Analysis of physical processes via imaging vectors

Abstract

Practically, all modeling processes in one way or another are random. The foremost formulated theoretical foundation embraces Markov processes, being represented in different forms. Markov processes are characterized as a random process that undergoes transitions from one state to another on a state space, whereas the probability distribution of the next state depends only on the current state and not on the sequence of events that preceded it. In the Markov processes the proposition (model) of the future by no means changes in the event of the expansion and/or strong information progression relative to preceding time. Basically, modeling physical fields involves process changing in time, i.e. non-stationay processes. In this case, the application of Laplace transformation provides unjustified description complications. Transition to other possibilities results in explicit simplification. The method of imaging vectors renders constructive mathematical models and necessary transition in the modeling process and analysis itself. The flexibility of the model itself using polynomial basis leads to the possible rapid transition of the mathematical model and further analysis acceleration. It should be noted that the mathematical description permits operator representation. Conversely, operator representation of the structures, algorithms and data processing procedures significantly improve the flexibility of the modeling process.