美赛模板
MCM美国大学生数学建模竞赛模板-公式
由假设得到公式1．We assume laminar flow and use Bernoulli’s equation:（由假设得到的公式）公式Where符号解释According to the assumptions, at every junction we have（由于假设）公式由原因得到公式2．Because our field is flat, we have公式, so the height of our source relative to our sprinklers does not affect the exit speed v2 （由原因得到的公式）；公式Since the fluid is incompressible(由于液体是不可压缩的), we have公式Where公式用原来的公式推出公式3．Plugging v1 into the equation for v2 ,we obtain（将公式1代入公式2中得到）公式11．Putting these together(把公式放在一起), because of the law of conservation of energy, yields：[]公式12．Therefore, from (2),(3),(5), we have the ith junction（由前几个公式得）公式Putting (1)-(5) together, we can obtain pup at every junction. In fact, at the last junction, we have公式Putting these into (1) ,we get（把这些公式代入1中）公式Which means that theCommonly, h is aboutFrom these equations, （从这个公式中我们知道）we know that ………引出约束条件4．Using pressure and discharge data from Rain Bird 结果,We find the attenuation factor （得到衰减因子，常数，系数）to be公式计算结果6．To find the new pressure ,we use the ( 0 0),which states that the volume of water flowing in equals the volume of water flowing out : （为了找到新值，我们用什么方程）公式Where() is ;;7．Solving for VN we obtain (公式的解)公式Where n is the …..8．We have the following differential equations for speeds in the x- and y- directions:公式Whose solutions are （解）公式9．We use the following initial conditions ( 使用初值) to determine the drag constant:公式根据原有公式10．We apply the law of conservation of energy（根据能量守恒定律）. The work done by the forces is公式The decrease in potential energy is （势能的减少）公式The increase in kinetic energy is (动能的增加)公式Drug acts directly against velocity, so the acceleration vector from drag can be found Newton’s law F=ma as : (牛顿第二定律)Where a is the acceleration vector and m is massUsing the Newton’s Second Law, we have that F/m=a and公式So that公式Setting the two expressions for t1/t2 equal and cross-multiplying gives公式22．We approximate the binomial distribution of contenders with a normal distribution:公式Where x is the cumulative distribution function of the standard normal distribution. Clearing denominators and solving the resulting quadratic in B gives公式As an analytic approximation to . for k=1, we get B=c26．Integrating, （使结合）we get PVT=constant, where公式The main composition of the air is nitrogen and oxygen, so i=5 and r=1.4, so23．According to First Law of Thermodynamics, we get公式Where ( ) . we also then have公式Where P is the pressure of the gas and V is the volume. We put them into the Ideal Gas Internal Formula:公式Where对公式变形13．Define A=nlw to be the ( )（定义）; rearranging (1) produces （将公式变形得到）公式We maximize E for each layer, subject to the constraint (2). The calculations are easier if we minimize 1/E.（为了得到最大值，求他倒数的最小值）Neglecting constant factors （忽略常数）, we minimize公式使服从约束条件14．Subject to the constraint （使服从约束条件）公式Where B is constant defined in (2). However, as long as we are obeying this constraint, we can write （根据约束条件我们得到）公式And thus f depends only on h , the function f is minimized at （求最小值）公式At this value of h, the constraint reduces to公式结果说明15．This implies（暗示）that the harmonic mean of l and w should be公式So , in the optimal situation. ………5．This value shows very little loss due to friction.（结果说明）The escape speed with friction is公式16．We use a similar process to find the position of the droplet, resulting in公式With t=0.0001 s, error from the approximation is virtually zero.17．We calculated its trajectory(轨道) using公式18．For that case, using the same expansion for e as above,公式19．Solving for t and equating it to the earlier expression for t, we get公式20．Recalling that in this equality only n is a function of f, we substitute for n and solve for f. the result is公式As v=…, this equation becomes singular (单数的).由语句得到公式21．The revenue generated by the flight is公式24．Then we have公式We differentiate the ideal-gas state equation公式Getting公式25．We eliminate dT from the last two equations to get （排除因素得到）公式22．We fist examine the path that the motorcycle follows. Taking the air resistance into account, we get two differential equations公式Where P is the relative pressure, we must first find the speed v1 of water at our source: （找初值）公式自己根据计算所画的图：1、为了…….(目的)，我们作了…….图。
美赛格式要求范文
美赛格式要求范文美赛（MCM/ICM）是美国大学生数学建模竞赛的英文缩写，是一项面向全球大学生的数学建模竞赛。
MCM/ICM每年提供若干个实际问题供参赛者选择，并规定参赛者提交一份由三人组成的队伍作品，要求队伍在规定的时间内解答问题并撰写一篇报告。
以下是美赛格式的一般要求：1.报告页数要求：参赛队伍通常需要撰写一篇1200字以上的报告。
具体的页数要求可以根据不同的问题和竞赛要求略有变化，但一般不超过20页。
尽管有页数限制，但在撰写报告时需要全面、清晰地阐述问题、解决方法和结论。
2.章节结构：一篇标准的美赛报告通常包括以下几个部分：-引言：介绍问题的背景和目的，明确解决问题的方法和目标。
-问题分析：对问题进行深入的分析和理解，包括重新表述问题、提出假设和限制条件，展开问题讨论。
