关键词： 小学数学   简便算法   教学思想   方法研究  

摘要： 简便算法也称为简便运算,是小学数学常见的简算方法和学习思想。教师在教学过程中应注重简便运算的融入,帮助学生形成简便运算意识,在学习过程中不断融入简便的思想和认识,通过具体简便案例的方式引导学生思考和实践简便运算内容,加深对简便算法的理解,提高学生的简便能力。

关键词： Iris localization   Noise   Three-value   Circle detection   Conformal geometric algebra (CGA)  

摘要： In practical iris applications, the obtained iris images are inevitably affected by noises brought by uneven illumination, off-angle view, eyelids, and eyelashes etc. Such influences can lead to poor accuracy and low efficiency of iris localization. This paper presents a novel conformal geometric algebra (CGA) based algorithm for accurate and fast iris localization. Firstly, two thresholds are obtained adaptively to convert the gray image into three-value image and Sobel edge detector is used to generate the edge points. Then an improved CGA-based circle detection algorithm is applied to detect the limbic and pupillary boundaries of the iris. Candidate boundaries are found with a priori knowledge of the eye structure. Finally, the CGA inner product is used to decide whether an edge point from candidate boundaries is on the circle or not. A defect ratio is defined to represent the completeness of each candidate boundary, and only those with the lowest defect ratio are set as the pupillary and limbic boundaries. Our algorithm detects candidate boundaries that satisfy a priori constraints rapidly and ensures the accuracy of iris localization. Experimental results on different datasets demonstrate the effectiveness and robustness of the algorithm. (C) 2020 Elsevier Inc. All rights reserved.

关键词： electric transport   optimization   mathematical programming   randomized algorithm  

摘要： We investigate the complex optimization problem that arises in the planning of the transition process from traditional public transport to electric transport. We define the assumptions, input and output parameters of the problem, as well as its mathematical model and a randomized algorithm for solving it. We also give an extensive bibliography of publications on the problem at hand.

关键词： Indexes   Mathematical model   Manifolds   Stability analysis   Control theory   Mechanical systems   Nonlinear systems   Constraint stabilization   differential-algebraic systems   nonlinear systems   numerical integration  

摘要： The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem, we propose a method based on a nonlinear stabilization mechanism that guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism.

摘要： This survey describes probabilistic algorithms for linear algebraic computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problems. The paper treats both the theoretical foundations of the subject and practical computational issues. Topics include norm estimation, matrix approximation by sampling, structured and unstructured random embeddings, linear regression problems, low-rank approximation, subspace iteration and Krylov methods, error estimation and adaptivity, interpolatory and CUR factorizations, Nystrom approximation of positive semidefinite matrices, single-view ('streaming') algorithms, full rank-revealing factorizations, solvers for linear systems, and approximation of kernel matrices that arise in machine learning and in scientific computing.

关键词： Matrix equations   Extended block Krylov subspace   Golub-Kahan bidiagonalization   Large-scale equations  

摘要： In this paper we propose a new projection method to solve both large-scale continuous-time matrix Riccati equations and differential matrix Riccati equations. The new approach projects the problem onto an extended block Krylov subspace and gets a low-dimensional equation. We use the block Golub-Kahan procedure to construct the orthonormal bases for the extended Krylov subspaces. For matrix Riccati equations, the reduced problem is then solved by means of a direct Riccati scheme such as the Schur method. When we solve differential matrix Riccati equations, the reduced problem is solved by the Backward Differentiation Formula (BDF) method and the obtained solution is used to build the low rank approximate solution of the original problem. Finally, we give some theoretical results and present numerical experiments. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： 高中数学   数学教育哲学   教学方法   课程标准  

摘要： 我国在2003年颁布的《普通高中数学课程标准(实验)》中，将算法初步首次引入高中数学课程。自此，算法初步的教学受到国内外数学教育研究者的广泛重视。了解发现:研究者已经从多方面，包括课程开发、学习心理的角度、教学实验的角度研究过算法，但是关于数学教育哲学下的算法教学研究却没有。哲学思想是指导人类一切活动的思想,不同时期的数学教育反映出了不同的数学教育哲学观点。本文将从一个教者的角度出发,探讨高中算法初步教学中与数学教育哲学理论的联系，同时在此理论基础上分析教学中的一些经验和教训，将思考的结果呈现出来,设计实验，研究解读实验，得到启示。　　在研究过程中，首先从数学教育哲学的数学观、数学教育价值观、学习观、教学观方面对算法初步教学进行剖析与解读。而后设计课堂实验，采取由点到面、逐步推进的模式。实验的阐述分为实验目的，实验对象，实验过程和实验结果四个部分。最终得到结论与启示：高中算法初步不同教学策略的优点，及不同实验方法在研究上的不同价值。

关键词： 高中数学   算法   功能分析   教学设计  

摘要： 随着信息社会和科学技术的发展，计算机在日常生活中起着越来越重要的作用。而算法是计算机工作的基础，了解算法知识及其思想成为现代社会每一个公民所应具备的基本素养。在许多发达国家，算法知识早已成为中学教材的重要内容。　　2003年4月教育部颁布《普通高中数学课程标准（试验）》，新课程开始陆续实施。作为新课程中首次出现的内容之一，算法的教学问题被人们所关注。湖北省于2010年才第一次进行必修3（含算法初步的内容）的教学。由于算法内容对刚实行新课改地区的中学数学老师来说是比较陌生的，心理上存在着畏惧情绪，在实际教学中缺少有效的教学指导，因此给他们的教学带来了全新的挑战。　　本文研究了国内外关于算法教学的研究及教学设计理论的发展，重点是国内的“双主”教学设计与“以活动为中心”的教学设计，对高中数学算法初步的内容进行了功能分析。结合教学实际，对算法初步的部分内容进行了教学设计。旨在为自己及同行的教学提供一个有益的探索与尝试。本文所给出算法设计方案只是初步的，有待于在今后的教学实践中进一步检验完善。

关键词： Symplectic similitude group   Orthogonal similitude group   Word problem   Gaussian elimination   Spinor norm   Double coset decomposition  

摘要： This paper presents some algorithms in linear algebraic groups. These algorithms solve the word problem and compute the spinor norm for orthogonal groups. This gives us an algorithmic definition of the spinor norm. We compute the double coset decomposition with respect to a Siegel maximal parabolic subgroup, which is important in computing infinite-dimensional representations for some algebraic groups.