Joint-tree model and the maximum genus of graphs

The vertex v of a graph G is called a 1-critical-vertex for the maximum genus of the graph, or for simplicity called 1-critical-vertex, if G-v is a connected graph and {\deg}M(G - v) = {\deg}M(G) - 1. In this paper, through the joint-tree model, we obtained some types of 1-critical-vertex, and get the upper embeddability of the Spiral Snm

Vertex Splitting and Upper Embeddable Graphs

The weak minor G of a graph G is the graph obtained from G by a sequence of edge-contraction operations on G. A weak-minor-closed family of upper embeddable graphs is a set G of upper embeddable graphs that for each graph G in G, every weak minor of G is also in G. Up to now, there are few results providing the necessary and sufficient conditions for characterizing upper embeddability of graphs. In this paper, we studied the relation between the vertex splitting operation and the upper embeddability of graphs; provided not only a necessary and sufficient condition for characterizing upper embeddability of graphs, but also a way to construct weak-minor-closed family of upper embeddable graphs from the bouquet of circles; extended a result in J: Graph Theory obtained by L. Nebesk{\P}y. In addition, the algorithm complex of determining the upper embeddability of a graph can be reduced much by the results obtained in this paper

The Chinese Advantage in Emergency Law

This Article has a twofold purpose. On the one hand, it offers comparative materials for an informed discussion of COVID-determined emergency law in China and Italy by assessing its normative implications and political genealogy. On the other hand, it explores the essential contiguity between the ‘state of exception’ triggered by the pandemic and the possible geopolitical shifts in global legal hegemony in the actual phase of surveillance capitalism which is witnessing a decline of law as a form of social organization and its replacement by the predictive models elaborated by technology. In this respect, the traditional Western iconography has long described the Chinese legal tradition as a “law without law”, a despotic regime with intrusive population surveillance whose distance from the Western paradigm is deemed almost unbridgeable. And yet the legal response to coronavirus both in Europe and in the U.S. somewhat replicates the allegedly distant Chinese model in terms of restrictions and surveillance mechanisms which are being deployed to counter the crisis in the face of a formal commitment to the rule of law. This Article concludes that the emerging pre-eminence of the “rule of technology” over the “rule of law” in a critical event of historic proportions like a pandemic should and will set the future agenda of comparative studies in a double direction. On the one hand it calls for a truly critical reconsideration of role of law in society which in turn impels to rethink the hold of the liberal constitutional model and the obsolescence of traditional legal taxonomies. On the other hand, it might point to the emergence of an unexpected Chinese legal leadership, determined by the progressive undoing of the Western legal and political narratives whose backbone has been relentlessly eroded by decades of neoliberalism and populism

The effect of calcium nitrate on the hydration of calcium aluminate cement at different curing temperatures

Phase conversion in calcium aluminate cements (CAC) induces significant volumetric instability; it would result in an increase in porosity and decrease in strength in CAC. In this study, calcium nitrate (CN) as a phase conversion inhibitor, the effect of CN on the hydration of CAC at different curing temperatures was studied. Xray diffraction, thermal analysis, SEM, isothermal calorimetry and the compressive strength were conducted on the CAC dosages of 0%, 5%, 10% and 15%CN cured at 20�, 30�, 40� and 50�. The results show CN can retard CAC hydration, alter the characters of the hydrates of CAC systems and avoid the conversion process. With increasing dosage of CN and curing temperature, the hydration products formed is different.in CAC systems with CN, NO3-AFm and NO3-AFt are more preferred than CAH10 and C2AH8 and are more thermostable than those typically hydrates. In the presence of CN, The phase conversion to a large extent can be avoided and the compressive strength is significantly improved. The CN dosage has a very important effect on CAC systems with CN. In this study, the optimum dosage for CN is 10 percent. This study may provide a new insight into avoiding the unstable phase conversion in calcium aluminate cements