-模型建立：建立一个或多个数学模型，以解决问题。
需要解释模型背后的理论基础和假设，并给出模型的描述和方程。
-模型求解：详细描述解决模型的方法、步骤和计算过程。
需要标注具体的计算公式、算法、图表和详细的计算结果。
-结果分析：对所得结果进行详细的解释和分析，包括结果的合理性和局限性，对模型的优缺点进行评价。
-结论与建议：总结所得结论，并提出可能的进一步研究方向和改进建议。
3.图表和数学符号的使用：美赛报告通常需要使用多个图表和数学符号，以支持和解释问题的分析和解决方法。
图表应该清晰、简洁，并配有必要的标注和说明。
数学符号应该统一、准确地使用，避免造成混淆。
5.语言表达：报告应使用准确、简练、清晰的语言表达问题、论证思路和解决方案。
语法、拼写和标点符号应正确无误。
尽管以上是一般的美赛报告要求，但具体的格式要求可能会因竞赛规则和题目的特殊性而有所不同。
建议参赛队伍在参赛前详细了解官方提供的竞赛规则和报告要求，并遵循官方给出的指导进行撰写报告。
同时，可以参考以往的优秀报告和获奖队伍的经验，借鉴其写作技巧和结构。
美赛数学建模模板
摘要：第一段：写论文解决什么问题1．问题的重述a. 介绍重点词开头：例1：“Hand move” irrigation, a cheap but labor-intensive system used on small farms, consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An (effective plan) is crucial to………b. 直接指出问题：例 1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes: the number of tollbooths that minimizes average delay experienced by cars.例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.例4: After mathematically analyzing the …… problem, our modeling group would like to present our conclusions, strategies, (and recommendations )to the …….例5：Our goa l is... that (minimizes the time )……….2．解决这个问题的伟大意义反面说明。
美赛写作模板及参赛经验
Tittle of paperSummary/Abstract Key words:I.Introduction（引言）Organ transplantation is a preferable treatment for the most serious forms of end-stage diseases. In recent years, advances in medical science and technology have made solid organ transplantation an increasingly successful and common medical procedure, a literal ''second chance at life". Not only does it offer the best hope for complete rehabilitation, but it has also proved to be the most cost-effective of all treatment options, including dialysis. Consequently, more and more people are benefiting from organ transplants and their survival rates are steadily improving. The surgical techniques involved have been mastered for half a century and are now considered as routine. The two main sources of kidneys for transplantation are deceased-donor kidneys and live-donations from family and friends. However, unfortunately, there is a considerable shortage of donor organs, compared to demands. As a matter of fact, efficient matching and allocation of organs donated has become an exigent problem.The United Network for Organ Sharing (UNOS), as the operator of the Organ Procurement and Transplantation Network (OPTN), is responsible for transplant organ distribution in the United States. UNOS oversees the allocation of many different types of transplants, including liver, kidney, pancreas, heart, lung, and cornea.Focusing on kidney transplantation, based on UNOS Kidney Allocation Model, we develop a mathematical model for US transplant networks. First, incoming organs are matched with waiting candidates by medical institutions considering the factors as ABO blood compatibility, the degree of recipient major HLA mismatch in order to obtain a matching degree applied on the allocation part. After that, from the patients’ perspective, on the basis of linear regression, priority weight is defined by pondering age, disease severity, time on waiting, PRA level, and region. Applying this mechanism of ranking, we realize MWBM (Maximum Weight Bipartite-graph Matching) and SMGS (Stable Matching based on Gale-Shapley algorithm). MWBM focuses on the optimal assignment of donors following the algorithm of bipartite-graph maximum weight matching; SMGS emphasizes the process of exchanges in order to obtain the stable exchanges between donors andcandidates on the waiting list.II.The Description of Problem（问题重述)III.Basic Assumptions●The level of mismatch is only relative to the number of antigens.●The data and information are accurately registered according to the medical measures ●The data and information are refreshed in time according to the status of the patients ●No differences in the quality of the donor kidneys●The quality of the donor kidney is constantIV.Definitions and Notations●Kidney transplantation: A kidney transplant is a surgical procedure to implant a healthykidney into a patient with kidney failure.