移动式喷灌系统优化设计的数学模型

基于MCM2006A题,建立了均匀喷洒的喷灌系统优化管理模型.首先通过水力学计算,得到喷头射程、间距、数量和布局.然后将喷灌规则的确定转化为用单一小矩形条覆盖矩形区域的二维覆盖问题,针对一般情况设计了算法,得到管道移动方案.对所给喷灌区域,计算结果表明了模型的可行性.     

均匀喷灌的最优策略

本文建立了一个草地喷灌系统的数学模型 ,研究了喷淋半径可以不同时喷灌系统的效率 ,证明了喷淋半径不同时喷灌系统的最大效率为 1 831 1π ≈ 90 .2 % .此结果优于焦莹所给出的喷灌系统的最大效率3 32π ≈ 82 .7% .     

导数在农田喷灌喷水滴落点建模中的应用

<正>微积分在生活中具有广泛的应用,如位移的导数是速度,速度的导数是加速度等等.本文利用高中物理中的牛顿第二定律和高中数学微积分部分导数知识对农田喷灌水滴落点进行建模和分析,探究影响水滴落点的远近的因素.一、问题背景在农田喷灌过程中,需要考虑到喷灌的喷头设计,使得喷出来的水滴均匀落在农田里,防止农作物浇灌既出现浇水太多、也不会太少,从而提高农作物的喷灌效率.这涉及到灌     

第六届北京高中数学知识应用竞赛决赛试题参考解答

1 (满分 2 0分 )田径队的小刚同学 ,在教练指导下进行 30 0 0米跑的训练 ,训练要求是 :起跑后 ,匀加速 ,1 0秒达到每秒 5米的速度 ,然后匀速跑到2分 ;接着开始均匀减速 ,到 5分时已减到每秒 4米 ,再保持匀速跑 4分时间 ;在 1分之内 ,逐渐加速达到每秒 5米的速度 ,保持匀速跑 ;最后 2 0 0米 ,均匀加速冲刺 ,使撞线时的速度达到每秒 8米 .请按照上面的要求( 1 )画出小刚跑步的时间与速度的函数图像的示意图 ;( 2 )写出小刚进行长跑训练时 ,跑步速度关于时间的函数解析式 .解　 ( 1 )( 2 )v(t) =t2 ,t∈ [0 ,1 0 ]5 ,t∈ ( 1 0 ,1 2 0 ]- t1 80…     

任意多边形匀面重心的计算方法

我们都知道 ,当一闭曲线所围几何图形Ω是一均匀薄片时 ,其重心计算公式是ｘ0 =1Ｍ Ωｘｄｘｄｙｙ0 =1Ｍ Ωｙｄｘｄｙ其中Ｍ= Ωｄｘｄｙ为薄片质量(设密度为 1 )但在作具体计算时我们都清楚 ,计算的难度完全取决于Ω的形状 ,而即使是像多边形这样的简单图形 ,当边数稍稍多一点 .运算量就颇大 .本文的目的在于寻找一种计算任意多边形(凸凹不限 )均匀薄片重心的方法 .为叙述方便 ,后文我们把多边形围成的均匀薄片的重心简称为多边形匀面重心 .定理 1　设Ω1 ,Ω2 ,… ,Ωｎ是对均匀薄片Ω的一个几何剖分 ,每个Ωｉ的面积记为Ｓｉ,∑ｎｉ=1…     

空间均匀Boltzmann方程的唯一性

本文讨论空间均匀的Boltzmann方程的唯一性.当碰撞核满足Grad假设且对某s>2初始值f0∈Ls1(R3) ∩L1logL1时,我们证明了该方程守恒解是唯一的.     

