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1999年全国初中数学联合竞赛第一试第2道题是:△ABC的周长是24,M是AB的中点,且MC=MA=5,则△ABC的面积是().(A)12(B)16(C)24(D)30解∵MA=MB=MC=5,∴∠ACB=90°.已知周长是24,则AC+BC=14,... 相似文献
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证明台体积公式的新方法吴小平(重庆师范学院数学系630047)本文利用共面定理,非常简明地证明了台的体积公式.如果两个四面体有一个公共面,称它们是一对共面四面体.共面定理:若直线PQ与△ABC所在的平面π交于M,则VP-ABCVQ-ABC=PMQM.... 相似文献
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平几中的“分点坐标公式”及应用116600大连开发区一中邹楼海定理如图1,P为△ABC的BC边上一点,一直线分别交AB、AC、AP干M、N、_、_.B尸*M*NQ.记人一_,。;一_.x,一_.、、··。-PC·-IMA”-‘NA”_Q。,。;.;,... 相似文献
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On Subspaces of Bloch Space and Series with Hadamard Gaps 总被引:4,自引:0,他引:4
本文研究了由修改的Besov模和Carleson测度所定义的Bloch空间的一类子空间.利用这类子空间与Hadamard缺项级数之间的关系,证明了他们之间的包含关系.作为所得结果的一个简单推论,本文对K.Stroethof关于BMOA和VMOA的一个未解决的问题作出了否定的回答. 相似文献
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此不等式是:若M 当且仅当M=1时等号成立.其证明极易,这里从略.由不等式所显示的信息知,它的结构简单,特征分明,其左端是一个分子为1的分式模型,右端则是与之相关的整式.这就意味着该不等式有把一个分式转化为一个整式的功能.正因为如此,运用不等式(*)可以使许多老问题获得新的解法.下面主要以一些竞赛题为例,说明不等式(*)的应用. 例1 设0<a<β<,求证: 证明 设原不等式左端为Q,先把Q化作依不等式(*)得 例 2 已知 P为△ABC内一点,BC-a,CA=b,AB=C.点P到BC、CA、AB的距离… 相似文献
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共享单车是我国大力提倡的低碳交通出行模式,加快共享单车发展是解决最后一公里、城市拥堵和环境污染等问题的重要途径。由于人们停放共享单车的无规律性,使得共享单车系统中各车桩的单车库存量存在不平衡。如何合理的对车桩中的单车进行重新调配,来满足用户的需求,是相关企业亟待解决的问题。共享单车的调配路线优化是优化车桩库存量的重要手段之一。本文研究多仓库条件下的货车调配路线优化问题,建立了一个混合整数非线性规划模型。不同于传统的路径优化问题的研究大多是以成本或时间为目标,本文采用基于车桩库存量的非线性惩罚函数来表示用户需求,从而使得所研究的问题是一个凸函数优化问题。为了简化本文的问题,将目标函数分段线性化。基于车桩网络的特点,设计了变邻域搜索算法,以及构建初始解的贪婪算法。最后,以某共享单车公司为例,进行算例分析,来说明模型和算法的合理性和有效性。 相似文献
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针对具有n个通讯站的局域网络,运用增加或调整虚设站的方法,给出一种在混合距离下的极小费用生成树的算法.并就MCM91问题B,求出了极小费用生成树,其总费用小于美国马里兰州里斯勃来莱州立大学数学科学系B.A.Fusaro所提供的论文中的费用. 相似文献
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L.F. Shampine 《Applied Numerical Mathematics》1985,1(2):107-119
Many problems have been proposed for the testing and evaluation of mathematical software for the solution of the initial value problem for a system of ordinary differential equations. The stiffness of a given problem is of great significance for testing, but the concept is at best somewhat vague and the few quantitative measures of stiffness being used are of limited value. A relatively precise and quantitative way is proposed to answer the questions: How does the stiffness vary in the course of the integration of a given problem? Is a given problem A stiffer than a given problem B, and if so, by how much? 相似文献
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《European Journal of Operational Research》1998,104(2):321-332
The location of a rapid transit line (RTL) represents a very complex decision problem because of the large number of decision makers, unquantifiable criteria and uncertain data. In this context Operational Research can help in the design process by providing tools to generate and assess alternative solutions. For this purpose two bicriterion mathematical programming models — the Maximum Coverage Shortest Path model and the Median Shortest Path model — have been developed in the past. In this paper a new bicriterion model, which can evaluate in a more realistic way the attractivity of an RTL is introduced. To calculate an estimation of the non-inferior solution set of the problem, a procedure based on a k-shortest path algorithm was developed. This approach was applied to a well-known sample problem and the results are discussed and compared with those obtained using a Median Shortest Path model. 相似文献
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Dehua Xu 《Applied mathematics and computation》2010,217(2):939-8824
The purpose of this paper is to point out that if there are some machines that do not process any job then the mathematical programming model provided by Eren [T. Eren, A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect, Applied Mathematics and Computation 209 (2009) 186-190] may not be a valid one. A simple way to fix this problem is given. Furthermore, based on the idea of Eren’s model, a general mathematical programming model is proposed. 相似文献
