Classification Of Such Systems Research Articles

Decomposable processes and continuous products of probability spaces

Sequences of independent random variables and products of probability spaces are just two ways of looking at the same thing. The natural generalization of a sequence of independent random variables is a decomposable process. We introduce a corresponding generalization of a product of probability spaces, which will be called a factored probability space, and study the structure and classification of such systems and their relation to decomposable processes.

Der Einfluß verschiedener Kräftearten auf die Stabilität linearer Systeme

Several general theorems concerning the stability of dynamical systems have been published during the last decades. Starting with a classification of such systems an attempt is made to define the range of validity for these known theorems. Emphasis is laid upon the effect of different forces, as for example velocity-forces (gyroscopic as well as damping or exciting ones) and of positional forces (potential as well as circulatory nonconservative ones). The text of 20 theorems is given.