参赛应用题选登

题 8　现在农田灌溉普遍使用喷灌设备 ,一套设备由一台口径为 0 .1米的抽水机和数节型号一样的输水软管组成 ,当用ｎ (ｎ∈Ｎ ,ｎ≤ 10 )节串连对接在抽水机出水口处的输水软管输水时 ,抽水机的出水速度ｖ(米 /秒 )是ｎ的一次函数 ,当ｎ =1时 ,ｖ =6,当ｎ= 3时 ,ｖ =5 .若将要浇的某块地划分为 10等份 ,每份所需水量相同 ,10份地由远到近依次需用 10 ,9,… ,2 ,1节串连的软管输水 ,记用ｎ节串连的软管输水所用的时间为ｔ(秒 ) .经测量知 :ｎ =1时 ,ｔ =60 0秒 .1)将ｔ表示为ｎ的函数 .2 )浇好此块地所用的总水量为多少立方米 ?解　 1)设ｖ =…     

方向数据的统计分析(Ⅵ)

5参数检验 类似于直线上的数据,方向数据统计分析也有参数检验问题.我们介绍最常用的几种参数检验方法. 本节要求观测数据θ1,θ2,…θN独立同分布,且N.密度函数为其中u0为总体平均方向,k为刻度参数. 5.1均匀性检验 许多实际问题中常会提出均匀性检验的问题,如鸽子回巢方向是否有“一定趋向,某一疾病的发病率是否有季节性,某产品的销售量是否有旺季淡季之分等. 假定样本来自M(u0,k)总体,由于当k=0时,M(u0,k)退化为均匀分布,因此均匀性检验问题等价于我们对于平均方向已知和未知这两种情形,分别给出均匀性检验的方法. 一、平均方向已知的均…     

第六届北京高中数学知识应用竞赛决赛

20 0 3年 3月 2 3日试　题1.(满分 2 0分 )田径队的小刚同学在教练指导下进行 30 0 0米跑的训练 ,训练要求是 :起跑后 ,匀加速 ,10秒达到每秒 5米的速度 ,然后匀速跑到 2分 ;接着开始均匀减速 ,到 5分时已减到每秒 4米 ,再保持匀速跑 4分时间 ;在 1分之内 ,逐渐加速达到每秒 5米的速度 ,保持匀速跑 ;最后 2 0 0米 ,均匀加速冲刺 ,使撞线时的速度达到每秒 8米 .请按照上面的要求(1)画出小刚跑步的时间与速度的函数图像的示意图 ;(2 )写出小刚进行长跑训练时 ,跑步速度关于时间的函数解析式 .2 .(满分 2 0分 )一农户收获土豆时 ,把土豆一堆一…     

车身非光滑表面凹坑排布对气动性能的影响

受仿生学非光滑旋成体减阻启发,以SAE(美国机动车工程师协会)标准模型为研究对象,采用CFD(计算流体力学)数值模拟方法,在SAE模型顶部布置不同排布形式和不同排布密度的凹坑单元,研究其对车身气动性能的影响.通过比较各模型的尾流、气流速度、压力场、湍流动能等流场性能指标,分析非光滑表面减阻机理以及造成各模型流场性质差异的原因.计算结果显示:当凹坑型非光滑单元以矩形排布时模型具有最小的气动阻力,且气动阻力随着凹坑密度的增加而减小,减阻率最高达到4.1%.     

静园草坪灌溉系统的改进

在本文中 ,我将讨论一个从自己的实际观察中总结出来的数学模型——静园草坪的灌溉系统问题 .文中证明了灌溉系统的最大效率是 3 32π .这个结论还可以应用于其他的一些领域 .这实际上是一个决策问题 ,它归结为用小块的图形去覆盖平面区域 .我们需要找到一种最佳的覆盖方法 ,使得重叠的部分最少 .这样 ,我们就有两个问题要解决 ,首先是如何评价覆盖方法的优劣 ,其次是如何找到最佳的覆盖方法 .文中给出了合理的评价准则 ,并且提出了一些深入研究的方向和建议 .     

Discriminantal Arrangements, Fiber Polytopes and Formality

Manin and Schechtman defined the discriminantal arrangement of a generic hyperplane arrangement as a generalization of the braid arrangement. This paper shows their construction is dual to the fiber zonotope construction of Billera and Sturmfels, and thus makes sense even when the base arrangement is not generic. The hyperplanes, face lattices and intersection lattices of discriminantal arrangements are studied. The discriminantal arrangement over a generic arrangement is shown to be formal (and in some cases 3–formal), though it is in general not free. An example of a free discriminantal arrangement over a generic arrangement is given.     