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Jia-Sheng heh 《Mathematical and Computer Modelling》1999,30(11-12)
Problem solving is a style of thinking, which transforms a given problem to the goal state through a so-called PS (problem solving) path. Different from the traditional GPS (General Problem Solver) approach, the focus in this paper is placed on how to judge the performance of PS paths, that is, the evaluation problem of problem solving.A series of PS paths point from the given source problem to the destination goal, then form a PSN (PS Network). This paper proposes an elaborated CPSN (Coordinate Problem Solving Network) as the evaluation model of problem solving. In CPSN, each problem is assigned a unique coordinate and then each PS path can have an evaluation vector. Several examples show such arrangement can give more insight to PS paths.Furthermore, an incremental learning algorithm is developed for the update of CPSN. When a new PS path is obtained, it is not necessary to recalculate the whole CPSN. Examples show such algorithm provides a more efficient way in finding new PS paths. 相似文献
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Theories of monochromatic high-frequency electromagnetic fields have been designed by Felsen, Kravtsov, Ludwig and others
with a view to portraying features that are ignored by geometrical optics. These theories have recourse to eikonals that encode
information on both phase and amplitude — in other words, are complex-valued. The following mathematical principle is ultimately
behind the scenes: any geometric optical eikonal, which conventional rays engender in some light region, can be consistently
continued in the shadow region beyond the relevant caustic, provided an alternative eikonal, endowed with a non-zero imaginary
part, comes on stage.
In the present paper we explore such a principle in dimension 2. We investigate a partial differential system that governs
the real and the imaginary parts of complex-valued two-dimensional eikonals, and an initial value problem germane to it. In
physical terms, the problem in hand amounts to detecting waves that rise beside, but on the dark side of, a given caustic.
In mathematical terms, such a problem shows two main peculiarities: on the one hand, degeneracy near the initial curve; on
the other hand, ill-posedness in the sense of Hadamard.We benefit from using a number of technical devices: hodograph transforms,
artificial viscosity, and a suitable discretization. Approximate differentiation and a parody of the quasi-reversibility method
are also involved.We offer an algorithm that restrains instability and produces effective approximate solutions. 相似文献
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C Lucas S A MirHassani G Mitra C A Poojari 《The Journal of the Operational Research Society》2001,52(11):1256-1266
A supply chain network-planning problem is presented as a two-stage resource allocation model with 0-1 discrete variables. In contrast to the deterministic mathematical programming approach, we use scenarios, to represent the uncertainties in demand. This formulation leads to a very large scale mixed integer-programming problem which is intractable. We apply Lagrangian relaxation and its corresponding decomposition of the initial problem in a novel way, whereby the Lagrangian relaxation is reinterpreted as a column generator and the integer feasible solutions are used to approximate the given problem. This approach addresses two closely related problems of scenario analysis and two-stage stochastic programs. Computational solutions for large data instances of these problems are carried out successfully and their solutions analysed and reported. The model and the solution system have been applied to study supply chain capacity investment and planning. 相似文献
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谢治州 《数学的实践与认识》2013,43(1)
基于CUMCM-2011 B题中关于嫌疑犯的封堵问题的研究.通过建立描述市区交通网络图的权矩阵,采用求最短路的Dijstra算法求出市区任意两节点的最短路径及路长,构作最佳路径阵和距离矩阵,以此为基点建立封堵路口的最优调度方案模型,再在此基础上建立封堵住嫌疑犯的最优模型,并设计了模型求解的算法.将算法应用于CUMCM-2011 B题中关于嫌疑犯的封堵问题,获得最优封堵方案. 相似文献