关键词： 小学数学   高年级   算理   算法  

摘要： 算理理解是小学数学运算教学的重要目标。随着新课改的深入,广大一线教师对算理教学的重视程度不断提升。“说理”教学作为一种重要的启发式教学手段,不仅促进学生在课堂中充分发挥主观能动性,还促进深度学习的实现。文章聚焦小学高年级数学算理课堂,在分析算理教学现状的基础上提升算理教学优化策略,以期为广大教师提供一些算理教学参考。

关键词： direction-of-arrival estimation   geometric algebra   ESPRIT algorithm   electromagnetic vector-sensor array  

摘要： Direction-of-arrival (DOA) estimation plays an important role in array signal processing, and the Estimating Signal Parameter via Rotational Invariance Techniques (ESPRIT) algorithm is one of the typical super resolution algorithms for direction finding in an electromagnetic vector-sensor (EMVS) array;however, existing ESPRIT algorithms treat the output of the EMVS array either as a "long vector", which will inevitably lead to loss of the orthogonality of the signal components, or a quaternion matrix, which may result in some missing information. In this paper, we propose a novel ESPRIT algorithm based on Geometric Algebra (GA-ESPRIT) to estimate 2D-DOA with double parallel uniform linear arrays. The algorithm combines GA with the principle of ESPRIT, which models the multi-dimensional signals in a holistic way, and then the direction angles can be calculated by different GA matrix operations to keep the correlations among multiple components of the EMVS. Experimental results demonstrate that the proposed GA-ESPRIT algorithm is robust to model errors and achieves less time complexity and smaller memory requirements.

关键词： replenishment algorithm   constructive algebras of sets   standard basis  

摘要： The algorithm described can be called the replenishment algorithm by analogy with the Buchberger and Knuth-Bendix algorithms. Specific implementations of the theoretical construction (abstract reduction system) in algebras of finite, numerical, and linear semi-algebraic sets, as well as in the algebra of multisets are given. The elementary number theory problem interpreted as a problem of multiset algebra is considered. The main purpose of this study is to draw attention to simple examples of the replenishment algorithm application.

关键词： Comparison   Division   Long division algorithm   Sense/meaning making   Teaching and learning of algorithms  

摘要： During their education cycle in mathematics, students are exposed to algorithms as early as primary school. Several studies show how students frequently learn to perform these algorithms without controlling the mathematical meanings behind them. On the other hand, several National Standards have highlighted the need to construct meanings in mathematics from the first cycle of education. In this paper we focus on division algorithms, investigating to what extent 6th graders can be guided to understanding the whys behind an algorithm, through the comparison of two different algorithms for integer division. Our results suggest, on the one hand, that "it could work!", and on the other hand, that the exposure to different algorithms for the same mathematical operation seems particularly significant for bringing out the whys behind such algorithms, as well as for capturing the difference between a mathematical operation and algorithms for calculating the result of such an operation.

关键词： Reactor networks synthesis   Optimization   Imperialist competition algorithm   Quasi linear programming   Continuous variables   Structural variables  

摘要： The Reactor network (RN) synthesis of optimization problems leads to mixed-integer non-linear programming (MINLP) models that are very difficult to solve, especially for non-isothermal cases. In this research, a new and simple robust approach is presented for RN synthesis. To reduce the complexity of the model, instead of solving discrete and continuous variables simultaneously, a combination of a stochastic algorithm (i.e. imperialist competition algorithm (ICA)) and mathematical methods (i.e. modified Quasi Linear Programming (QLP)) has been used. The ICA is used to produce structural configuration, whereas continuous variables are handled using a modified QLP formulation. Each structure of the RN generated by ICA includes continuous stirred tank reactor (CSTR), plug flow reactor (PFR), PFR with recycle stream, and differential side-stream reactor (DSR) which are addressed by generating numerical codes in a vector. The RNs structures are then sent to the modified QLP to compute the amount of overall objective function (OOF). In the modified QLP model, first, the continuous variables are divided into two groups I and II, and the optimal values of these variables are obtained at internal and external levels respectively, taking into account the OOF. With this method, the complex MINLP model of RN synthesis is converted to an IAC + modified QLP which is much easier to solve. The cases studied showed that this method can reach better solutions compared to the literature. ? 2021 Elsevier Ltd. All rights reserved.

关键词： 数学算法   计算机编程   优化设计  

摘要： 在计算机软件运行过程中,计算机的编程效率直接影响着软件运行的效率,由此可见,提升软件效率的重要性,首先对计算机编程与数学算法的基本内容进行详细的分析;其次说明了几种基于数学算法的计算机编程设计;最后结合实际的情况,阐述了几种数学算法实例,同时,计算机编程人员还应该树立自主创新的意识,优化并改进传统的计算机编程方法,科学运用计算机编程和数学算法的关系,为计算机管理模式的提升奠定夯实的基础。

关键词： 非一致分布   在线学习   分位数回归   再生核希尔伯特空间  

摘要： 本文研究了多阈值和非一致分布下的在线分位数回归算法,在每一次迭代中,样本会来自不同的分布和取不同的阈值.利用边缘分布在对偶空间中多项式收敛的性质,我们得到了算法的学习速度,并且做了相应的数值模拟来支持我们的结论.

关键词： 机械工业出版社   机器学习   人工智能   数据分析   优化理论   计算机的发展   新兴学科   科学的发展  

摘要： 人工智能和统计学的发展衍生出了关于数据分析的机器学习。这门新兴学科是数据分析领域的研究人员重点探究的方向。有科学家将机器学习定义为,计算机通过储存的数据经验不断提高其自身性能的行为。机器学习是指计算机通过固有的规律性信息获得新的经验和知识,从而提升计算机的智能,达到像人类一样作出决策的目的。随着计算机科学的发展,机器学习的探究和应用取得了很大成就,研究机器学习的数学理论和算法对计算机的发展有重要作用。由史斌和艾扬格编著、机械工业出版社出版的《机器学习的数学理论》一书,详细介绍了机器学习的数学理论,讨论了机器学习的优化理论,为提高计算机研究人员对于机器的认知、实现机器的自动化具有重要指导价值。

关键词： 两步聚类算法   数字化   数学   教学资源   归并   分类方法  

摘要： 传统的数学教学资源分类方法效率低,为此,提出两步聚类算法的数学教学资源归并分类方法。利用互信息技术的获取增量数据,提取数字化数学教学资源特征;根据两步聚类算法构建数学教学资源特征树,依据层次凝聚算法对特征树叶节点进行分组,采用欧式平方距离获得数学教学资源平方根测度连续变量,最大增长距离的聚类数即最终聚类数量。结果表明,该方法可实现数学教学资源的有效归并分类。

关键词： 农田喷灌系统   区间数学控制   土壤温度   土壤湿度   自动化   智能化  

摘要： 以农田喷灌系统为研究对象,综合考虑农田土壤温度与土壤湿度,基于区间数学控制算法建立了一种模糊控制喷灌控制系统。以土壤温度和湿度为控制目标,通过农田喷灌来达到目标控制;综合运用土壤温度与土壤湿度的隶属度关系函数曲线,给定不同隶属度条件下的系统控制规则,模拟土壤温度与土壤湿度,进行控制系统的仿真模糊合成计算,确定出喷灌的时长函数,并进行土壤温度和土壤湿度的对比,得出偏差量,形成相关迭代控制过程。系统可实现农业生产过程中土壤湿度的定量控制,促进了土地灌溉的自动化和智能化。