A generalization of Vassiliev's planarity criterion

Motivated by his studies in knot theory V. Vassiliev introduced $X$-graphs as regular 4-valent graph with a structure of pairs of opposite edges at each vertex. He conjectured the conditions under which $X$-graph can be embedded into a plane respecting the the $X$-structure at every vertex. The conjecture was proved by V.Manturov. Here we generalize these results for graphs with vertices of valency 4 or 6, *-graphs. A problem of such generalization was posted by A.Skopenkov

Review of Klippenstein\u27s Peace and War, Mennonite Conscientious Objectors in Tsarist Russia and the Soviet Union before World War II, and other COs in Eastern Europe

Review of Lawrence Klippenstein, Peace and War, Mennonite Conscientious Objectors in Tsarist Russia and the Soviet Union before World War II, and other COs in Eastern Europe, Winnipeg, MB. 2017. 367pp. $30.00 including postage outside Canada

Emmaus--The Artist\u27s Way

Sermon preached at Rockway Mennonite Church, Kitchener

Certainty of Punishment versus Severity of Punishment- An Experimental Investigation

Compliance with laws and regulations depends on the expected penalty facing violators. The expected penalty depends on both the probability of punishment and the severity of the punishment if caught. A key question in the economics of crime literature is whether increasing the probability of punishment is a more effective deterrent than an equivalent increase in the severity of punishment. This paper uses laboratory experiments to investigate this issue, and finds that increasing the severity of punishment is a more effective deterrent than an equivalent increase in the probability of punishment. This result contrasts with the findings of the empirical crime literature.