●Prioritization●MD: Matching Degree●PW: Prioritization weight●MWSM: Maximum Weight Bipartite Matching●SMGS: Stable Matching based on Gale-Shapley algorithm或V.ModelsThrough the investigation of US transplantation network, we draw a general picture ofthe mechanism. With reference to some resources available on the website of UNOS, a flow chart (Figure 1) is developed showing the procedure of the network.Currently, the initial waiting list is composed of patients who are waiting for a kidney or combined kidney-pancreas transplant. For the first time, the patients are requested to show the correct and scientific information to the US kidney transplant network which is needed for donor-recipient matching, the ranking of patients on the waiting list, and determining the outcome of those transplanted. The patients’ waiting lists are composed of initial patients, historical patients and unsuccessful recipient after transplantation. Historical patients refer to registered patients whose status have changed and have an influence on the procedure. A patient is taken off the waiting list when a graft is offered and accepted by that patient or the patient is dead while waiting for a transplant. Unsuccessful recipients refer to the patients who have a bad result of transplantation calling for transplantation again, as it is so-called relistFigure 1. A schematic depicting the steps occurring in the transplantation networks......Table 1.Survival rate involving HLA mismatchVI.Conclusions.Our model for the optimal allocation of the donor organs is established by three modules, procurement of MD and PW, optimal assignment by MWBM model and Stable Matching of Gale-Shapley algorithm. The model has offered a convincing procedure of the allocation with the ……VII.Strengths and weaknesses(模型优缺点)Strengths●……Weaknesses●VIII.References注意文献的积累，不要等到文章写完再去重新寻找文献。
美国赛写作模版模板
CONTENTSAbstract (1)Ⅰ Introduction (2)ⅡGeneral Assumptions (3)ⅢKey Terminology (3)ⅣModel Development.......................................................................... (3)4.1 (4)4.1.1 (4)4.1.2 (4)4.1.3 (4)4.2 (5)4.2.1 (5)4.2.2 …………………………………................................................................ .64.2.3 (9)4.3 (9)4.3.1 (9)4.3.2 (10)4.3.3 (10)4.4 (10)4.4.1 (10)4.4.2 (10)4.4.3 (10)4.5 (13)4.5.1 (13)4.5.2 (13)4.5.3 (13)ⅤStrengths and Weakness (14)ⅥConclusion (15)ⅦReferences (16)ⅧAppendix (16)TITLEAbstract♦In our essay, we first develop a basic model to account for the fundamental but important phenomena in baseball game and then three improved models for some details. When developing the basic model, in order to analyze overall hitting process clearly, we focus on simplifying the practical problem into a mechanical model.We resolve basic model through three steps, each step considering one important part of the model that greatly impacts our searching for the “sweet spot”. After resolving the basic model, we begin to revise the model to make it more practical.♦Before resolving the basic model, we establish a criteria for evaluation-the proportion of effective energy transmission r, a criteria used to determine at which spot of the bat the maximum proportion of energy output by human is transferred to the ball. Our three steps are designed as follows:⑴In our first step, we mainly investigate the action process between the simplified baseball bat andbaseball. Ignoring other influencial factors, we find one “sweet spot”.⑵In our second step, our focus moves to the relationship between the hand and the bat. Ignoringother influencial factors, we find another “sweet spot”.⑶In our last step, we integrate merits of each “sweet spot ” in above two steps so that we find out a“sweet spot zone”. Then we figure out the variation of r in “sweet spot zone”and find the maximum r.♦After resolving the basic model, we revise our model in three aspects to make it more practical.⑴In our first improvement, we restore the simplified line and particle with objects of different shapeand find out the “sweet spot”after revision.⑵In our second improvement, we consider the shape change of the baseball bat when the bat hits theball and also calculate the lost energy consumed by the shape change of bat made of different material.After revision, we find that the position of the practical “sweet spot”should be a bit more closely than that of “sweet spot”calculated in basic model to the thin end of the bat.⑶In our last improvement, we take into account the vibration that might also impact our searchingfor the “sweet spot”.After detailed analysis, we calculated the lost energy consumed by vibration when the ball hits different spot on the bat and figure out that the position of the practical “sweet spot”should also be a bit more closely than that of “sweet spot”calculated in basic model to the thin end of the bat.