For a field k of characteristic zero, we study the field of Noetherian power series, k〈〈tQ〉〉, which consists of maps z : Q → k whose supports are Noetherian (i.e., reverse well-ordered) subsets of Q. There is a canonical valuation LE : k〈〈tQ〉〉 → Q ∪ {−∞} that sends a nonzero series to the maximum element of its support. Given a nonzero polynomial f(x, y) ∈ k[x, y] and a series z ∈ k〈〈tQ〉〉 that ...

In this paper the long time asymptotic behavior of solutions of semilinear symmetric hyperbolic system including Maxwell s equations and the scalar wave equation in an ar bitraty domain are investigated The possibly nonlinear damping term may vanish on a certain subset of the domain It is shown that the solution decays weakly to zero if and only if the initial state is orthogonal to all station...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.