In this paper, we consider the minimizing total weighted completion time in preemptive equal-length job with release dates scheduling problem on a single machine. This problem is known to be open. Here, we give some properties of optimal schedules for the problem and its special cases.
We study the characteristic features of the detection zone for an onboard radar station for an early radar detection system operating in the impulse–Doppler mode. We show that due to these features, there exist covert trajectories such that objects flying along such trajectories are not detected by this onboard radar station. We derive differential equations that define covert trajectories, find various forms of covert trajectories, and study their properties.
The theoretical fundamentals for solving the linear quadratic problems may be some times used to design the optimal control actions for the nonlinear systems. The method relying on the Riccati equation with state-dependent coefficients is promising and rapidly developing tools for design of the nonlinear controllers. The set of possible suboptimal solutions is generated by ambiguous representation of the nonlinear system as a linearly structured system with state-depended coefficients and the lack of sufficiently universal algorithms to solve the Riccati equation also having state-depended coefficients. The paper proposed a method to design a guaranteed control for the uncertain nonlinear plant with state-depended parameters. An example of design the controller for an uncertain nonlinear system was presented.
The problem of building the rating of a remote training system by processing the results of a run of tests was considered. The Rasch model extended to a run of tests was used. A recurrent algorithm based on the maximum-likelihood procedure and the Newton method was proposed to calculate the rating.