♦ⅠIntroductionOn the softball field, hitters usually attempt their best to hit the baseball.In addition to the physical strength the player applied to the baseball, the hitting spot also has great influence on our searching for the sweet spot. Usually, according to the moment of momentum theorem, it seems that the fat end of the baseball bat should be the best hitting spot. However, this is known to be empirically incorrect. Experienced player usually chooses a spot called “sweet spot”to be the best hitting spot, at which the maximum power is transferred to the baseball, thus the hit ball travelling the longest distance. Howard Brody(1989) conducted a series of experiments and investigated that vibration of the baseball would affect the choice of the best hitting spot. Rod Cross(1998) proved that both center of percussion and vibration of the bat affect the searching for the sweet spot through a series of experiment. However, none of scientistshas given a theoretical method to find out the solution. In our essay, we attempt to find out and explain that the sweet spot does not lies on the end of the bat.ⅡGeneral Assumption♦The baseball and baseball bat are assumed to move at uniform velocity. Air friction and gravity can be neglected♦The direction of the velocity of the particle is assumed to collinear that of the linear veloc ity of the action point.♦Baseball bats made of different materials are assumed to attain identical energy after accelerated by human.ⅢKey TerminologyTable 1.Symbols.Symbols Description UnitsⅣModel Development4.1 Simplifying the situationIn order to address the problem, we need to simplify the hitting process. It is reasonable to abstract the process as follows: replacing the baseball bat with a single line, on which the mass is distributed uniformly, and substituting a particle for the baseball; fixing one end of the line so that the line can oscillate on the smooth ground freely; using the process that a baseball hits an oscillating rod to simulate the process that a baseball hits a bat.This is the basic and simplest model that we can extract from hitting process, based on which we can analyze the most basic motion of these two objects. However, we cannot ignore the importance of the elasticity, the vibration and the antihunt action, which might also have impact on our searching for the sweet spot.4.1.1 Basic ModelWe analyze the whole hitting process:Step oneAt the beginning of hitting, the particle moves at a fixed velocity to the line that is oscillating at a fixed angular velocity and linear velocity. The moment of the momentum of the overall system with respect to o is:1112o L m v d J ω=-+, (1) After the hitting, the particle and the line separate and move respectively. The moment of the momentum ofthe overall system with respect to o is2112o L m v d J ω''=+As exterior impulsive moment vanishes, we can then get:12o o L L =that is112112m v d J m v d J ωω''-+=+ (2) Given the material of the line and the particle, we can achieve the coefficient of the restitution between the line and the particle, a coefficient that will help us to achieve the relationships of the linear velocity of the line and the particle.1212v v k v v ''-=+ (3)22v d ω= , 22v d ω''= (4)Putting .Eq (1),(2),(3)and (4) together, we have junctions()221122121221233d m v l m v k v v v m d m l-+++⎡⎤⎣⎦'=+ (4) ()22111222222123133d k m v d km L m d m l m ωωω-+-+'=+ (5)When considering at which spot of the line the maximum power is transferred to the particle, we attempt to work out a spot at which the hit particle reaches the fastest velocity. Differentiating 1v 'with respect to d , we will achieve that when123d m ω=(6)the hit particle reaches the fastest velocity. We just define this spot as the spot of moment(SOM).Step twoIt is necessary for us to take the function of the hands into account if we want to simulate the hitting process exactly. At the instant of hitting the particle, the impulse of the particle will rotate the line unless the particle hits a specified spot on the line-the center of percussion(COP) at which the impulse will only move the translationally with no rotation. According to the momentum theorem()22221111122ox I m l m l m v v ωω''=--+ (7)If the particle hits the COP exactly, the momentum theorem o x I should be 0. Inserting .Eq (4) and (5) into .Eq (7)leads to equation:()()()1212212132062w k d l lm mvd d m l m ω+-+=+ (8)Because all of the parameters in .Eq (8)are greater than 0, only under condition that 320d l -= can the .Eq (8) result in a proper solution. Then we can know the position of the COP:23C O P d l =(9)Step threeAccording to the investigation of ……..