It was shown earlier that product (xy) for (k=6lpm 1) is a universalfunction in the class of linear functions of two variables, and there exist no universal polynomials for even (k) in classes of linear functions of two variables. This work proves that polynomial (xy+xz+yz) is universal for classes of linear functions of three variables for arbitrary odd (k) and polynomial (xy+zw) is universal for classes of linear functions of four variables for arbitrary (k).
The problem of maximizing the horizontal coordinate of a mass point moving in a vertical plane driven by gravity, viscous drag, curve reaction force, and thrust is considered. It is assumed that inequality-type constraints are imposed on the angle of inclination of the trajectory. The system of equations belongs to a certain type that allows us to reduce the optimal control problem with constraints on the state variable to the optimal control problem with control constraints. The sequence and the number of switchings of the state constraints along the optimal trajectory are determined, and a scheme for optimal control is designed.
A study is performed of a single-channel queuing system with two classes of priority requests, a relative priority discipline, a Poisson incoming flow with random intensity, and an infinite number of waiting places. The intensity is selected at the moment the countdown begins until the next request arrives, and the intensity does not change with a predetermined probability. The limit distribution of the number of requests of the lowest priority class at a critical system load is found.
It is shown that the class of dictionary functions defined on the basis of bounded prefix concatenation coincides with the familiar complexity class (textrm{TC}^{0}).
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