We consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input...

A method for analyzing parallel systems with the help of structured Markovian models is presented. The overall model is built from interdependent submodels, and symmetries are exploited automatically by grouping similar submodels in classes. During model analysis, this leads to a state space reduction, based on the concept of exact lumpability.

Insight in the global structure of a state space is of great help in the analysis of the underlying process. We present a tool to visualize the structure of very large state spaces. It uses a clustering method to obtain a simplified representation, which is used as a backbone for the display of the entire state space. With this tool we are able to answer questions about the global structure of ...

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...

In this paper, we study the generation problem of Riesz basis for a general network of strings with joint damping at each vertex. First, we give a basic spectral property of the system operator A. Under certain conditions, we prove that the spectrum of A is distributed in a strip parallel to the imaginary axis. By the discussion of the completeness of generalized eigenvectors of the operator A,...

We show that the no betting characterisation of the existence of common priors over finite type spaces extends only partially to improper priors in the countably infinite state space context: the existence of a common prior implies the absence of a bounded agreeable bet, and the absence of a common improper prior implies the existence of a bounded agreeable bet. However, a type space that lacks...