(), if viewing hand as soft tissue, we can get the relationship between the force pressed on the tissue and the degree at which the hands ’ shape changes012aseF a-= (10)where♦ 0F represents the force pressed on hands♦ s denotes the relative displacement of the point on palm♦ b and c are constants which have been discussed in !!!!!!!!!!!!!!!!!!!!!!!!!文献As the the force pressed on palm generates the relative displacement, the hand apply negative force on the line, thereby absorbing part of the energy transferred from our arms to the particle. We can easily figure out the lost energy through definite integral:100s w F ds =⎰(11)212ase asa-+-=At the instant of hitting, the energy transferred from the line to the particle is:22222221126w J m l ωω== (12)The energy achieved by the particle is:22011111122w m v m v '=- (13) To transfer the maximum proportion of power output from the human body to the particle, we define this proportion as12w p w w =+ (14)Plugging .Eq (4),(5),(10),(11),(12),(13) into .Eq (14),we have()()()2222211121222112222122231122310.3672as m d m v K l m v dl m K m v d m l mp easaωω-+++-++=-+-+空As the value of p varies when the hitting spot on the rod changes, the variation of p with respect to0d and K is pictured in Fig.14.1.2 Improvement ⅠWith the purpose of improving the practicability, we have to restore the single line and the particle with bodies of axisymmetry (In effect, both the baseball and the bat are axisymmetry). In this way, our model more closely resembles the real hitting process. In this situation, we regard the two bodies as rigid bodies. Unlike the moment of inertia of a line, the moment of inertia of the bat has to be calculated through definite integral. Since we cannot attain the equation of the generating line of the equation, here is an example to compute the moment of inertia of a circular cone to illustrate our methods.In practice, the motion state of an axisymmetrical body, the mass of which is distributed uniformly, is usually equivalent to that of its axis line, on which the mass of the body concentrates. However, the mass is unevenly distributed on the axis line. By computing the moment of inertia of the axis line, we will reach the same result as calculating the moment of inertia of the circular cone. Like circular cone, all of the axisymmetrical bodies can also be figured out in this way.4.1.4 Improvement ⅡAssume that the ball is completely elastic and the energy dissipation mainly stems from the deformation of the bat. As suggested by Adair (2002), the hitting between the bat and the baseball can be reasonably modeled by a ball and a flat without introducing large error. This collision can be simply described as Figure 1. Denoting by R the radius of the ball and by δ the depth of the indentation, the equation of the sphere, on the surface of contact, is[]222()r z R R δ++-= (14)Figure 1. The indentation by a baseball.For shallow indentations /1R δ and /1z R , where in the second inequality the coordinate z is meant to be on the indented surface. According to Asaro and Lubarda (2006), the distributed force takes theform1/2202()1r q r q a ⎛⎫=- ⎪⎝⎭ (15)The total hitting force is1/22200202213a r P q rdr a q a ππ⎛⎫=-=⎪⎝⎭⎰(16)The displacement of the indented surface is given as22212a r w R a ⎛⎫=- ⎪⎝⎭r a ≤ (17) or alternatively, in terms of the depth δ of the indentation,22rw Rδ=-r ≤ (18)Consequently, the energy bat E absorbed by the bat can be expressed as4200232d 55a bat q a a P E qwr r RRππ==⎰(19)4.1.4 Improvement ⅢBy employing the d ’Alembert ’s Principle, one gets the equilibrium equation:()()22,s s s F y x dx F F dx f x t dx t x ρ∂∂⎛⎫=-++ ⎪∂∂⎝⎭(20)where()x ρdenotesthe quality of the unit lengths F is shear force(),f x t is external excitation.Here the shear deformation and the rotation of the cross section are neglected. The small element satisfies the momentum balance which requires(),02s Mdx M dx M F dx f x t dxx ∂⎛⎫+---= ⎪∂⎝⎭(21)Droping the high order small quantity yieldss M F x∂=∂ (22)According to the mechanics of materials, the moment relates the deflection by:()()()2,,y x tM x t E I x x∂=∂ (23) Inserting .Eq (22) and (23) into (21) leads to:()()()()()222222,,,y x t y x t EI x x f x t x x t ρ⎡⎤∂∂∂+=⎢⎥∂∂∂⎣⎦(24)The dynamic equation (24) provides unified theoretical framwork for considering the vibration arbitrayrod or beam. When the rod is uniform, in both quality and shape, the .Eq (24) reduces to()()()4242,,,y x t y x t EIfx t xtρ∂∂+=∂∂ (25)Under our current interest, namely, the hitting between the baseball and