The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bou...The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.展开更多
<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robb...<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level through the duration of the game;the second is when the cop and robber sober up as a function of time;the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through <strong>M</strong> rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.</span>展开更多
Kinetics of natural rubber （NR） vulcanization by lanthanum O, O＇-diisopropyldithiophosphate [ La（DiPDP）3 ] was studied. La（DiPDP）3 had remarkable accelerating effect on the vulcanization of NR. The rate constan...Kinetics of natural rubber （NR） vulcanization by lanthanum O, O＇-diisopropyldithiophosphate [ La（DiPDP）3 ] was studied. La（DiPDP）3 had remarkable accelerating effect on the vulcanization of NR. The rate constant k6 of the reaction that turned polysulphidic cross-links into the modified main chain was higher than that of desulfuration reaction of polysulfidic cross-links （k3 ）. The activation energies （Ea2, Ea3, and Ea6） of the formation, desulfuration, and decomposition of polysulfidic cross-links were 87.57,102.34, and 95.01 kJ · mol^-1, respectively. Activation energy （Eas） of the reaction that turned the cross-link precursors into the modified main chain was 82.67 kJ · mol^-1. It could be concluded that the proportion of polysulphidic cross-links was higher than mono- and di- sulphidic cross-links during induction and curing periods, mono- and di- sulphidic cross-links increased as curing temperature rose. In the temperature range of 140 - 160 ℃, the amounts of polysulphidic cross-links were similar. However, over 160℃, mono- and di- sulphidic cross-links increased rapidly. Moreover, cross-link density of the vulcanizates was determined from the equilibrium-swelling data. A chemical probe detected the concentration of polysulphidic cross-links of vulcanizates. The change trend of the results predicated from equation corresponded to that of the experimental results.展开更多
文摘The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of the corresponding class of graphs. In this paper, we analyze the game of cops and robbers on H^(-)-free digraphs. However, it is not the same as the case of undirected graph. So we give a new concept(H^(-)^(*)-free digraph) to get a similar conclusion about the case of undirected graph.
文摘<span style="font-family:Verdana;">In this paper we analyze and model three open problems posed by Harris, Insko, Prieto-Langarica, Stoisavljevic, and Sullivan in 2020 concerning the tipsy cop and robber game on graphs. The three different scenarios we model account for different biological scenarios. The first scenario is when the cop and robber have a consistent tipsiness level through the duration of the game;the second is when the cop and robber sober up as a function of time;the third is when the cop and robber sober up as a function of the distance between them. Using Markov chains to model each scenario we calculate the probability of a game persisting through <strong>M</strong> rounds of the game and the expected game length given different starting positions and tipsiness levels for the cop and robber.</span>
基金Project supported by the Guangdong Natural Science Foundation (05006563)
文摘Kinetics of natural rubber （NR） vulcanization by lanthanum O, O＇-diisopropyldithiophosphate [ La（DiPDP）3 ] was studied. La（DiPDP）3 had remarkable accelerating effect on the vulcanization of NR. The rate constant k6 of the reaction that turned polysulphidic cross-links into the modified main chain was higher than that of desulfuration reaction of polysulfidic cross-links （k3 ）. The activation energies （Ea2, Ea3, and Ea6） of the formation, desulfuration, and decomposition of polysulfidic cross-links were 87.57,102.34, and 95.01 kJ · mol^-1, respectively. Activation energy （Eas） of the reaction that turned the cross-link precursors into the modified main chain was 82.67 kJ · mol^-1. It could be concluded that the proportion of polysulphidic cross-links was higher than mono- and di- sulphidic cross-links during induction and curing periods, mono- and di- sulphidic cross-links increased as curing temperature rose. In the temperature range of 140 - 160 ℃, the amounts of polysulphidic cross-links were similar. However, over 160℃, mono- and di- sulphidic cross-links increased rapidly. Moreover, cross-link density of the vulcanizates was determined from the equilibrium-swelling data. A chemical probe detected the concentration of polysulphidic cross-links of vulcanizates. The change trend of the results predicated from equation corresponded to that of the experimental results.
