4,410 research outputs found

    Generalized nowhere zero flow

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    Let G be an undirected graph, A be an (additive) abelian group and A* = A - {lcub}0{rcub}. A graph G is A-connected if G has an orientation D(G) such that for every function b : V(G ) A satisfying SvāˆˆVG b(v) = 0, there is a function f : E(G) A* such that at each vertex v āˆˆ V(G), āˆ‚f(v), the net flow out from v, equals b( v). An A-nowhere-zero-flow (abbreviated as A-NZF) in G is a function f : E(G) A* such that at each vertex v āˆˆ V(G), āˆ‚f(v) = 0.;In this paper, we investigate the group connectivity number Lambda g(G) = min{lcub}n : if A is an abelian group with |A| ā‰„ n, then G is A-connected{rcub} for certain families of graphs including complete bipartite graphs, chordal graphs, wheels and biwheels. We also give some general results and methods to approach nowhere zero flow and group connectivity problems

    Analysis of National Patent Cooperation between Jiangsu Province and the Belt and Road Initiative

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    With the further advancement of the ā€œOne Belt, One Roadā€ strategy, patent cooperation between Jiangsu Province and countries along the route has been further strengthened. At the US Patent and Trademark Office (USTPO) and the Jiangsu Provincial Productivity Promotion Center, we searched for cooperation patents and technology alliances between China and 65 countries along the Belt and Road Initiative, and analyzed the current situation of time series distribution, spatial distribution, and main technical fields. The results show that: ā‘ Science and technology cooperation generally maintains a growth trend, which can be divided into three stages: start-up period, volatility growth period and rapid growth period; ā‘”the cooperation area presents an unbalanced feature, and the cooperation patents of the top five countries account for 85.06% of the total. ā‘¢The technical fields and directions of cooperation are more focused, and the cooperation patents are concentrated in the fields of electricity, human life, and physics. ā‘£ Technology transfer and paper cooperation are mainly distributed in West Asia, South Asia, CIS, Eastern Europe, Central and Eastern Europe, and lack of innovative cooperation with East Asia and Central Asia. The conclusions of the study can provide reference for further scientific cooperation and policy formulation in the future
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