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以教学研究项目推动课程资源建设,是保证课程资源高质量和高水平的重要抓手.本文以"数学建模在线开放课程群"项目为例,从课程及资源建设现状、作者队伍组建、课程资源内容建设和出版等方面阐述了教学研究项目对于推动优质课程资源建设和共享的重要作用. 相似文献
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论微分方程课程的教学设计 总被引:1,自引:0,他引:1
在分析微分方程课程教学现状的基础上,提出了微分方程课程的教学设计策略.克服以往传统教学中存在的缺陷,剖析教学上的难点,实施以"融合背景、剖析思想、多维表达、多层训练"为主要内容的微分方程课程教学设计策略,培养学生的理论分析能力、解决问题的能力和创新能力. 相似文献
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国家课程思政建设目标对数学建模课程教改提出了新的挑战.以金课为目标将课程思政融入数学建模课程,从更高的视角对教学内容、教学方式、考核要求和教学设计等要素进行了重构.具体表现在,高阶性是以"五位一体"的方式重构课程内容体系;创新性以开设慕课的形式,内容中融入课程思政元素,同时线上线下共同协作,进行混合式教学;挑战度可在课程考核中增加课程思政元素的要求,课堂讨论中增加价值取向、探索精神等内容,另外让学生面对真实世界的思政问题.文章最后给出了课程思政融入建模教学过程中的几个关键点. 相似文献
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探讨数学分析课程的教学改革和教学质量的提高 总被引:1,自引:0,他引:1
数学分析课程是数学类专业学生进校后首先学习的重要的基础课,它的理论、计算方法以及分析数学思想的形成,对后续课程产生了深远的影响.为了提高课程的教学质量,作者通过多年的思考和实践,提出教改的四方面:一把握当代大学生的新特点、新变化,提倡"快乐"的教学;二提高数分教学艺术;三综合运用各种教学方法和手段,不断提高教学效果;四数分课程学习效果考核的多样化. 相似文献
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In this paper, the dimensions of bivariate spline spaces are studied using the Smoothing Cofactor-Conformality method. Based on the analysis on the conformality condition at one interior vertex, the stability (or singularity to the contrary) of the dimensions of general spline spaces is discussed in detail. By the aid of directed partition some new results on dimensions are obtained with the corresponding constraints depending on the degree, the smoothness order of the spline spaces and the structure of the partition as well. 相似文献
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The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve.
In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a
variety of results on the width, some having stronger versions assuming a conjecture of Cilleruelo and Granville asserting
a uniform bound for the number of lattice points on the circle lying in short arcs. 相似文献
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Several “distances” between the spectra of two matrices are discussed and compared. Optimal bounds are given, which enable us to reduce certain bounds on the eigenvalue variation of matrices by a factor of about two. The results of Bhatia and Mukherjea and of Bhatia and Friedland on the eigenvalue variation are derived in an elementary way using results of Henrici on the spectral variation. 相似文献
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本文给出了直线上Marion集的Hausdorff测度的一个有效计算方法,并通过几个实例得出如何利用此方法计算出直线上分形的Hausdorff测度的精确值. 相似文献
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Recently, there has been a revival of interest in the Pfaff identity on hypergeometric series because of the specialization of Simons and a generalization of Munarini. We present combinatorial settings and interpretations of the specialization and the generalization; one is based on free Dyck paths and free Schröder paths, and the other relies on a correspondence of Foata and Labelle between the Meixner endofunctions and bicolored permutations, and an extension of the technique developed by Labelle and Yeh for the Pfaff identity. Applying the involution on weighted Schröder paths, we derive a formula for the Narayana numbers as an alternating sum of the Catalan numbers. 相似文献
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主要考虑在半轴上Camassa-Holm方程解的动量密度紧支集大小的估计,方法是根据区间长度与区间特征值的关系,通过估计第一Dirichlet特征值来估计动量密度紧支集的长度.因为知道动量密度紧支集外解的性态,所以通过估计动量密度支集的大小可以得到方程解的更多信息. 相似文献
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The Neumann system on the two-dimensional sphere is used as a tool to convey some ideas on the bi-Hamiltonian standpoint on separation of variables. We show that from this standpoint, its separation coordinates and its integrals of motion can be found systematically. 相似文献
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《Applied and Computational Harmonic Analysis》2020,48(2):682-705
In a recent paper, Flandrin [16] proposed filtering based on the zeros of a spectrogram with Gaussian window. His results are based on empirical observations on the distribution of the zeros of the spectrogram of white Gaussian noise. These zeros tend to be uniformly spread over the time–frequency plane, and not to clutter. Our contributions are threefold: we rigorously define the zeros of the spectrogram of continuous white Gaussian noise, we explicitly characterize their statistical distribution, and we investigate the computational and statistical underpinnings of the practical implementation of signal detection based on the statistics of the zeros of the spectrogram. The crux of our analysis is that the zeros of the spectrogram of white Gaussian noise correspond to the zeros of a Gaussian analytic function, a topic of recent independent mathematical interest [24]. 相似文献
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《Journal of Computational and Applied Mathematics》2012,236(5):765-774
In this paper, the dimensions of bivariate spline spaces are studied using the Smoothing Cofactor-Conformality method. Based on the analysis on the conformality condition at one interior vertex, the stability (or singularity to the contrary) of the dimensions of general spline spaces is discussed in detail. By the aid of directed partition some new results on dimensions are obtained with the corresponding constraints depending on the degree, the smoothness order of the spline spaces and the structure of the partition as well. 相似文献
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指出四元数矩阵A的右特征的虚部的模值是唯一确定的,得到了一些关于A的右特征值的虚部模的估计,推广改进了屠伯埙教授的相应结果. 相似文献