the rod, the impulse reads()(),,0F x d tfx t δ⎧-=⎨⎩(26)Where F represents the impulse force By writing()()(),y x t x q t φ=we have()()()2200qt q t E I x ωφωρφ⎧+=⎪⎨''''-=⎪⎩(27) ()()()440x x φβφ-= (28)Obiviously, the solution of ()q t is()()sin q t A t ωθ=+ (29)The homogeneous solution of (27)is()1234cos sin cosh sinh x c x c x c x c x φββββ=+++ (30) Where ()1,2,3,4i c i =are constants which are yet to be determined by following boundary conditions:()()()()()00, 000EI K l l φφφφφ'''=-=⎧⎪⎨'''''==⎪⎩(31) From .Eq (31),we obtain the frequency equation()()()()()()c o s h s i n c o s s i n h 0K l K c o n s l E I l E I l l βββββββ+⋅+-= (32)If 0K =, .Eq (32) reduces tot a n t a n h l l ββ=(33)Normalizing .Eq (32)as:()()()()()00cosh cos sin cos sinh 0K l K l l l l βββββ++-=⎡⎤⎣⎦ (34)with 0K K EI β=Assigning K with a certain value ranged from 0 to 1, we attempt to find out the numerical solution offrequency.The variation of .Eq (34) with respect to l β is illustrated in Fig.1. As can be seen from the figure, the first two-oder frequencies are 3.87701 and 7.01587, respectively, when 0.1K =.重画图4.2 Model ⅡBecause wood has been removed from the bat and replaced by some substance with a s maller density than the wood, not only is the bat lighter, but the center of the gravity of the bat moves closer to the thin end. Since center of percussion(COP) and is relavant to the center of the gravity , the COP also movesJ M α=212t t ωαϕα=⎧⎪⎨=⎪⎩22αϕω⇒= We can get the mechanical energy of the bat:212E J ω=122E J J αϕαϕ=⋅=E Mϕ=4.2.14.2.24.2.34.3 Model Ⅲ4.3.14.3.24.3.34.44.4.14.4.24.4.34.54.5.14.5.24.5.3ⅤStrengths and WeaknessesStrengths♦Our basic model’s strength is that we consider the whole process of energy transmission, energy from hand to bat to baseball.♦We view the palm of the hand as soft tissue and consider the shape change of the hand so that we can model the strengths the hand press on the bat.♦The improvement in basic model take into account the energy loss from vibration, and we develop the “simple support and spring” model to model the function of human hand.♦We consider and compute the lost energy consumed by the shape change of the bat.WeaknessesSince neglecting the data of several parameters in the model, we have difficulty in deducing a perfect solution. We introduce some examples so as to illustrate our method.ⅥConclusionⅦReferencesⅧAppendix。
美赛论文模板(超实用)
TitileSummaryDuring cell division, mitotic spindles are assembled by microtubule-based motor proteins1, 2. The bipolar organization of spindles is essential for proper segregation of chromosomes, and requires plus-end-directed homotetrameric motor proteins of the widely conserved kinesin-5 (BimC) family3. Hypotheses for bipolar spindle formation include the 'push−pull mitotic muscle' model, in which kinesin-5 and opposing motor proteins act between overlapping microtubules2, 4, 5. However, the precise roles of kinesin-5 during this process are unknown. Here we show that the vertebrate kinesin-5 Eg5 drives the sliding of microtubules depending on their relative orientation. We found in controlled in vitro assays that Eg5 has the remarkable capability of simultaneously moving at 20 nm s-1 towards the plus-ends of each of the two microtubules it crosslinks. For anti-parallel microtubules, this results in relative sliding at 40 nm s-1, comparable to spindle pole separation rates in vivo6. Furthermore, we found that Eg5 can tether microtubule plus-ends, suggesting an additional microtubule-binding mode for Eg5. Our results demonstrate how members of the kinesin-5 family are likely to function in mitosis, pushing apart interpolar microtubules as well as recruiting microtubules into bundles that are subsequently polarized by relative sliding. We anticipate our assay to be a starting point for more sophisticated in vitro models of mitotic spindles. For example, the individual and combined action of multiple mitotic motors could be tested, including minus-end-directed motors opposing Eg5 motility. Furthermore, Eg5 inhibition is a major target of anti-cancer drug development, and a well-defined and quantitative assay for motor function will be relevant for such developmentsContentTitile (1)Summary (1)1Introduction (1)1.1Restatement of the Problem (1)1.2Background (1)1.1.1Common Solving Technique (1)1.1.2Previous Works (1)1.3Example (1)2Analysis of the Problem (1)2.1Outline of the Approach (1)2.2Basic Assumptions (2)2.3Definitions and Key Terms (2)3Calculating and Simplifying the Model (2)4The Model Results (3)5Validating the Model (3)6Strengths and Weaknesses (3)6.1Strengths (3)6.2Weaknesses (3)7Food for Thought (3)8Conclusion (3)References (4)Appendices (4)Appendix A Source Code (4)Appendix B (4)1Introduction1.1Restatement of the Problem …1.2Background…1.1.1Common Solving Technique…1.1.2Previous Works…1.3Example…2Analysis of the Problem …2.1Outline of the Approach…2.2Basic Assumptions●●●●●2.3Definitions and Key Terms●●●●Table 1.