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This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra G d = E M /N introduced in part I and Colombeau's original algebra G e. Three main results are established: First, a simple criterion describing membership in N (applicable to all types of Colombeau(More)
We extend the construction of the authors' paper of 2002 by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby obtain a universal algebra of generalized tensor fields canonically containing the space of(More)
We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and(More)
Extending the construction of the algebrâ G(M) of scalar valued Colombeau functions on a smooth manifold M (cf. [4]), we present a suitable basic space for eventually obtaining tensor valued generalized functions on M , via the usual quotient construction. This basic space canonically contains the tensor valued distributions and permits a natural extension(More)
The theory of hyperbolic conservation laws was developed to study phenomena in unsteady compressible gas dynamics, especially the propagation of nonlinear waves, and the formation and evolution of shock discontinuities. Comparison with experiments shows that the theory is reasonably successful. Although a rigorous theory of conservation laws encompassing(More)
Probabilistic finite automata as acceptors for languages over finite words have been studied by many researchers. In this paper, we show how probabilistic automata can serve as acceptors for /spl omega/-regular languages. Our main results are that our variant of probabilistic Buchi automata (PBA) is more expressive than non-deterministic /spl(More)
We present a geometric approach to deening an algebra ^ G(M) (the Colombeau algebra) of generalized functions on a smooth manifold M containing the space D 0 (M) of distributions on M. Based on diierential calculus in convenient vector spaces we achieve an intrinsic construction of ^ G(M). ^ G(M) is a diierential algebra, its elements possessing Lie(More)
Twenty-six different concrete representations of the space of vector valued distributions on a smooth manifold of dimension n are presented systematically, most of them new. In the particular case of representations as module homomorphisms acting on sections of the dual bundle resp. on n-forms, the continuity of these homomorphisms is already a consequence(More)