Special network algorithms with gains

Several optimalization algorithms have been proposed for the solution the minimal and the multiterminal minimal path of a network having cost (distance) function. In this paper we present these algorithms in a special network in which on the edges a gain function is given. On the edge (x,y) of the network a t(x,y) transportation cost is defined. In the course of the transportation on the edge (x,y) the goods loose a part of there weight. If one unit of goods is transported from point x to point y then k(x,y) unite of goods arrive at point y, where 0≪k(x,y)≪1. The above mentioned 2 algorithms are presented in the network having gains. These problems are interested not only theoretically, but in the practice too. For example the maximal flow problem could be used in the case of electrical network, where we are interested to know the amount of electricity on the edges of the network.