We study a variant of intersection representations with unit balls: unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far edges, the goal is to represent the vertices of the graph by unit-size balls so that the balls for two adjacent vertices intersect if and only if the corresponding edge is near. We consider ...

We study a variant of intersection representations with unit balls, that is, unit disks in the plane and unit intervals on the line. Given a planar graph and a bipartition of the edges of the graph into near and far sets, the goal is to represent the vertices of the graph by unit balls so that the balls representing two adjacent vertices intersect if and only if the corresponding edge is near. ...

We consider the problem of assigning objects probabilistically among a group of agents who may have multi-unit demands. Each agent has linear preferences over the (set of) objects. The most commonly used extension of preferences to compare probabilistic assignments is by means of stochastic dominance, which leads to corresponding notions of envy-freeness, efficiency, and strategy-proofness. We ...

The title compound C(19)H(27)N(3)O(3)S, crystallizes with two unique mol-ecules in the asymmetric unit. The benzene ring of each benzothia-zole unit carries a dipropyl-carbamoyl substituent in the 6-position and a tert-butyl carbamate unit on each thia-zole ring. In the crystal structure, inter-molecular N-H⋯N and weak C-H⋯O hydrogen bonds form centrosymmetric dimers. Additional C-H⋯O contacts ...