This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of...In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.展开更多
Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical ...Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical model and a new energy saving strategy with Software Defined Network (SDN) technology [1]. Our Model solution is based on the Modified SPRING Protocol (MSP). In this paper, we simulated our work and compared it to that of the authors [2] and [3]. The OMNET++ simulator was used for our work. Thus, the results of the simulations gave a delay that tends to zero, a packet loss of the order of 10% and a constant jitter of 4% better than the previous authors.展开更多
随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科...随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科为例进行分析和探讨.在教育领域,知识图谱的构建对于整理和系统化学科知识具有重要意义,然而传统的知识图谱构建方法在数据标注方面存在效率低、耗费大量人工成本等问题.研究旨在通过大语言模型来解决这些问题,从而提升知识图谱构建的自动化和智能化水平.基于国内大语言模型的现状,探讨了其在学科知识图谱自动标注中的应用,以道德与法治和数学学科为例,阐述了相关方法和实验结果.首先,探讨了研究背景和意义.接着,综述了国内大语言模型的发展现状和学科知识图谱的自动标注技术.在方法与模型部分,尝试探索一种基于国内大语言模型的自动标注方法,力图完善其在学科知识图谱上的应用.还探讨了学科知识图谱人工标注方法模型,以此作为对比,评估自动标注方法的实际效果.在实验与分析部分,通过在道德与法治和数学学科的自动标注实验和对其结果的分析,发现两个学科的知识图谱自动标注均取得了较高的准确率和效率,与人工标注结果进行了深入比较分析,得出了一系列有价值的结论,验证了所提出方法的有效性和准确性.最后,对未来的研究方向进行了展望.总体而言,研究为学科知识图谱的自动标注提供了一种新的思路和方法,有望推动相关领域的进一步发展.展开更多
利用文献计量分析软件及内容分析,对《Journal for Research in Mathematics Education》等3本SSCI期刊2000-2023年刊载论文进行分析,基于科学知识图谱的实证分析,从国际数学教育研究的时空分布、基础知识、主题分布和前沿演变进行系统...利用文献计量分析软件及内容分析,对《Journal for Research in Mathematics Education》等3本SSCI期刊2000-2023年刊载论文进行分析,基于科学知识图谱的实证分析,从国际数学教育研究的时空分布、基础知识、主题分布和前沿演变进行系统分析和梳理。研究发现,21世纪以来国际数学教育呈现出少数国家(地区)集中的态势,美国成为国际数学教育研究的主要力量之一,中国也正在成为重要研究力量;美国特拉华大学的蔡金法等高产作者已经形成稳定的作者群。数学学习研究、数学课堂教学研究、数学课程研究、数学教师教育研究、数学教育评价研究、数学教育技术研究等成为国际数学教育研究的主题。管窥国际数学教育研究的发展现状和主要趋势,进一步为我国数学教育研究的创新发展和建设提供全新的视野,更好地推动国内数学教育者追踪了解国际数学教育进展与前沿。展开更多
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
文摘In this paper we develop modeling techniques for a social partitioning problem. Different social interaction regulations are imposed during pandemics to prevent the spread of diseases. We suggest partitioning a set of company employees as an effective way to curb the spread, and use integer programming techniques to model it. The goal of the model is to maximize the number of direct interactions between employees who are essential for company’s work subject to the constraint that all employees should be partitioned into components of no more than a certain size implied by the regulations. Then we further develop the basic model to take into account different restrictions and provisions. We also give heuristics for solving the problem. Our computational results include sensitivity analysis on some of the models and analysis of the heuristic performance.
文摘Several works by the authors have shown that energy consumption in communication networks does not only depend on the traffic load but on all connected equipment in the network. We have contributed a new mathematical model and a new energy saving strategy with Software Defined Network (SDN) technology [1]. Our Model solution is based on the Modified SPRING Protocol (MSP). In this paper, we simulated our work and compared it to that of the authors [2] and [3]. The OMNET++ simulator was used for our work. Thus, the results of the simulations gave a delay that tends to zero, a packet loss of the order of 10% and a constant jitter of 4% better than the previous authors.
文摘随着人工智能技术的迅猛发展,大语言模型(large language models,LLMs)在自然语言处理和各种知识应用中展现了强大的能力.研究了国内大语言模型在中小学学科知识图谱自动标注中的应用,重点以义务教育阶段道德与法治学科和高中数学学科为例进行分析和探讨.在教育领域,知识图谱的构建对于整理和系统化学科知识具有重要意义,然而传统的知识图谱构建方法在数据标注方面存在效率低、耗费大量人工成本等问题.研究旨在通过大语言模型来解决这些问题,从而提升知识图谱构建的自动化和智能化水平.基于国内大语言模型的现状,探讨了其在学科知识图谱自动标注中的应用,以道德与法治和数学学科为例,阐述了相关方法和实验结果.首先,探讨了研究背景和意义.接着,综述了国内大语言模型的发展现状和学科知识图谱的自动标注技术.在方法与模型部分,尝试探索一种基于国内大语言模型的自动标注方法,力图完善其在学科知识图谱上的应用.还探讨了学科知识图谱人工标注方法模型,以此作为对比,评估自动标注方法的实际效果.在实验与分析部分,通过在道德与法治和数学学科的自动标注实验和对其结果的分析,发现两个学科的知识图谱自动标注均取得了较高的准确率和效率,与人工标注结果进行了深入比较分析,得出了一系列有价值的结论,验证了所提出方法的有效性和准确性.最后,对未来的研究方向进行了展望.总体而言,研究为学科知识图谱的自动标注提供了一种新的思路和方法,有望推动相关领域的进一步发展.
文摘利用文献计量分析软件及内容分析,对《Journal for Research in Mathematics Education》等3本SSCI期刊2000-2023年刊载论文进行分析,基于科学知识图谱的实证分析,从国际数学教育研究的时空分布、基础知识、主题分布和前沿演变进行系统分析和梳理。研究发现,21世纪以来国际数学教育呈现出少数国家(地区)集中的态势,美国成为国际数学教育研究的主要力量之一,中国也正在成为重要研究力量;美国特拉华大学的蔡金法等高产作者已经形成稳定的作者群。数学学习研究、数学课堂教学研究、数学课程研究、数学教师教育研究、数学教育评价研究、数学教育技术研究等成为国际数学教育研究的主题。管窥国际数学教育研究的发展现状和主要趋势,进一步为我国数学教育研究的创新发展和建设提供全新的视野,更好地推动国内数学教育者追踪了解国际数学教育进展与前沿。
