The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we get convergence of order , where is the classical order of the IRK and is the stage order. For transferable...
An example of a countable Butler group that is not a pure subgroup of a completely decomposable group was published in 1986. Recently, an error in the proof was discovered. This note includes a corrected argument, as well as a proof that this group has no pure precobalanced subgroups of rank one.
The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p³ is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.
Almost completely decomposable groups with a critical typeset of type and a -primary regulator quotient are studied. It is shown that there are, depending on the exponent of the regulator quotient , either no indecomposables if ; only six near isomorphism types of indecomposables if ; and indecomposables of arbitrary large rank if .
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