关键词： 小学数学   计算教学   算理与算法   有效结合  

摘要： 在小学的数学教学过程中，数学计算能力的培养尤为重要，而在计算能力的教学过程中，需要将算法以及算理等问题进行有效结合。所谓算理，即在计算过程中所蕴藏的计算道理，同样也指的是在计算过程中的思考思维方式；而算法指的就是计算方法。在对学生计算能力的教学过程中，这两点是需要重点关注与培养的，将二者进行有机结合，使学生的计算能力能够得到更深层次的锻炼与培养。

关键词： 空间相贯线   平面展开曲线   直线逼近   数控加工代码  

摘要： 为实现两异径圆管相贯的理想焊接，需要对相贯线的切割轨迹进行控制，加工出满足一定精度要求的相贯曲线。首先，通过齐次坐标变换建立了两异径圆管偏置斜交的空间相贯线的数学模型，并将其展成平面曲线；再利用MATLAB对空间相贯曲线及其平面展开曲线进行仿真，验证了曲线模型的正确性。最后，依据等间距原理，VB编程实现了直线逼近平面展开曲线并生成相应的数控加工代码，为相贯线的研究设计奠定了技术基础。

关键词： 算法   数学   爱因斯坦   科学家   算术题   朋友  

摘要： 有一次，著名科学家爱因斯坦生了一场大病，躺在家里休息了好些日子。有一位朋友前来探望，爱因斯坦非常高兴，把朋友拉到床前，要求对方出道算术题给他做。

关键词： Game theory   Competitive facility location   Nash equilibrium   Approximation algorithm   Cooperative competition  

摘要： This paper deals with cooperative competition in facility location problems in which potential players (investors) are in competition (or conflict) over acquiring suitable sites and clients. In order to formulate the problem, a game-theoretical multi-objective model with the objective of maximizing investor utility is presented. In the proposed method, an acceptance threshold constraint is applied to facility allocation that is based on a combination of distance between a facility and clients, and investors' product prices. Since the common solution methods for multi-objective optimization, such as weighted sums, epsilon-constraints, multi-objective meta-heuristic algorithms, etc. are not efficient enough, and cannot guarantee achieving Nash equilibrium points, a new approach is developed to solve the presented problem. Moreover, according to the computational complexity of the problem, an approximation algorithm is introduced for large-sized problems. Finally, the computational results demonstrate that the proposed algorithm performs efficiently in obtaining Nash equilibrium points. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Solvers   Nonlinear Equations   Computations on Polynomials   Numerical algebraic geometry   homotopy continuation   polynomial system   real solutions   cell decompositions  

摘要： Bertini_real is a compiled command line program for numerically decomposing the real portion of a positive-dimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. The implemented decomposition algorithms are similar to the well-known cylindrical algebraic decomposition (CAD) first established by Collins in that they produce a set of connected cells. In contrast to the CAD, Bertini_real produces cells with midpoints connected to boundary points by homotopies, which can easily be numerically tracked. Furthermore, the implemented decomposition for surfaces naturally yields a triangulation. This CAD-like decomposition captures the topological information and permits further computation on the real sets, such as sampling, visualization, and three-dimensional printing.

关键词： detached currents   local ventilation suction funnel   method of discrete vortices   ventilation coefficient  

摘要： The field velocities near a round suction channel with funnel are determined by means of a newly developed iteration procedure for the construction of the free surface of a flow. A series of limiting trajectories of the dust particles are constructed and dependences of the ventilation coefficient on the length of the funnel and its inclination are constructed. [ABSTRACT FROM AUTHOR]

关键词： Radical parametrization   Tracing index   Reparametrization   Implicitization  

摘要： In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, n variables, the four field operations and radical extractions). We provide algorithms to implicitize radical parametrizations and to check whether a radical parametrization can be reparametrized into a rational parametrization. (C) 2017 Elsevier B.V. All rights reserved.

关键词： 教学模型   研究  

ISBN: (数字)9787561565667 ISBN: (纸本)9787561565667

摘要： 《数学建模实例与优化算法》是作者在多年数学建模课程教学的基础上，结合对优化算法科学研究形成的。编著过程中力求通俗易懂，既注重基础性、可读又趣味和应用。不同数学程度的学生都能在本书找到能学会的数学模型；并针对财经类专业学生，优选几种几种经济管理数学模型供参考。

关键词： 算法思想   渗透   高中数学教学   框图  

摘要： 从高中数学模块复习时知识点归纳教学、概念与公式教学、教学难点突破、解题方法指导教学等四个方面来谈算法思想在高中数学教学中的渗透,从而培养学生思维的条理性,体会数学是具体的、简单明了的及可操作的,进一步提高学生对数学学习的自信心.