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Viscosity solutions of the Isaacs equation οn an attainable set

Leszek Zaremba — 1994

Applicationes Mathematicae

We apply a modification of the viscosity solution concept introduced in [8] to the Isaacs equation defined on the set attainable from a given set of initial conditions. We extend the notion of a lower strategy introduced by us in [17] to a more general setting to prove that the lower and upper values of a differential game are subsolutions (resp. supersolutions) in our sense to the upper (resp. lower) Isaacs equation of the differential game. Our basic restriction is that the variable duration time...

The theorems of Koenig and Birkhoff and their connection with the minimization of the duration time of the measurements of automatic telecommunication channels

Szczepan Perz;  Leszek Zaremba — 1982

Mathematica Applicanda

A problem (P) of minimization of the duration time of the measurements of automatic telecommunication channels is considered. P is a discrete optimization problem solved by graph theory methods. It is defined by (i)-(v), where: (i) for each i, 1≤i≤p, and j, 1≤1≤p, there are given k ij channels to be measured between node ”i” and node ”j”; (ii) measurement of one channel lasts one unit; (iii) there are exactly two devices, say A, B, in each node (the case where there is an arbitrary number of devices...

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