关键词： 小学数学   算法多样化   科技进步   教学方法   课堂氛围   思维能力的培养   参与课堂活动  

摘要： 随着科技进步,教师的教学方法也有了很多改变,在小学数学中算法的多样化有利于学生思维能力的培养,也有利于学生积极参与课堂活动,营造良好的课堂氛围。

关键词： 数学教学   数学史   阿基米德   弓形面积   抛物线   技术   算法   数学课程标准  

摘要： 如何将数学史融入中小学的数学教学是数学教育领域的一个重要课题。正如《普通高中数学课程标准(2017年版)》所指出的那样,“通过数学概念和思想方法的历史发生发展过程,一方面可以使学生感受丰富多彩的数学文化,激发数学学习的兴趣;另一方面也有助于学生对数学概念和思想方法的理解。”

关键词： 数学模型   通信数据   智能挖掘   加速算法  

摘要： 数学模型模式多样,形成了具有多种方式的通信数据挖掘加速算法,但仍有查询精度低、速度较慢等缺点,为此提出基于数学模型的通信数据智能挖掘加速算法。以数学模型为依据,选取候选属性子集,进行拟合度挖掘计算。与传统算法对比,可知本文算法的数据挖掘速度远高于传统算法,为我国通信数据智能挖掘加速算法查询的精确度和速度的大幅度提升做出了贡献。

关键词： 导弹制导打击模型   空气阻力   地球自转   风力因素  

摘要： 论文通过对导弹运动轨迹建立三维模型,并结合空气阻力、地球自转和风力因素的影响,综合分析多种因素的影响,得到了导弹的制导打击模型。并通过对导弹的运动规律的分析和相应的性能的考虑,确定导弹绝对弹道位置的相关参数和运动过程的位置参数,定性定量分析导弹弹道模型。

关键词： 校园网贷   数学算法   安全教育   对策分析  

摘要： 针对校园网贷防范控制问题,本文从数学算法视角出发,普及银行常见两种还款方式和算法启示,结合网贷案例,给出校园网贷三种还款计算方式,提出“破、解、对、溯”四条对策。通过算法思想,帮助学生正确认识校园网贷,切实提高网贷安全教育防控能力。

关键词： Lie algebra   Invariant bilinear form   Nilpotent   Free nilpotent   Derivation   Automorphism  

摘要： Taking into account the theoretical results and guidelines given in this work, we introduce a computational method to construct any 2-step nilpotent quadratic algebra of d generators. Along the work we show that the key of the classification of this class of metric algebras relies on certain families of skewsymmetric matrices. Computational examples for d <= 8 will be given. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Channel estimation   massive MIMO   training sequence design   tensor factorization   low-complexity  

摘要： We consider downlink (DL) channel estimation for frequency division duplex-based massive multiple-input multiple-output (MIMO) systems under the multipath model. Our goal is to provide fast and accurate channel estimation from a small amount of DL training overhead. Prior art tackles this problem using compressive sensing or classic array processing techniques (e.g., ESPRIT and MUSIC). However, these methods have challenges in some scenarios, e.g., when the number of paths is greater than the number of received antennas. Tensor factorization methods can also be used to handle such challenging cases, but it is hard to solve the associated optimization problems. In this paper, we propose an efficient channel estimation framework to circumvent such difficulties. Specifically, a structural training sequence that imposes a tensor structure on the received signal is proposed. We show that with such a training sequence, the parameters of DL MIMO channels can be provably identified even when the number of paths largely exceeds the number of received antennas-under very small training overhead. Our approach is a judicious combination of' Vander-monde tensor algebra and a carefully designed conjugate-invariant training sequence. Unlike existing tensor-based channel estimation methods that involve hard optimization problems, the proposed approach consists of very lightweight algebraic operations, and thus, real-time implementation is within reach. Simulation results are carried out to showcase the effectiveness of the proposed methods.

关键词： Face detection   AdaBoost   Haar-like pattern   weak classifier   Conformal Geometric Algebra  

摘要： In this paper, we propose a novel face detection method based on the AdaBoost algorithm. In the past few years, a variety of variant AdaBoost approaches has been proposed and obtained increasing success in both performance and robustness. However, those approaches have not focused much on the geometric characteristics of face images. A new way to apply AdaBoost is introduced in this paper with the utilization of Conformal Geometric Algebra for extracting features from input samples. By analysis and experiments, using Conformal Geometric Algebra, we can find the hyper-spheres (-planes) that mostly fit data points and yield very low error for classification in both frontal and in-plane rotated face detection. Haar-like patterns are used as well but in a more pertinent approach to achieve more informative features. In comparison with the state-of-the-art face detection method developed by Paul Viola and Michael J. Jones, our proposed method can gain approximately the same accuracy as their framework. From a sufficient number of experiments, we prove that a small subset of the feature set can be totally adequate to develop a strong classifier with comparable performance and accuracy. Thus, iterating over the whole set of features to choose the best one for each round of AdaBoost is no longer needed. Besides, the memory usage for training is significantly reduced if we compare with the Viola-Jones system and a large amount of RAM is no longer required to store feature values as in their method.

关键词： LiDAR   Point cloud data   Particle size   Aggregate   Mathematical method   Algorithm  

摘要： A number of methods and machines based on these methods have been developed to determine particle size. Image analysis has been used for many years to determine the particle size distribution of materials especially relatively coarse sized, in large quantities, or spread over a large area where screen analysis cannot be applied. The three-dimensional data supporting the classical digital image analysis method working with two-dimensional data were recently introduced to increase the accuracy of the analysis results. In this study, the piles formed by aggregate mixtures with known particle size distributions were scanned with terrestrial laser scanner to obtain point cloud data and then the particle size distributions of these piles were determined with the help of the algorithm given here. An important step of the algorithm used is to determine the local minimum points on the scan surfaces. Three different mathematical methods have been used at this stage. When the particle size distribution curves obtained by sieve analysis of the mixtures are taken into consideration, the most accurate result is obtained in the morphological reconstruction approach. It has been concluded that the particle size distributions of the aggregate piles can be reliably determined with the use of the point cloud data and the algorithm using that approach.

关键词： Electrocardiograph   Compression   Genetic programming   Mathematical modeling  

摘要： Telemedicine refers to a group of modern medical services that are provided on the platform of advanced telecommunication technologies. One of these services is the screening for heart diseases, which are the leading cause of mortality across the world. But the development of telemedicine systems for cardiac screening faces multiple challenges. One of these challenges is the large volume of ECG signals, which makes them difficult to store and transfer. Of the many algorithms proposed for the compression of ECG signals, most rely on the processing of data as discrete numerical values. The alternative approach followed in this study is to model the signal compression problem into a regression problem and then convert it into a text compression problem. Using this approach, the paper presents a new genetic programming based method for the compression of ECG signals. The proposed method starts with denoising and smoothing the ECG signal with discrete wavelet transform and then constructing its mathematical model with a genetic programming based algorithm. This model is a piecewise mathematical function where each sub-function models one part of the signal. Next, the model is converted to a character string and regular expressions are used to extract the function coefficients and encode the symbols contained in the string. Finally, the strings and coefficients are compressed using the 12W and arithmetic encoding methods, respectively. The efficiency of the algorithm is evaluated through compression ratio (CR), percent root-mean-square difference (PRD), root-mean-square-error (RMSE) and quality score (QS) on MIT-BIH Arrhythmia Database records. The evaluation results demonstrate the good performance of the proposed method in comparison with other state-of-the-art techniques. (C) 2019 Elsevier Ltd. All rights reserved.