In this note we introduce a new model for the mailing problem in branched transportation that takes into account the orientation of the moving particles. This gives an effective answer to Bernot et al. (2009, Problem 15.9). Moreover we define a convex relaxation in terms of rectifiable currents with group coefficients. We provide the problem with a notion of calibration. Using similar techniques we define a convex relaxation and a corresponding notion of calibration for a variant of the Steiner tree problem in which a connectedness constraint is assigned only among a certain partition of a given set of finitely many points.

中文翻译：

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定向邮件问题及其凸松弛

在本说明中，我们针对分支运输中的邮件问题引入了一种新模型，该模型考虑了移动粒子的方向。这为Bernot等人提供了有效的答案。（2009年，问题15.9）。此外，我们根据具有组系数的可整流电流定义了凸松弛。我们以校准的概念提供问题。使用类似的技术，我们为Steiner树问题的变体定义了凸松弛和相应的校准概念，在该变体中，仅在给定的有限多个点集的特定分区之间分配了连通性约束。