No Finite Invariant Density for Misiurewicz Exponential Maps

For exponential mappings such that the orbit of the only singular value 0 is bounded, it is shown that no integrable density invariant under the dynamics exists on the complex plane

Process density functions in the problem of the identification of a barrier in the functioning of a certain inventory storage and issue system

The subject matter of the investigation is a barrier to the functioning of a certain inventory system in the case where the storage input is a non-aggregated dynamic-parameter process. The authors derive a system of differential equations satisfied by probability distribution density functions for the intermediate states of subsystem L. The system of equations expresses relations between the densities and the parameters of the functioning of the transport subsystem and the parameters of the products supply process.inventory system, barrier, transport, system of differential equations

Probabilities of a lower-limit barrier in the problem of the identification of a barrier in the functioning of a certain inventory storage and issue system

The paper investigates a barrier in the functioning of certain inventory system. Assuming that the storage input is a non-aggregated dynamic-parameter process, the paper derives a system of differential equations satisfied by the probabilities of a lower-limit barrier in subsysyem L. The system of equations expresses relations between the distributions of the probability of the lower-limit barrier on the one hand and the parameters of the product supply process and the parameters of the functioning of the transport subsystem on the other hand.inventory system, barrier, transport, system of differential equations