In this paper, analyzing the problems related to the safety and to the comfort in railway train transport, we develop a particular mathematical model in order to interpret systematically the interactions between the circulatory phenomenon (binomial ”man-vehicle”), the different components of the railway net (branch, knot, plant, etc.) and environment of pertinence. Preliminary we build the set of the "satisfaction’s states” for the standards of quality for the trip from the consumer and after individualizing a particular subset of the "states disconfortless”, through opportune mathematical developments, we represent geometrically the problem with an iper-space; in this iper-space we are resolution to represent the elements of the system man-vehicle-infrastructure-environment that characterize the states of comfort during the trip.
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