…Symbol Meaning Unit3Calculating and Simplifying the Model …4The Model Results……5Validating the Model…6Strengths and Weaknesses6.1S trengths●●●●6.2W eaknesses●●●●7Food for Thought…8Conclusion….References…AppendicesAppendix A Source CodeHere are the simulation programmes we used in our model as follow. Input matlab source:……….Appendix B…….Input C++ source：…………..…………..。
【完整解析】美赛-数学建模-写作模版(各部分)
Summary：clearly describe your approach to the problem and,most prominently,your most important conclusions.●Restatement and clarification of the problem:State in your own words what you aregoing to do.●Explain assumptions and rationale（principle）/justification:Emphasize the assumptionsthat bear on the problem.Clearly list all variables used in your model.●Include your model design and justification for type model used or developed.●Describe model testing and sensitivity analysis,including error analysis,etc.●Discuss the strengths and weaknesses of your model or approach摘要第一段：写论文解决什么问题.1．问题的重述a.介绍重点词开头：例1：“Hand move”irrigation,a cheap but labor-intensive system used on small farms,consists of a movable pipe with sprinkler on top that can be attached to a stationary main.例2:……is a real-life common phenomenon with many complexities.例3：An(effective plan)is crucial to………b.直接指出问题：例1：We find the optimal number of tollbooths in a highway toll-plaza for a given number of highway lanes:the number of tollbooths that minimizes average delay experienced by cars.我们找到了在给定XX的情况下最佳的……例2：A brand-new university needs to balance the cost of information technology security measures with the potential cost of attacks on its systems.XX需要具有B性能的C例3：We determine the number of sprinklers to use by analyzing the energy and motion of water in the pipe and examining the engineering parameters of sprinklers available in the market.我们通过分析参数B确定A，并且检验了现实情况C例4:After mathematically analyzing the……problem,our modeling group would like to present our conclusions,strategies,(and recommendations)to the…….在数学分析B后，我们的模型组将呈现了我们的结论和建议We begin by considering only the rigid recoil effects of the bat–ball col-LisionOur main goal is to understand the sweet spot.A secondary goal is tounderstand the differences between the sweet spots of different bat types.Because the collision happens on such a short time-scale(around1ms),we treat the bat as a free body.That is to say,we are not concerned with the batter’s hands exerting force on the bat that may be transferred to the ball....Our paper is organized as follows....例5：Our goal is...that(minimizes the time)……….2．解决这个问题的伟大意义反面说明。
美赛论文优秀模版可编辑
2015Mathematical Contest in Modeling (MCM/ICM) Summary SheetIn order to evaluate the performanee of a coach, we describe metrics in five aspects: historicalrecord, game gold content, playoff performanee, honors and contribution to the sports. Moreover, each aspect is subdivided into several sec on dary metrics. Take playoff performa nce as example, we collect postseas on result (Sweet Sixtee n, Final Four, etc.) per year from NCAA official website, Wikimedia and so on.First, ****grade.To eval*** , in turn, are John Wooden, Mike Krzyzewski, Adolph Rupp, Dean Smith and Bob Kni ght.Time line horizon does make a difference. According to turning points in NCAA history, we divide theprevious century into six periods with different time weights which lead to the cha nge of ranking.We con duct sen sitivity an alysis on FSE to find best membership fun cti on and calculati on rule. Sen sitivity an alysis on aggregation weight is also performed. It proves AM performs better than single model. As a creative use,top 3 presidents (U.S.) are picked out: Abraham Lincoln, George Washi ngton, Fran kli n D. RooseveltAt last, the stre ngth and weak ness of our mode are discussed, non-tech ni cal expla nati on is prese nted and the future work is poin ted as well.Key words: Ebola virus diseaseEpidemiology West Africa; ******ContentsI. I ntroduct ion (2)1.1 ............................................................................................................................................................................... 