Normal subgroups of classical groups over Banach algebras.
On the best choice of a damping sequence in iterative optimization methods.
Some iterative methods of mathematical programming use a damping sequence {α} such that 0 ≤ α ≤ 1 for all t, α → 0 as t → ∞, and Σ α = ∞. For example, α = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {α} depending only on time t is computed. The computation is used to find the best damping sequence.
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A. We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain...
On subgroups of GL2 over non-commutative local rings which are normalized by elementary matrices.
Work of Pere Menal on normal subgroups.
We describe subgroups of GLA which are normalized by elementary matrices for rings A satisfying the first stable range condition, Banach algebras A, von Neumann regular rings A, and other rings A.
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