关键词： 数学语言   运算方法   学生数学思维   数学建模   数学算法   数学概念   数学模型   三种境界  

摘要： 数学模型可以帮助学生将生活中的事物抽象概括成数学语言,通过建立模型的方式求解数学问题。从数学解题方法来看,数学概念和运算方法都可以用模型来解释。也就是说,数学模型可以帮助学生理解数学算法和概念,使学生在建立模型的过程中掌握数学学习的基本思路。但是,大部分数学教师还没有意识到数学模型对于学生数学思维发展的重要作用。本文将从探究数学建模的三种境界入手,提出小学数学教学中的几种建模方法。

关键词： Ring of integers modulo n   Galois field   Irreducible polynomials   Group action   S-box   Image encryption  

摘要： The arithmetic properties of a finite field have a remarkable impact on the security features of symmetric and asymmetric cryptosystems. Conventionally, in modern symmetric-key cryptosystems, a 256 elements Galois field depending on a single 8 degree primitive irreducible polynomial overDOUBLE-STRUCK CAPITAL Z(2)is used for designing an S-box, the main nonlinear component in AES. The experience of S-box based image encryption schemes is not appreciable than chaotic systems based methods. In this study, we improve the S-box based image encryption algorithms by the usage of all 16 distinct degree 8 primitive irreducible polynomials overDOUBLE-STRUCK CAPITAL Z(2)and by introducing a new role of the ringDOUBLE-STRUCK CAPITAL Z(n)of integers modulonin the permutation steps. The strength of this novel 2-algebraic structures based image encryption scheme is evaluated by some statistical analyses and a significant performance level is achieved. A comparison of encryption quality with some of the recent chaos-based image encryption algorithms is given and evidently the newly launched scheme spectacles high performance. Thus this new development in image encryption methods may provide an alternative to chaos dependent image encryption.

关键词： data-driven optimization   differential algebraic equations   dynamic optimization   steam cracking   support vector machines  

摘要： Support vector machines (SVMs) based optimization framework is presented for the data-driven optimization of numerically infeasible differential algebraic equations (DAEs) without the full discretization of the underlying first-principles model. By formulating the stability constraint of the numerical integration of a DAE system as a supervised classification problem, we are able to demonstrate that SVMs can accurately map the boundary of numerical infeasibility. The necessity of this data-driven approach is demonstrated on a two-dimensional motivating example, where highly accurate SVM models are trained, validated, and tested using the data collected from the numerical integration of DAEs. Furthermore, this methodology is extended and tested for a multidimensional case study from reaction engineering (i.e., thermal cracking of natural gas liquids). The data-driven optimization of this complex case study is explored through integrating the SVM models with a constrained global grey-box optimization algorithm, namely the ARGONAUT framework.

关键词： Connected Component   Distributed memory   GraphBLAS  

摘要： Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a class of parallel connected-component algorithms designed using linear-algebraic primitives. These algorithms are based on a PRAM algorithm by Shiloach and Vishkin and can be designed using standard GraphBLAS operations. We demonstrate two algorithms of this class, one named LACC for Linear Algebraic Connected Components, and the other named FastSV which can be regarded as LACC's simplification. With the support of the highly-scalable Combinatorial BLAS library, LACC and FastSV outperform the previous state-of-the-art algorithm by a factor of up to 12x for small to medium scale graphs. For large graphs with more than 50B edges, LACC and FastSV scale to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperform previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights. (C) 2020 Elsevier Inc. All rights reserved.

关键词： 人工智能   算法   学习   网络   选择  

摘要： 本文探究人工智能中的蚁群算法,对该算法的数学生物原理进行分析,并结合具有代表性的旅行商算法进行求解。通过仿真计算表面,所探究的算法对于解决复杂数学难题具有很好的效果,是结合数学、生物和编程的交叉知识运用,对于青少年能力提升有一定借鉴价值。

关键词： 图像处理   车牌识别(LPR)   数学形态学   边缘检测  

摘要： 图像或视频中的车牌识别(LPR)算法包括车牌区域的提取、车牌字符的分割和车牌字符的识别3个部分。由于车牌格式的多样性和采集过程中室外光照条件的不均匀性,增加了车牌定位识别的难度。因此,大多数识别方法只能在有限的条件下实施,如固定的照明、限制一定的车速、指定的路线和固定的背景等。车牌识别(LPR)算法由两个模块组成,一个模块用于定位牌照,一个模块用于牌照中字符的识别。对静止图像或视频序列中的车辆,利用边缘检测和数学形态学算法进行车牌定位和识别;通过算法优化,测试并调整处理时间的实验,验证了定位计算能力和识别效率;为研究人员提供了一个公共图像数据库。

关键词： 计算机技术   数学方法   计算机算法   应用  

摘要： 计算机技术在当今社会中发展迅速并且具有广泛的应用,对于计算机技术的研究以及开发而言,对计算机算法的特定应用分析具有巨大的研究价值。以当下的发展趋势来说,在计算机技术的特定应用中,数学方法被广泛应用于计算机算法中。也就是说,数学方法在计算机方法的应用中扮演着重要的角色,因此分析数学方法在计算机算法中的应用,对于计算机算法的改进以及发展方面具有十分重要的意义。本文重点分析了数学方法在计算机算法中的实际应用,以期为提高计算机算法的实用性提供借鉴。

关键词： 小学数学   算法算理   计算能力  

摘要： 在小学数学的教学过程中,掌握好数学计算能力是非常重要的,但是在数学计算过程中需要将算法与算理进行有效的结合。在数学学习中算理就是在计算过程中蕴含的数学上的原理,所谓的算法就是指在进行数学运算的时候使用的方法。在小学数学的学习过程中计算能力对于学生在数学上的学习是非常关键的,在数学教学中如果能够将两者进行有效的结合,就能够让学生的计算能力得到更大的进步,数学学习的效果也变得更好。

关键词： Nonsymmetric algebraic Riccati equation   minimal positive solution   accelerated iterative algorithm   convergence analysis  

摘要： In this paper, some accelerated iterative algorithms are developed to find the minimal positive solution of the nonsymmetric algebraic Riccati equation arising in transport theory. The convergence analysis shows that the sequences of vectors generated by iterative algorithms with the initial vector are monotonically increasing and converge to the minimal positive solution of the vector equations. Numerical examples are provided to illustrate the efficiency of the proposed algorithms and testify the conclusions suggested in this paper.