After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this...In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.展开更多
[目的/意义]通过最大瓦解结构准确识别科学研究前沿中的关键节点并追踪其演化路径,为把握领域发展规律、优化科研资源配置提供支持,突破现有研究聚焦孤立节点的局部特征,以及难以捕捉知识网络中具有协同作用且对全局连通性有级联破坏力...[目的/意义]通过最大瓦解结构准确识别科学研究前沿中的关键节点并追踪其演化路径,为把握领域发展规律、优化科研资源配置提供支持,突破现有研究聚焦孤立节点的局部特征,以及难以捕捉知识网络中具有协同作用且对全局连通性有级联破坏力的关键节点集合的问题。[方法/过程]以量子通信领域为例,基于2015—2024年Web of Science的6538篇文献构建关键词共现网络,融合多中心性指标并利用熵权法评估节点重要性,采用贪心算法识别MDS,分析其功能协同特征与演化轨迹。[结果/结论]研究表明,MDS仅占网络规模的18%~22%,移除该集合后网络最大连通组件规模下降超过70%,效果显著优于传统方法。关键节点在功能上呈现“主题—方法—工具—目标”的互补协同结构,其演化路径清晰展示了量子通信从理论奠基、技术攻坚到应用落地的三阶段发展轨迹,验证了MDS框架的有效性和实用性。展开更多
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
基金X.Li’s research was supported in part by NSFC(11301344)Y.Yong’sresearch was supported in part by NSFC(11201301)
文摘In this article, we study the 1-dimensional bipolar quantum hydrodynamic model for semiconductors in the form of Euler-Poisson equations, which contains dispersive terms with third order derivations. We deal with this kind of model in one dimensional case for general perturbations by constructing some correction functions to delete the gaps between the original solutions and the diffusion waves in L2-space, and by using a key inequality we prove the stability of diffusion waves. As the same time, the convergence rates are also obtained.
文摘[目的/意义]通过最大瓦解结构准确识别科学研究前沿中的关键节点并追踪其演化路径,为把握领域发展规律、优化科研资源配置提供支持,突破现有研究聚焦孤立节点的局部特征,以及难以捕捉知识网络中具有协同作用且对全局连通性有级联破坏力的关键节点集合的问题。[方法/过程]以量子通信领域为例,基于2015—2024年Web of Science的6538篇文献构建关键词共现网络,融合多中心性指标并利用熵权法评估节点重要性,采用贪心算法识别MDS,分析其功能协同特征与演化轨迹。[结果/结论]研究表明,MDS仅占网络规模的18%~22%,移除该集合后网络最大连通组件规模下降超过70%,效果显著优于传统方法。关键节点在功能上呈现“主题—方法—工具—目标”的互补协同结构,其演化路径清晰展示了量子通信从理论奠基、技术攻坚到应用落地的三阶段发展轨迹,验证了MDS框架的有效性和实用性。
