It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of th...It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible.展开更多
考察了平面近三角剖分图的最大亏格与独立边集之间的关系．设G*是平面近三角剖分图G的一个平面嵌入的几何对偶,如果G*有[1/2φ]个独立边集,那么图G的最大亏格γM(G)≥[1/2β(G)]-11,这里φ和β(G)分别表示图G在平面上嵌入的面数与G的Be...考察了平面近三角剖分图的最大亏格与独立边集之间的关系．设G*是平面近三角剖分图G的一个平面嵌入的几何对偶,如果G*有[1/2φ]个独立边集,那么图G的最大亏格γM(G)≥[1/2β(G)]-11,这里φ和β(G)分别表示图G在平面上嵌入的面数与G的Betti数．特别地,如果φ=0 mod 2,即G有1-因子,则G是上可嵌入的．作为应用．证明了几个已知的结果．展开更多
Particle suspension and deposition dynamics are significant factors affecting the level of mixing quality in solidliquid two-phase stirring processes. In general, the ability to increase the suspension rate and minimi...Particle suspension and deposition dynamics are significant factors affecting the level of mixing quality in solidliquid two-phase stirring processes. In general, the ability to increase the suspension rate and minimize depositioneffects is instrumental in improving the uniformity of particle mixing, accelerating the reaction of involved solidliquid two-phase, and improving the efficiency of production operations. In this work, suspension and depositionindicator based on the Betti number and a uniformity indicator are introduced and obtained by means of imageanalysis. The influence of the blade type, rotation speed, blade diameter and blade bottom height on the particlesuspension/deposition characteristics and mixing uniformity are carefully investigated. The experimental resultsshow that the two-phase motion region can be divided into three local regions, including a bottom motion alongthe wall, a low-degree suspension region under the blade and a high suspension region above the blade. The bestdegree of particle suspension is attained by the double-inclined blade paddle at a speed of 270 r/min, a paddlediameter ratio of 0.414, and a height-diameter ratio of 0.086. The double-inclined blade paddle has a better effecton promoting particle suspension and solid-liquid two-phase mixing uniformity.展开更多
It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the...It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the 3-regular graphs. Let G be a 2-edge connected 3-regular graph.We prove that G is up-embeddable if and only if G can be obtained from the graphs θ, θ or K4by a series of M- or N-extensions. Meanwhile, we also present a new structural characterization of such graph G provided that G is up-embeddable.展开更多
基金National Natural Science Foundation of China!(No.19801013).
文摘It is known (for example see [2]) that the maximum genus of a graph is mainly determined by the Betti deficiency of the graph. In this paper, the authors establish an upper bound on the Betti deficiency in terms of the independence number as well as the girth of a graph, and thus use the formulation in [2] to translate this result to lower bound on the maximum genus. Meantime it is shown that both of the bounds are best possible.
文摘考察了平面近三角剖分图的最大亏格与独立边集之间的关系．设G*是平面近三角剖分图G的一个平面嵌入的几何对偶,如果G*有[1/2φ]个独立边集,那么图G的最大亏格γM(G)≥[1/2β(G)]-11,这里φ和β(G)分别表示图G在平面上嵌入的面数与G的Betti数．特别地,如果φ=0 mod 2,即G有1-因子,则G是上可嵌入的．作为应用．证明了几个已知的结果．
基金support from the Yunnan Fundamental Research Project,China(No.202201BE070001-026)Interdisciplinary Research Project of Kunming University of Science and Technology(No.KUST-xk2022001)+2 种基金Yunnan Major Scientific and Technological Projects(No.202302AQ370001-4)Open Foundation of State Environmental Protection Key Laboratory of Mineral Metallurgical Resources Utilization and Pollution Control(No.HB202204)Young Elite Scientist Sponsorship Program by China Association for Science and Technology,China(No.YESS20210106).
文摘Particle suspension and deposition dynamics are significant factors affecting the level of mixing quality in solidliquid two-phase stirring processes. In general, the ability to increase the suspension rate and minimize depositioneffects is instrumental in improving the uniformity of particle mixing, accelerating the reaction of involved solidliquid two-phase, and improving the efficiency of production operations. In this work, suspension and depositionindicator based on the Betti number and a uniformity indicator are introduced and obtained by means of imageanalysis. The influence of the blade type, rotation speed, blade diameter and blade bottom height on the particlesuspension/deposition characteristics and mixing uniformity are carefully investigated. The experimental resultsshow that the two-phase motion region can be divided into three local regions, including a bottom motion alongthe wall, a low-degree suspension region under the blade and a high suspension region above the blade. The bestdegree of particle suspension is attained by the double-inclined blade paddle at a speed of 270 r/min, a paddlediameter ratio of 0.414, and a height-diameter ratio of 0.086. The double-inclined blade paddle has a better effecton promoting particle suspension and solid-liquid two-phase mixing uniformity.
文摘It is known[5] that an investigation of the up-embeddability of the 3-regular graphs shows a useful approach to that of the general graph. But as far, very few characterizations of the upembeddability are known on the 3-regular graphs. Let G be a 2-edge connected 3-regular graph.We prove that G is up-embeddable if and only if G can be obtained from the graphs θ, θ or K4by a series of M- or N-extensions. Meanwhile, we also present a new structural characterization of such graph G provided that G is up-embeddable.
基金Supported by the National Natural Science Foundation of China(10271048)and Shanghai Priority Academic Discipline and Sci-ence and Technology Commission of Shanghai Municipality(04JC14031).
