We compute the equilibrium measure in dimension $$d=s+4$$ associated to a Riesz s-kernel interaction with an external field given by power of Euclidean norm. Our study reveals that can be mixture continuous part and singular part. Depending on value power, threshold phenomenon occurs consists reduction or condensation In particular, logarithmic case $$s=0$$ ( $$d=4$$ ), there is sphere special ...

We consider the problem of demand estimation for public transport networks. Given an origin-destination matrix representing demand, distribution flow among different lines can be obtained assuming that it corresponds to a certain equilibrium characterized by optimization problem. The knowledge is expensive and sometimes unaffordable in practice. Traditionally, estimated using statistical or eco...