关键词： 直观模型   数学运算   运算能力  

摘要： 小学数学运算学习中使用的直观模型多种多样,不同模型在运用的过程中对计算教学产生不同的影响。在教学中,教师要适当地利用直观模型进行探究性学习,运用不同的直观模型能帮助学生经历、感受建模过程,体会模型思想,由具体到抽象,帮助学生领悟算理,习得算法,以促进小学生数学运算能力的提升。

关键词： 高考命题   算法   数学   实际应用问题   计算机学科   基础知识   命题原则   知识网络  

摘要： “算法初步”是新课标数学新增板块,它既是数学领域的重要内容,也是计算机学科的基础知识.“算法初步”与函数、数列、概率、统计、实际应用问题都能较好地结合,符合“在知识网络交会处设计试题”的命题原则,是全国和各地方高考命题的新“靓点”,甚至成了必考题.笔者结合近几年高考数学全国卷Ⅰ中“算法初步”试题,阐述对这类试题的些许见解.

关键词： 参数学习   威胁评估   离散动态贝叶斯网络   遗传算法   无人水下航行器   决策  

摘要： 针对复杂海洋环境下存在不确定事件对无人水下航行器自主作业和安全性所带来的威胁。本文设计了基于动态贝叶斯网络的威胁评估模型和决策推理模型,采用遗传算法实现了离散动态贝叶斯网络参数学习,最终得到最优的模型参数,进而增强了推理模型对海洋环境的快速反应能力。仿真实验结果证明:提出的算法可以得到真实的离散动态贝叶斯网络参数,能够有效地解决复杂海洋环境下UUV威胁评估问题,为UUV的自主任务决策提供有效的参数保障。

关键词： Feature extraction   Water body extraction   Satellite image processing   Mathematical morphology  

摘要： The detection and extraction of water bodies from satellite imagery is very important and useful for several planning and developmental activities such as shoreline identification, mapping riverbank erosion, watershed extraction and water resource management. Popular techniques for water body extraction like those based on the normalized difference water index (NDWI) require reflectance information in the green and near-infrared (NIR) bands of the light spectrum. Moreover, some commonly used approaches may perform differently according to the spatial resolution of the images. In this regard, mathematical morphological (MM) techniques for image processing have been employed for spatial feature extraction as they preserve edges and shapes. This study proposes a flexible MM driven approach which is very effective for the extraction of water bodies from several satellite images with different spatial resolution. MM provides effective tools for processing image objects based on size and shape and is particularly adapted for water bodies that have typically specific spatial characteristics. In greater details, the proposed extraction algorithm preserves the actual size and shape of the water bodies since it is based on morphological operators based on geodesic reconstruction. Moreover, the choice of the filter size (called structural element (SE) in MM) in the proposed algorithm is done dynamically allowing one to retain the most precise results from different set of inputs images of different spatial resolution and swath. The availability of more than one spectral band of satellite imagery is not necessary for the proposed algorithm as it utilizes only a single band for its computation. This makes it convenient to apply in single band imageries obtained from satellites such as Cartosat thereby making the proposed approach effective over commonly used methods. The accuracy assessment was carried out and compared with the maximum likelihood (ML) classifier and methods base

关键词： 计算机   编程优化   数学算法作用  

摘要： 在计算机编程中,合理地运用数学算法所拥有的优势不但可以完好地针对所拥有的问题进行总结分类归纳,还可以将其归纳作为基础从而进行针对性的统一计算,并且能够将非常复杂的问题进行整体的简化并且将其中所拥有的规律体现出来,计算机编程正是因为这项技术进行针对性的将与编程相关的语言整理编辑。所以对计算机编辑工作人员来讲有效地促进数学算法,可以说是有效地提高了计算机编程工作的进程与质量。在此针对我国目前计算机研究的现状进行针对编程方面全面的研究与分析。

关键词： 数学运算   核心素养   高考   算法优化  

摘要： 数学运算能力并非一种孤立的数学能力,而是运算技能与逻辑思维等的有机整合.文章选取2018年浙江省数学高考卷的3个典型考题,浅谈在解决问题的过程中,如何分析运算条件、探究运算方向、选择运算方法、设计运算程序,从而使运算符合算理且合理简洁,即以优化算法为目标,提升学生数学运算核心素养.

关键词： 电力系统   谐波与间谐波检测   数学形态学   改进Prony算法   谐波参数估计  

摘要： 由于传统Prony算法对谐波与间谐波的检测易受噪声影响,为了提高参数估计精度,准确提取谐波和间谐波的频率、幅值和相位,提出了一种基于数学形态学和改进Prony算法的谐波与间谐波参数估计方法。该方法主要思路是先用数学形态学构建形态滤波器去除噪声,可以克服传统Prony算法对噪声敏感的不足;然后再将去噪拟合后的谐波信号进行改进Prony分析。该方法针对原始Prony方法优化了实际阶数和线性参数的求解过程,对比小波消噪求解谐波各参数的方法优化了去噪效果。通过MATLAB对谐波信号进行编程分析,发现该方法在噪声情况下仍能得到较高精度的谐波与间谐波幅值、频率和相位参数估计,验证了该方法的可行性和有效性。

关键词： SYMMETRY (Mathematics)   FRACTIONS   ALGEBRA   ALGORITHMS   MATRICES  

摘要： The paper establishes the invariance of the simplex-module algorithm for expanding real numbers α = (α₁, …, α_d) in multidimensional continued fractions under linear-fractional transformations α′=(α1′…αd1)=U〈α〉 with matrices U from the unimodular group GL_d+1(ℤ). It is shown that the convergents of the transformed collections of numbers α^′ satisfy the same recurrence relation and have the same approximation order. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.