基于PDCA循环理论的完全线上教学模式探索与实践*——以化工原理课程为例

为保障新冠疫情期间“停课不停学”的高质量开展,以化工原理课程教学为例,探讨了PDCA循环理论在“3+1+4+3”完全线上教学模式中的应用,实践教学表明2者的融合能有效保证教学顺利有序开展,对于提高学生学习动力效果显著。     

Matching theory and Barnette's conjecture

Barnette's Conjecture claims that all cubic, 3-connected, planar, bipartite graphs are Hamiltonian. We give a translation of this conjecture into the matching-theoretic setting. This allows us to relax the requirement of planarity to give the equivalent conjecture that all cubic, 3-connected, Pfaffian, bipartite graphs are Hamiltonian.A graph, other than the path of length three, is a brace if it is bipartite and any two disjoint edges are part of a perfect matching. Our perspective allows us to observe that Barnette's Conjecture can be reduced to cubic, planar braces. We show a similar reduction to braces for cubic, 3-connected, bipartite graphs regarding four stronger versions of Hamiltonicity. Note that in these cases we do not need planarity.As a practical application of these results, we provide some supplements to a generation procedure for cubic, 3-connected, planar, bipartite graphs discovered by Holton et al. (1985) [14]. These allow us to check whether a graph we generated is a brace.     

基于CEEMD特征提取的无绝缘轨道电路补偿电容故障诊断

本文利用电路网络理论和传输线理论构建ZPW-2000A轨道电路传输模型,仿真并分析了补偿电容故障对轨面电压的影响,提出基于互补的总体经验模式分解(CEEMD)特征提取的补偿电容故障诊断方法。实验结果表明,相比于传统经验模式分解(EMD)和总体经验模式分解(EEMD),基于CEEMD特征提取的补偿电容故障诊断方法可以有效地克服EMD方法引起的模态混叠和能量泄露现象,减少EEMD方法在信号重构过程中的白噪声残留,为补偿电容的故障诊断提供了一种快速准确的方法,为保证信号传输质量提供了参考依据。     

Diffusion determines the recurrent graph

We consider diffusion on discrete measure spaces as encoded by Markovian semigroups arising from weighted graphs. We study whether the graph is uniquely determined if the diffusion is given up to order isomorphism. If the graph is recurrent then the complete graph structure and the measure space are determined (up to an overall scaling). As shown by counterexamples this result is optimal. Without the recurrence assumption, the graph still turns out to be determined in the case of normalized diffusion on graphs with standard weights and in the case of arbitrary graphs over spaces in which each point has the same mass.     

Exact and asymptotic results on coarse Ricci curvature of graphs

Ricci curvature was proposed by Ollivier in a general framework of metric measure spaces, and it has been studied extensively in the context of graphs in recent years. In this paper we obtain the exact formulas for Ollivier’s Ricci-curvature for bipartite graphs and for the graphs with girth at least 5. These are the first formulas for Ricci-curvature that hold for a wide class of graphs, and extend earlier results where the Ricci-curvature for graphs with girth 6 was obtained. We also prove a general lower bound on the Ricci-curvature in terms of the size of the maximum matching in an appropriate subgraph. As a consequence, we characterize the Ricci-flat graphs of girth 5. Moreover, using our general lower bound and the Birkhoff–von Neumann theorem, we give the first necessary and sufficient condition for the structure of Ricci-flat regular graphs of girth 4. Finally, we obtain the asymptotic Ricci-curvature of random bipartite graphs G(n,n,p)$G(n,n,p)$ and random graphs G(n,p)$G(n,p)$, in various regimes of p$p$.     

Discrepancy of random graphs and hypergraphs

Answering in a strong form a question posed by Bollobás and Scott, in this paper we determine the discrepancy between two random k‐uniform hypergraphs, up to a constant factor depending solely on k. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 47, 147–162, 2015     

The evolution of subcritical Achlioptas processes

In Achlioptas processes, starting from an empty graph, in each step two potential edges are chosen uniformly at random, and using some rule one of them is selected and added to the evolving graph. AlthouSgh the evolution of such ‘local’ modifications of the Erd?s–Rényi random graph process has received considerable attention during the last decade, so far only rather simple rules are well understood. Indeed, the main focus has been on ‘bounded‐size’ rules, where all component sizes larger than some constant B are treated the same way, and for more complex rules very few rigorous results are known. In this paper we study Achlioptas processes given by (unbounded) size rules such as the sum and product rules. Using a variant of the neighbourhood exploration process and branching process arguments, we show that certain key statistics are tightly concentrated at least until the susceptibility (the expected size of the component containing a randomly chosen vertex) diverges. Our convergence result is most likely best possible for certain generalized Achlioptas processes: in the later evolution the number of vertices in small components may not be concentrated. Furthermore, we believe that for a large class of rules the critical time where the susceptibility ‘blows up’ coincides with the percolation threshold. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 174–203, 2015     

Edge‐disjoint Hamilton cycles in random graphs

We show that provided we can with high probability find a collection of edge‐disjoint Hamilton cycles in , plus an additional edge‐disjoint matching of size if is odd. This is clearly optimal and confirms, for the above range of p, a conjecture of Frieze and Krivelevich. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 397–445, 2015     

Group representations that resist random sampling

We show that there exists a family of groups G_n and nontrivial irreducible representations ρ_n such that, for any constant t, the average of ρ_n over t uniformly random elements has operator norm 1 with probability approaching 1 as . More quantitatively, we show that there exist families of finite groups for which random elements are required to bound the norm of a typical representation below 1. This settles a conjecture of A. Wigderson. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 605–614, 2015     

On the kernel size of clique cover reductions for random intersection graphs

Covering all edges of a graph by a minimum number of cliques is a well known $\mathsf{NP}$-hard problem. For the parameter k being the maximal number of cliques to be used, the problem becomes fixed parameter tractable. However, assuming the Exponential Time Hypothesis, there is no kernel of subexponential size in the worst-case.We study the average kernel size for random intersection graphs with n vertices, edge probability p, and clique covers of size k. We consider the well-known set of reduction rules of Gramm, Guo, Hüffner, and Niedermeier (2009) [17] and show that with high probability they reduce the graph completely if p is bounded away from 1 and $k<c\log n$ for some constant $c>0$. This shows that for large probabilistic graph classes like random intersection graphs the expected kernel size can be substantially smaller than the known exponential worst-case bounds.