in this paper, we generalize some transfer theorems.~in particular, we derive one of the main results of gagola(contemp math 524:49--60, 2010) from our results.

The class of commutator-free Magnus integrators is known to provide a favourable alternative to standard Magnus integrators, in particular for large-scale applications arising in the time integration of non-autonomous linear evolution equations. A high-order commutator-free Magnus integrator is given by a composition of several exponentials that comprise certain linear combinations of the value...

Charles Sims has asked whether or not, for a free group F , the lower central subgroup γn(F ) coincides with the normal closure in F of the set of basic commutators of weight n. In this paper, we will show that Sims’ question has a positive answer when n = 5. The longest part of the proof is showing that this is true when F has rank 3. Once this is known, the results for higher ranks follow fai...

Let Mb be the operator of pointwise multiplication by b, that is Mb f = bf . Set [A,B] = AB−BA. The Reisz potentials are the operators Rα f(x) = ∫ f(x− y) dy |y|α , 0 < α < 1. They map L 7→ L, for 1 − α + 1 q = 1 p , a fact we shall take for granted in this paper. A Theorem of Chanillo MR84j:42027 [6] states that one has the equivalence ‖[Mb,Rα]‖p→q ≃ ‖b‖BMO with the later norm being that of th...

Two new measures to assess spatial ability are presented: the mental cutting test “Schnitte” (Fay & Quaiser-Pohl, 1999; English version: Fay, Quaiser-Pohl, & Rönicke, 2003), a test for selecting people with extraordinary spatial abilities, and the Picture Rotation Test (Hinze, 2002; Hinze & Quaiser-Pohl, 2003), a mental rotation test for preschool children. Both overcome some of the limits of t...

In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for br...

In this paper we characterize when the semi-commutator TfTg − Tfg of two Toeplitz operators Tf and Tg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T 2 are given.

We discuss bipermutive cellular automata from a combinatorial and topological perspective. We prove a type of topological randomizing property for bipermutive CA, show that the commutator of a bipermutive CA is always small and that bipermutive affine CA have only affine CA in their commutator. We show the last result also in the multidimensional case, proving a conjecture of [Moore-Boykett, 97].

These brief remarks have been prepared in connection with a conference in honor of my thesis advisor, Richard Rochberg.

It is shown that there exists a finitely generated infinite simple group of infinite commutator width and infinite square width in which every conjugation-invariant norm is stably bounded, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.