本文主要探讨了数学建模在生物医学、社会科学和计算机科学等多个学科中的交叉应用与整合。数学建模作为一种跨学科的工具,通过数学方法和模型在不同学科领域中解决复杂问题,促进了学科之间的交流与合作。本文通过分析数学建模在各学科...本文主要探讨了数学建模在生物医学、社会科学和计算机科学等多个学科中的交叉应用与整合。数学建模作为一种跨学科的工具,通过数学方法和模型在不同学科领域中解决复杂问题,促进了学科之间的交流与合作。本文通过分析数学建模在各学科中的具体应用案例,展示了数学建模在促进跨学科研究发展和理论创新方面的重要作用。This paper mainly discusses the cross-application and integration of mathematical modeling in biomedical science, social science and computer science. As an interdisciplinary tool, mathematical modeling solves complex problems in different subject areas through mathematical methods and models, and promotes exchanges and cooperation between disciplines. By analyzing the specific application cases of mathematical modeling in various disciplines, this paper demonstrates the important role of mathematical modeling in promoting the development of interdisciplinary research and theoretical innovation.展开更多
图G的均匀k-划分是将图G的顶点划分,使得每个划分类导出的子图是一个森林且任意两个划分类中的顶点数最多相差1。图G的强均匀点荫度是最小整数k,使得对任意的k′≥k,图G都有一个均匀k′-划分。本文证明每个无割点的外平面图G,它的强均...图G的均匀k-划分是将图G的顶点划分,使得每个划分类导出的子图是一个森林且任意两个划分类中的顶点数最多相差1。图G的强均匀点荫度是最小整数k,使得对任意的k′≥k,图G都有一个均匀k′-划分。本文证明每个无割点的外平面图G,它的强均匀点荫度至多为,继而证明了无割点的外平面图满足猜想:对任何平面图G,强均匀点荫度至多是。同时,得到平方图的强均匀点荫度的下界为⌈ Δ+12⌉,证明圈Cn的平方图在n=5时,强均匀点荫度为3,当n≠5时,强均匀点荫度为2,从而证明圈的平方图满足强均匀点荫的猜想。An equitable k-partition of a graph G is a partition of the vertex set of G such that the subgraph induced by each partition class is a forest and the sizes of any two parts differ by at most one. The strong equitable vertex arboricity of G is the minimum integer k so that G has an equitably k′- partitioned for an k′≥k. This paper proves that the strong equitable vertex arboricity of each outerplanar has no cut-vertices G is at most 2, and then proves that the outerplanar satisfies the conjecture that for any plan G, the strong equitable vertex arboricity is at most 3. Meanwhile, the lower bound of the strong equitable vertex arboricity of the square graph is ⌈ Δ+12⌉, which proved that the square graph of the circuits Cnis 3 when n=5, and the strong equitable vertex arboricity is 2 when n≠5, so that the square graph of the circuits satisfies the conjecture of strong equitable vertex arboricity.展开更多
文摘本文主要探讨了数学建模在生物医学、社会科学和计算机科学等多个学科中的交叉应用与整合。数学建模作为一种跨学科的工具,通过数学方法和模型在不同学科领域中解决复杂问题,促进了学科之间的交流与合作。本文通过分析数学建模在各学科中的具体应用案例,展示了数学建模在促进跨学科研究发展和理论创新方面的重要作用。This paper mainly discusses the cross-application and integration of mathematical modeling in biomedical science, social science and computer science. As an interdisciplinary tool, mathematical modeling solves complex problems in different subject areas through mathematical methods and models, and promotes exchanges and cooperation between disciplines. By analyzing the specific application cases of mathematical modeling in various disciplines, this paper demonstrates the important role of mathematical modeling in promoting the development of interdisciplinary research and theoretical innovation.
文摘图G的均匀k-划分是将图G的顶点划分,使得每个划分类导出的子图是一个森林且任意两个划分类中的顶点数最多相差1。图G的强均匀点荫度是最小整数k,使得对任意的k′≥k,图G都有一个均匀k′-划分。本文证明每个无割点的外平面图G,它的强均匀点荫度至多为,继而证明了无割点的外平面图满足猜想:对任何平面图G,强均匀点荫度至多是。同时,得到平方图的强均匀点荫度的下界为⌈ Δ+12⌉,证明圈Cn的平方图在n=5时,强均匀点荫度为3,当n≠5时,强均匀点荫度为2,从而证明圈的平方图满足强均匀点荫的猜想。An equitable k-partition of a graph G is a partition of the vertex set of G such that the subgraph induced by each partition class is a forest and the sizes of any two parts differ by at most one. The strong equitable vertex arboricity of G is the minimum integer k so that G has an equitably k′- partitioned for an k′≥k. This paper proves that the strong equitable vertex arboricity of each outerplanar has no cut-vertices G is at most 2, and then proves that the outerplanar satisfies the conjecture that for any plan G, the strong equitable vertex arboricity is at most 3. Meanwhile, the lower bound of the strong equitable vertex arboricity of the square graph is ⌈ Δ+12⌉, which proved that the square graph of the circuits Cnis 3 when n=5, and the strong equitable vertex arboricity is 2 when n≠5, so that the square graph of the circuits satisfies the conjecture of strong equitable vertex arboricity.
