The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The methodologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results.
The presented article points to the issues of self-consciousness and the possibilities of its development. It defines in this context also concepts of self-evaluation, self-respect, self-appreciation, self-recognition, self-confidence and self-realization. In the text, it is emphasized that self-consciousness is related to the awareness of one´s own psychophysical and social identity - I myself and the world and my place in it. An important means for the development of the healthy self-consciousness is also praise. In the conclusion of the article, attention is paid to the psycho-hygiene as prevention of the failure.