关键词： 新课程   高中数学算法   教学策略  

摘要： 随着计算机技术的快速发展,高中数学作为中学阶段最基础、最重要的一门学科也应顺应时代要求,在新课改形势下积极进行教学改革,实现人才培养目标。高中数学新课程标准将算法列为高中数学的一项重要的教学内容,数学算法教学得到了广泛的关注。本文研究新课程背景下高中数学算法教学的应用,首先分析高中数学算法教学现状,指出目前高中数学算法教学中存在的问题,并在充分理解高中数学新课程标准的基础上提出新课程背景下高中数学算法教学的几点措施,以促进高中数学算法教学质量的提高。

关键词： 小学低年级   数学算法   计算错误   数学成绩   数学学习内容   算理   具体形象思维   学习活动过程   学习过程   估商  

摘要： “除法运算”是小学低年级数学算法教学中的重要组成部分。“除法运算”相对于同年段的其他学习内容来说,是学生学习的难点。学生在计算中反映出来的情况不容乐观,由于计算错误,很多学生的数学成绩不理想,并且直接影响了进一步的学习。为了帮助学生准确进行除法的运算,提高运算效率,达到有效运算的目的,针对学生笔算除法时出现的错误、困难和教师教学时的困惑,就低年级“笔算除法”的教学及有效运算,做一些研究探索很有必要。

关键词： Mathematical programming   Scheduling   Earliness/tardiness   Automated guided vehicle (AGV)  

摘要： In this paper, a scheduling problem for multiple automated guided vehicles (AGVs) in a manufacturing system is proposed and formulated. Considering the due date of AGVs requiring for material handling among shops in a jobshop layout, their earliness and tardiness are significant in satisfying the expected cycle time and from an economic view point. Earliness results in AGVs waiting and tardiness causes temporary part storages in the shop floor. Therefore, we propose a mathematical program to minimize the penalized earliness and tardiness. Since the mathematical program is difficult to solve with a conventional method, an optimization method in two stages, namely searching the solution space and finding optimal solutions are proposed. The performance of the proposed mathematical model is tested in a numerical example and compared with several methods in the current literature. (C) 2015 Elsevier B.V. All rights reserved.

关键词： boost converter   global maximum power point (GMPP)   partially shaded condition (PSC)   photovoltaic (PV)   perturb and observation (P & O)   series-parallel configuration (SP)  

摘要： Photovoltaic (PV) systems represent a clean, renewable source of energy that has non-linear current-voltage (I-V) and power-voltage (P-V) characteristics. To increase the efficiency, a PV system must operate at the maximum power point (MPP) to produce the maximum available power. Under uniform conditions, there is only a single MPP in the P-V curve of a PV system;however, determining the MPP is more complicated under partially shaded conditions (PSCs) because multiple peak power points exist. In recent years, various studies have been performed to obtain the highest peak power point under PSCs, which is referred to as the global maximum power point (GMPP). In this paper, a novel method based on mathematical analysis that reduces the search zone and simultaneously identifies the possible MPPs in the specified zone is proposed;this proposed method is called the dual search maximum power point (DSMPP) algorithm. To evaluate the effectiveness of the proposed method, simulation and hardware implementations are carried out. The results show that the search time of GMPP is significantly reduced and the GMPP is detected in the minimum amount of time with high accuracy and minimum oscillation in the power produced.

关键词： Quantifier elimination   Algebraically closed field   Comprehensive Grobner system  

摘要： We introduce new algorithms for quantifier eliminations (QE) in the domain of an algebraically closed field. Our algorithms are based on the computation of comprehensive Grobner systems (CGS). We study Suzuki-Sato's CGS computation algorithm and its successors in more detail and modify them into an optimal form for applying to QE. Based on this modified algorithm, we introduce two QE algorithms. One is pursuing the simplest output quantifier free formula which employs only the computations of CGS. The other consists of parallel computations of CGS and GCD of parametric unary polynomials. It achieves faster computation time with reasonably simple output quantifier free formulas. Our implementation shows that in many examples our algorithms are superior to other existing algorithms such as a QE algorithm adopted in the Mathematica package Reduce and Resolve or a QE algorithm adopted in the Maple package Projection which are the most efficient existing implementations as far as we know.

