Systematic generation of multibody equations of motion suitable for recursive and parallel manipulation

The formulation of a method known as the joint coordinate method for automatic generation of the equations of motion for multibody systems is summarized. For systems containing open or closed kinematic loops, the equations of motion can be reduced systematically to a minimum number of second order differential equations. The application of recursive and nonrecursive algorithms to this formulation, computational considerations and the feasibility of implementing this formulation on multiprocessor computers are discussed

Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs

Primely generated refinement monoids

We extend both Dobbertin's characterization of primely generated regular refinement monoids and Pierce's characterization of primitive monoids to general primely generated refinement monoids.The first-named author was partially supported by DGI MINECO MTM2011-28992-C02-01, by FEDER UNAB10-4E-378 "Una manera de hacer Europa", and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The second-named author was partially supported by the DGI and European Regional Development Fund, jointly, through Project MTM2011-28992-C02-02, and by PAI III grants FQM-298 and P11-FQM-7156 of the Junta de Andalucía

Exchange Leavitt path algebras and stable rank

We characterize those Leavitt path algebras which are exchange rings in terms of intrinsic properties of the graph and show that the values of the stable rank for these algebras are 1, 2 or ∞. Concrete criteria in terms of properties of the underlying graph are given for each case

Diagonalization of matrices over regular rings

Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices

Diagonalization of matrices over regular rings

Square matrices are shown to be diagonalizable over all known classes of (von Neumann) regular rings. This diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings. These results are proved in greater generality, namely for matrices and modules over exchange rings, where attention is restricted to regular matrices

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph