，采用的是渐进式，但不是连续式。
数学建模全国优秀论文范文
数学建模全国优秀论文范文随着科学技术特别是信息技术的高速发展，数学建模的应用价值越来越得到众人的重视，数学建模全国优秀论文1：《浅谈数学建模教育的作用与开展策略》数学建模本身是一个创造性的思维过程，它是对数学知识的综合应用，具有较强的创新性，以下是一篇关于数学建模教育开展策略探究的论文范文，欢迎阅读参考。
大学数学具有高度抽象性和概括性等特点，知识本身难度大再加上学时少、内容多等教学现状常常造成学生的学习积极性不高、知识掌握不够透彻、遇到实际问题时束手无策，而数学建模思想能激发学生的学习兴趣，培养学生应用数学的意识，提高其解决实际问题的能力。
数学建模活动为学生构建了一个由数学知识通向实际问题的桥梁，是学生的数学知识和应用能力共同提高的最佳结合方式。
因此在大学数学教育中应加强数学建模教育和活动，让学生积极主动学习建模思想，认真体验和感知建模过程，以此启迪创新意识和创新思维，提高其素质和创新能力，实现向素质教育的转化和深入。
一、数学建模的含义及特点数学建模即抓住问题的本质，抽取影响研究对象的主因素，将其转化为数学问题，利用数学思维、数学逻辑进行分析，借助于数学方法及相关工具进行计算，最后将所得的答案回归实际问题，即模型的检验，这就是数学建模的全过程。
一般来说",数学建模"包含五个阶段。
1.准备阶段主要分析问题背景，已知条件，建模目的等问题。
2.假设阶段做出科学合理的假设，既能简化问题，又能抓住问题的本质。
3.建立阶段从众多影响研究对象的因素中适当地取舍，抽取主因素予以考虑，建立能刻画实际问题本质的数学模型。
4.求解阶段对已建立的数学模型，运用数学方法、数学软件及相关的工具进行求解。
5.验证阶段用实际数据检验模型，如果偏差较大，就要分析假设中某些因素的合理性，修改模型，直至吻合或接近现实。
如果建立的模型经得起实践的检验，那么此模型就是符合实际规律的，能解决实际问题或有效预测未来的，这样的建模就是成功的，得到的模型必被推广应用。
全国大学生数学建模竞赛论文1
目录一 问题重述问题重述......................................................... ......................................................... 1 二 问题分析问题分析......................................................... ......................................................... 2 三 模型假设模型假设......................................................... ......................................................... 2 四 符号说明符号说明......................................................... ......................................................... 2 五 模型的建立与求解模型的建立与求解................................................. ................................................. 3 六结果分析六结果分析......................................................... (12)一 问题重述通常加油站都有若干个储存燃油的地下储油罐，并且一般都有与之配套的“油位计量管理系统”，采用流量计和油位计来测量进/出油量与罐内油位高度等数据，等数据，通过预先标定的罐容表通过预先标定的罐容表通过预先标定的罐容表（即罐内油位高度与储油量的对应关系）（即罐内油位高度与储油量的对应关系）（即罐内油位高度与储油量的对应关系）进行实进行实时计算，以得到罐内油位高度和储油量的变化情况。
2007全国大学生数学建模竞赛 基于Floyd的公交出行路线研究
四、 符号说明
1、 Ld ：第 d 条公汽线路， d 1, 2
520 3957, i j
2、 Si ( j ) ：第 i ( j ) 个公汽站点， i( j ) 1, 2
3、 nij ：第个站点到第个站点之间经过的站数 4、 k ：换乘次数， k 0,1, 2 5、 S ru ：换乘站， u 1, 2,
3957
1, nir1 20 Pir1 2, 20 nir1 40 nir1 40 3,
1, nr3 j 20 Pr3 j 2, 20 nr3 j 40 nr3 j 40 3,
1, nr1r2 20 Pr1r2 2, 20 nr1r2 40 nr1r2 40 3,
min(Tij ) i, j 1, 2 min( Pij ) Tij t1nij
1, nij 20 Pij 2, 20 nij 40 3, nij 40
4
3957
换乘一次
min(Tir1 Tr1 j ) i, j 1, 2 min( Pir1 Pr1 j ) Tir1 t1nir1 Tr1 j t1nr1 j t3
起讫点 S3359 → S1828 S1557 → S0481 S0971 → S0485 S0008 → S0073 S0148 → S0485 S0087 → S3676
换乘数 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
时间 101 64 69 106 99 128 106 105 83 67 63 106 102 65 46 51
二、 问题分析
本题主要在三种不同情况下，研究任意两站点之间的线路选择问题。联系实 际， 公众乘坐公交车主要考虑的因素包括转乘次数、 行程时间及乘车费用等因素。 为满足一般公众的乘车需求， 主要按照公众对不同乘车信息的重视程度，确定出 最佳的乘车路线。 仅考虑公汽线路的情况下，首先，需要Байду номын сангаас据题目给出的公交线路信息数据， 对每条线路进行抽象处理， 将分上下行的线路、双向行驶的线路和环行线路抽象 为两条。然后，在最少转乘次数的基础上考虑共众对其他因素的需求，给出供公 众选用的多种参考方案。 并考虑以时间为主要目标的情况下，建立最优化模型确 定任意两站点行程时间最短的方案。 在考虑问题二的情况下， 根据地铁与邻近站点可换乘的信息，可将每个地铁 站点及其对应的所有公交站点抽象成一个点处理。 对于两条地铁线路可按照与问 题一相同的抽象方法处理。 在此基础上按照相同的思路确定任意两站点间的最佳 方案。 考虑到问题三的步行情况。 首先，继续将每个地铁站点及其对应的所有公交 站点抽象成一个点处理，这样地铁线就等同于公交路线。另外，将步行看成特殊 的换乘方式， 如果两个站点的步行时间小于 5 分钟，我们就认为这两个站点之间 可以相互换乘。 这样对于每个公交车站我们实际只需要考虑三种换乘方式，分别 为同站台换乘、步行到其它站台换乘和通过地铁站换乘。 对于问题三， 如果从另一个角度考虑，会发现根据公交及地铁站点的实际分 布情况， 有时会出现步行小段距离再转车的情况更能节省时间或转车次数。将步 行视作一种与地铁、公汽相同的出行方式，限定一定的步行距离，在此范围内优 于地铁与公汽，并用直达矩阵的方式进行处理。
数学建模国赛一等奖论文
电力市场输电阻塞管理模型摘要本文通过设计合理的阻塞费用计算规则，建立了电力市场的输电阻塞管理模型。
通过对各机组出力方案实验数据的分析，用最小二乘法进行拟合，得到了各线路上有功潮流关于各发电机组出力的近似表达式。
按照电力市场规则，确定各机组的出力分配预案。
如果执行该预案会发生输电阻塞，则调整方案，并对引起的部分序容量和序外容量的收益损失，设计了阻塞费用计算规则。
通过引入危险因子来反映输电线路的安全性，根据安全且经济的原则，把输电阻塞管理问题归结为：以求解阻塞费用和危险因子最小值为目标的双目标规划问题。
采用“两步走”的策略，把双目标规划转化为两次单目标规划：首先以危险因子为目标函数，得到其最小值；然后以其最小值为约束，找出使阻塞管理费用最小的机组出力分配方案。
当预报负荷为982.4MW时，分配预案的清算价为303元/MWh，购电成本为74416.8元，此时发生输电阻塞，经过调整后可以消除，阻塞费用为3264元。
当预报负荷为1052.8MW时，分配预案的清算价为356元/MWh，购电成本为93699.2元，此时发生输电阻塞，经过调整后可以使用线路的安全裕度输电，阻塞费用为1437.5元。
最后，本文分析了各线路的潮流限值调整对最大负荷的影响，据此给电网公司提出了建议；并提出了模型的改进方案。
一、问题的重述我国电力系统的市场化改革正在积极、稳步地进行，随着用电紧的缓解，电力市场化将进入新一轮的发展，这给有关产业和研究部门带来了可预期的机遇和挑战。
电网公司在组织电力的交易、调度和配送时，必须遵循电网“安全第一”的原则，同时按照购电费用最小的经济目标，制订如下电力市场交易规则：1、以15分钟为一个时段组织交易，每台机组在当前时段开始时刻前给出下一个时段的报价。
各机组将可用出力由低到高分成至多10段报价，每个段的长度称为段容量，每个段容量报一个段价，段价按段序数单调不减。
2、在当前时段，市场交易-调度中心根据下一个时段的负荷预报、每台机组的报价、当前出力和出力改变速率，按段价从低到高选取各机组的段容量或其部分，直到它们之和等于预报的负荷，这时每个机组被选入的段容量或其部分之和形成该时段该机组的出力分配预案。