关键词： beta invariant   Leibniz algebra   abelian ideal   algorithm   abelian subalgebra   alpha invariant   68Q25   17A60   17-08   17A32   68W30  

摘要： In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law. In order to implement this method, the symbolic computation package MAPLE 12 is used. Moreover, we also show a brief computational study considering both the computing time and the memory used in the two main routines of the implementation. Finally, we determine the maximal dimension of abelian subalgebras and ideals for 3-dimensional Leibniz algebras and 4-dimensional solvable ones over .

关键词： 心电信号   数学形态学   有限长单位冲激响应滤波器  

摘要： 本文针对心电信号的工频干扰和基线漂移,提出一种基于有限长单位冲激响应(FIR)滤波器和数学形态学的综合滤波方法,该方法首先采用形式简单的FIR平滑滤波器滤除心电信号的50 Hz工频及其高频谐波,接着将数学形态滤波器应用于滤除基线漂移。实验结果表明,本文设计的综合滤波方法能够有效地滤除工频干扰和基线漂移,为心电信号进一步的分析提供良好的基础。

关键词： 数学算法   计算机编程   优化  

摘要： 数学算法是一种统一计算的数学思想,它将许多的问题进行归纳总结,从而得到结果,是数学中的精华内容所在。在计算机领域,数学算法是计算机技术的最基础的应用,计算机编程语言和编程逻辑就是建立在数学算法的基础上。随着我国计算机技术的发展,计算机编程质量的高低会对计算机软件的效率产生深刻的影响。本文主要分析了数学算法对计算机编程的优化途径。

关键词： 木材单板   节子   图像识别   图像分割   数学形态学   自动分等  

摘要： 【目的】提出一种基于数学形态学的木材单板节子识别改进算法,对木材单板表面节子进行快速识别和面积判断,旨在转化生产中由计算机智能控制自动分等代替人力分拣,提高木材单板分等效率。【方法】选取带有节子的木材单板为研究对象,以图像识别初步结果为基础,首先采集木材单板图像并进行灰度变换;然后根据灰度图像中节子和背景占据的不同灰度级范围,运用最大熵原理选择灰度阈值对图像进行分割,使节子从背景中初步分离出来;接着通过形态学运算去除各初选节子外部的干扰特征量,使节子外轮廓得以较准确显现;最后增加检出特征的外形轮廓判定,以防止板面可能存在的裂缝、污痕等其他特征量因颜色较深从背景中分离出来,被误检识别为节子。【结果】图像分割处理后节子周围存在的一些干扰特征量,通过形态学膨胀处理可切断干扰特征量和节子之间的联系,膨胀后继续进行腐蚀操作可保持节子真实大小,比较形态学开闭运算2种处理方法,形态学闭运算处理后节子更容易被识别出;检出的特征轮廓在进行椭圆拟合后辅以符合节子外形的条件限制可以提高识别精度,防止非节子被检出,其中通过计算特征轮廓点和拟合椭圆的匹配度大小可以初选是否符合节子特征,节子外形的条件限制主要用于过滤一些虽能拟合为椭圆但为长形物体比如裂隙等的影响。【结论】通过本项研究,可直观获取单板表面的节子数量和节子相对大小,其实际生产中使用硬件对接后,根据图像采集设备与待采集对象的相对位置、采集图像的分辨率等情况,结合系统判定结果可得出节子的真实大小,实现木材单板的自动分等。

关键词： 非线性互补约束   数学规划问题   广义梯度投影   全局收敛性  

摘要： 结合罚函数思想和广义梯度投影技术,提出求解非线性互补约束数学规划问题的一个广义梯度投影罚算法.首先,通过扰动技术和广义互补函数,将原问题转化为序列带参数的近似的标准非线性规划;其次,利用广义梯度投影矩阵构造搜索方向的显式表达式.一个特殊的罚函数作为效益函数,而且搜索方向能保证效益函数的下降性.在适当的假设条件下算法具有全局收敛性.