关键词： 高中数学   算法教学   现状   对策  

摘要： 随着社会不断的发展,我国现代化信息技术水平逐渐提高,现有的高中数学计算教学也正处于不断的创新、完善阶段,并在一定程度上加强数学课程教学与现代化信息技术的有效整合,只有这样才能将高中数学教学模式创新、完善,从而提高高中数学教学质量与学生的学习效率。基于此,本文对高中数学算法教学现状进行了简单的研究,并对数学教学算法的成因制定出了有效的解决对策,只有这样才能促进高高中数学教学快速发展。

关键词： Semisimple complex Lie algebras   BGG category   Verma modules   Irreducible modules   Weight multiplicities   Freudenthal's formula  

摘要： Let g be a finite-dimensional semisimple Lie algebra over C having rank l and let V be an irreducible finite-dimensional g-module having highest weight lambda. Computations of weight multiplicities in V, usually based on Freudenthal's formula, are in general difficult to carry out in large ranks or for lambda with large coefficients (in terms of the fundamental weights). In this paper, we first show that in some situations, these coefficients can be "lowered" in order to simplify the calculations. We then investigate how this can be used to improve the aforementioned formula of Freudenthal, leading to a more efficient version of the latter in terms of complexity as well as to a way of dealing with certain computations in unbounded ranks. We conclude by illustrating the last assertion with a concrete example. (C) 2016 Elsevier Inc. All rights reserved.

关键词： 高中数学   新课程   算法思想  

摘要： 算法是数学学科中的重点内容,也是一个数学运算过程,可以将复杂的问题简单化,是高中数学阶段学习的重点内容。本文主要探讨算法的重要性,并针对高中数学新课程中的算法思想进行分析。

关键词： 数学算法   C程序   技巧   应用  

摘要： 当前,C语言已经在应用软件及系统软件的程序设计中得到广泛应用,而数学乃为计算机之始祖,同时还是决定一个计算机程序质量如何的关键。本文以一个常用程序为例,探讨不同数学算法对其所具有的影响,最后深入剖析数学算法在C程序设计中的应用意义。

关键词： 计算机编程   数学方法   数学算法   高中数学  

摘要： 随着经济全球化的到来和世界激烈的经济竞争,科学技术和人才已经成为衡量一个国家综合实力的重要标准。而计算机在其中就扮演着举足轻重的角色。目前计算机的应用已融入到社会的各个领域,得到了人们的认可和普及。同时,目前国家也急需大量的计算机人才。在教育体系中,高中学习是学生自主学习的黄金阶段。作为一名高中生来说。

关键词： 知识学习   数学   创新   学说   教材   算法   素养   学生  

摘要： 1 学习内容解析 章建跃博士在文献[1]中指出，任何一门学科的教师在备课、上课等工作中，都有一些基本问题需要思考和回答：

关键词： 数学算法   计算编程   优化策略  

摘要： 计算机编程对人们利用计算机解决实际问题起到了重要的作用。而数学算法是计算机编程的基础,它直接决定了计算机编程的效率,也影响着计算机软件的运行效率与稳定性,因此,有必要对计算机编程进行优化。笔者从实例出发,阐述了合理利用数学算法对计算机语言编程进行优化的策略,优化逻辑分析工作,严格按照程序来设计编程的流程图,确保编程工作可以合乎逻辑地有效开展。

关键词： Algebraic connectivity   Laplacian matrix   cut edge   upper and lower bounds  

摘要： In the graph of a complex network, the algebraic connectivity is the second smallest eigenvalue of a Laplacian matrix. In this paper, we present a cut algorithm based on edge centrality by minimizing the algebraic connectivity of graph. The edge centrality cut algorithm (ECCA) cuts k edges at a time in order to reduce temporal complexity, the algebraic connectivity of which experiences the fastest decline. To prevent nodes from overcutting, each edge sets the weight. We use the advanced ECCA (AECCA) to detect overlapping communities by calculating the correlation coefficients of the nodes. This paper also proposes upper, lower and weaker lower bounds of algebraic connectivity. We demonstrate that our algorithms are effective and accurate at discovering community structure in both artificial and real-world network data and that the algebraic connectivity of the cut algorithm lies between the upper and lower bounds. Our algorithms offer new insights into community detection by calculating the edge centrality.

关键词： Symbolic computation   real algebraic geometry   non-linear computational geometry   connectivity queries   algorithms   complexity  

摘要： A roadmap for a semi-algebraic set S is a curve which has a non-empty and connected intersection with all connected components of S. Hence, this kind of object, introduced by Canny, can be used to answer connectivity queries (with applications, for instance, to motion planning) but has also become of central importance in effective real algebraic geometry, since it is used in higher-level algorithms. In this article, we provide a probabilistic algorithm which computes roadmaps for smooth and bounded real algebraic sets. Its output size and running time are polynomial in (nD)(nlog(d)), where D is the maximum of the degrees of the input polynomials, d is the dimension of the set under consideration and n is the number of variables. More precisely, the running time of the algorithm is essentially subquadratic in the output size. Even under our assumptions, it is the first roadmap algorithm with output size and running time polynomial in (nD)(nlog(d)).

关键词： Canonical polyadic decomposition   CANDECOMP/PARAFAC decomposition   CP decomposition   Tensor   Uniqueness of CPD   Uni-mode uniqueness   Eigenvalue decomposition   Singular value decomposition  

摘要： Canonical Polyadic Decomposition (CPD), of a third-order tensor is a minimal decomposition into a sum of rank-1 tensors. We find new mild deterministic conditions for the uniqueness of individual rank-1 tensors in CPD and present an algorithm to recover them. We call the algorithm "algebraic" because it relies only on standard linear algebra. It does not involve more advanced procedures than the computation of the null space of a matrix and eigen/singular value decomposition. Simulations indicate that the new conditions for uniqueness and the working assumptions for the algorithm hold for a randomly generated I x J x K tensor of rank R >= K >= J >= I >= 2 if R is bounded as R <= (I + J + K - 2)/2 + (K - root(I - J)(2) + 4K)/2 at least for the dimensions that we have tested. This improves upon the famous Kruskal bound for uniqueness R <= (I+J+K - 2)/2 as soon as I >= 3. In the particular case R = K, the new bound above is equivalent to the bound R <= (I - 1)(J - 1) which is known to be necessary and sufficient for the generic uniqueness of the CPD. An existing, algebraic algorithm (based on simultaneous diagonalization of a set of matrices) computes the CPD under the more restrictive constraint R(R - 1) <= I(I - 1) J (J - 1)/2 (implying that R < (J - 1/2)(I - 1/2)/root 2 + 1. We give an example of a low-dimensional but high-rank CPD that cannot be found by optimization-based algorithms in a reasonable amount of time while our approach takes less than a second. We demonstrate that, at least for R <= 24, our algorithm can recover the rank-1 tensors in the CPD up to R <= (I - 1)(J - 1). (C) 2016 Elsevier Inc. All rights reserved.