2 For office use only Team Con trol Number For office use only T1 _____________________ 11111 T2 ______________________ F1 _____________________ F2 _____________________ T3 ____________________ T4 ____________________Problem Chose nABCD F3 _____________________ F4 _____________________1.2 (2)1.3 (2)1.4 (2)1.5 (2)1.6 (2)II.The Descripti on of the Problem (2)2.1How do we approximate the whole course of pay ing toll? (2)2.2How do we defi ne the optimal configuration? (3)2.3The local optimizati on and the overall optimization (3)2.4The differe nces in weights and sizes of vehicles (3)2.5What if there is no data available? (3)III....................................................................................................................................................................................... M odels (3)3.1Basic Model (3)3.1.1Terms, Definitions and Symbols (3)3.1.2Assumpti ons (3)3.1.3The Foun datio n of Model (4)3.1.4Soluti on and Result (4)3.1.5An alysis of the Result (4)3.1.6Stren gth and Weakness (4)3.2Improved Model (4)3.2.1Extra Symbols (5)3.2.2Additi onal Assumpti ons (5)3.2.3The Foun datio n of Model (5)3.2.4Soluti on and Result (5)3.2.5An alysis of the Result (6)3.2.6Stren gth and Weakness (6)IV.Con clusi ons (6)4.1Con clusi ons of the problem (6)4.2Methods used in our models (6)4.3Applicati ons of our models (6)V.Future Work (6)5.1Ano ther model (6)5.1.1The limitations of queuing theory (6)5.1.2 (6)5.1.3 (7)5.1.4 (7)5.2Ano ther layout of toll plaza (7)5.3The n ewly- adopted chargi ng methods (7)VI.References (8)VII.Appe ndix (8)I.I ntroductionIn order to indicate the origin of the toll way problems, the following background is worth men ti oning.1.11.21.31.41.51.6II.The Description of the Problem2.1How d o we approximate the whole course of pay ing toll?2.2How d o we defi ne the optimal con figurati on?1)From the perspective of motorist:2)From the perspective of the toll plaza:3)Compromise:2.3The l ocal optimization and the overall optimizationVirtually:2.4The differe nces in weights and sizes of vehicl es2.5What if there is no data availabl e?III.Models3.1Basic Model3.1.1Terms, Definitions and SymbolsThe sig ns and defi niti ons are mostly gen erated fronqueu ing theory.3.1.2Assumpti ons3.1.3The Foun dation of Model1)The utility functionThe cost of toll plaza:The loss of motorist:The weight of each aspect:Compromise:2)The integer programmingAccord ing to queu ing theory, we can calculate the statistical properties as follows.3)The overall optimization and the local optimizationThe overall optimization:The local optimization:The optimal number of tollbooths:3.1.4Solution and Result1)The solution of the integer programming:2)Results:3.1.5An alysis of the ResultLocal optimization and overalloptimization:Sensitivity: The result is quite sen sitive to the cha nge of thehree parametersTrend:Comparison:3.1.6Stre ngth and Weak nessStrength: In despite of this, the model has provedhat . Moreover, we have draw n some usefulcon clusi on sabout . The model is fit for, such asWeakness:This model just applies to . As we havestated, . That' s just whatwe should do in the improved model.3.2 Improved Model3.2.1Extra SymbolsSigns and defi niti ons in dicated above are still valid. Here are some extra sig ns and defi niti ons.3.2.2Additi onal Assumpti onsAssumpti ons concerning the an terior process are the same as the Basic Model.3.2.3The Foun dation of Model1) How do we determine the optimal number?As we have con cluded from the Basic Model,3.2.4Solution and Result1)Simulation algorithmBased on the analysis above, we design our simulation arithmetic as follows.Step1:Step2:Step3:Step4:Step5:Step6:Step7:Step8:Step9:2)Flow chartThe figure below is the flow chart of the simulatio n.3)Solution3.2.5 Analysis of the Result3.2.6 Stre ngth and Weak nessStrength: The Improved Model aims to make up forthe n eglect of . The result seems to declare that this model is more reas on able tha n the Basic Model and much more effective tha n the existi ng desig n.Weakness: . Thus the model is still an approximate on a large scale. This hasdoomed to limit the applications of it.IV. Conclusions4.1 Con clusi ons of the probl em4.2 Methods used in our mod els4.3 Applicati ons of our mod elsV. Future Work5.1 Ano ther model5.1.1 The limitations of queuing theory5.1.25.1.35.1.41)2)3)4)5.2 Ano ther layout of toll plaza5.3 The newly- ad opted charging methodsVI. References[1][2][3][4]VII. Appe ndix。