Modeling and optimization of salinization of irrigated soil

Considered in the paper is a filtering model with concentrated sources, which can be used in problems of sprinkler, furrow, etc. irrigation. The problem of optimal control of a parabolic system is investigated, in which control effects enter in both the coefficients of the model under investigation and the right-hand side, which can be an element of a negative Hilbert space. The problem posed is regularized, and an explicit form of the gradient of a quality criterion is obtained. Bibliography: 5 titles. Translated fromObchyslyuval' na ta Prykladna Matematyka, No. 80, 1996, pp. 3–11.     

CONTROLLING GROUNDWATER QUALITY WITH ENDOGENOUS REGULATORY INSTRUMENTS

ABSTRACT. This research presents a competitive dynamic model that endogenously evaluates the economics of regulatory tax-policy options. This model is then applied to an irrigated corn production area west of Kearney, Nebraska, where the average groundwater contamination level from nitrates is reported to be 8.7 parts per million (ppm). Results indicate that no regulatory policies are necessary for maintaining potable groundwater quality with either a surge-flow irrigation system or a sprinkler irrigation system. In areas where conventional furrow irrigation technology is being used, higher net economic benefits result from the adoption of a variable-tax on nitrogen fertilizer use, followed by a constant-unit tax and a pollution tax.     

An Algorithm for Reducibility of 3-arrangements

We consider a central hyperplane arrangement in a three-dimensional vector space. The definition of characteristic form to a hyperplane arrangement is given and we could make use of characteristic form to judge the reducibility of this arrangement. In addition, the relationship between the reducibility and freeness of a hyperplane arrangement is given     

The diffeomorphic types of the complements of arrangements in CP~3Ⅱ

For any arrangement of hyperplanes in CP~3,we introduce the soul of this arrangement. The soul,which is a pseudo-complex,is determined by the combinatorics of the arrangement of hyper- planes.In this paper,we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other.In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected.This generalizes our previous result on hyperplane point arrangements in CP~3.     

Optimal Risk-Sharing When Risk Preferences are Uncertain

In many cases, a firm or agency needs a product that only one vendor can supply and for which the final cost is uncertain. An optimal risk-sharing arrangement is sought when the buyer and contractor agree on the probability distribution of cost but the buyer is uncertain of the contractor's risk-preferences. We find that when the buyer and contractor have exponential utilities, the optimal profit arrangement for the higher risk-averse contractor is no longer linear but concave in the costs. The degree of concavity is affected by the probabilistic beliefs on the contractor's risk-preferences. As the more risk-averse contractor becomes more likely, her chosen profit arrangement becomes less concave approaching the ideal, linear arrangement. The less risk-averse contractor is provided a profit arrangement with a certainty equivalent above her reservation price. This is the price the buyer must pay in order to entice a less risk-averse contractor into agreeing to accept a more risky profit arrangement.Another formulation is considered that assumes the buyer and contractor maximize approximations to their certainty equivalents in order to provide a more practical and possibly viable approach to sole-source contracting.     

Reducibility of hyperplane arrangements

Certain problems on reducibility of central hyperplane arrangements are settled. Firstly, a necessary and sufficient condition on reducibility is obtained. More precisely, it is proved that the number of irreducible components of a central hyperplane arrangement equals the dimension of the space consisting of the logarithmic derivations of the arrangement with degree zero or one. Secondly, it is proved that the decomposition of an arrangement into a direct sum of its irreducible components is unique up to an isomorphism of the ambient space. Thirdly, an effective algorithm for determining the number of irreducible components and decomposing an arrangement into a direct sum of its irreducible components is offered. This algorithm can decide whether an arrangement is reducible, and if it is the case, what the defining equations of irreducible components are.     

The diffeomorphic types of the complements of arrangements in ℂℙ3 II

For any arrangement of hyperplanes in ??³, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. In this paper, we give a sufficient combinatoric condition for two arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient conditions on combinatorics for the arrangement of hyperplanes whose moduli space is connected. This generalizes our previous result on hyperplane point arrangements in ??³.