TWO–COMPONENT RESTORABLE TOOL SYSTEM MULTI–PURPOSE MACHINE WITH AN INSTANTLY REFILLED TIME RESERVE

The object of the research is the technical system of a multipurpose machine tool, the tools of which can fail and be restored. A failed tool remains functional for some time due to a temporary reserve until a parametric failure occurs, the magnitude of which is random. All random variables describing the system have general distributions. The apparatus for constructing a mathematical model of the described system is a semi–Markov process with a discrete–continuous phase space of states. The stationary distribution of the embedded Markov chain is found explicitly. For systems with parallel connection, series connection with disconnection and without disconnection of elements, the stationary time between failures of the system, the stationary time spent in the state of failure and the stationary system availability factor are found. A numerical example shows the dependence of the stationary characteristics of the system on the size of the time reserve.

Quantum margulis expanders

We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart, e.g., it has the same degree and spectrum. Unlike previous constructions of quantum expanders, our method does not rely on non-Abelian harmonic analysis. Analogues for continuous variable systems are mentioned. Indeed, the construction seems one of the few instances where applications based on discrete and continuous phase space methods can be developed in complete analogy.