As the development of the singular integral operators, their commutators have been well studied (see [1, 2, 3, 14]). From [2, 3, 9, 13], we know that the commutators and multilinear operators generated by the singular integral operators and the Lipschitz functions are bounded on the Triebel-Lizorkin and Lebesgue spaces. The purpose of this paper is to introduce the multilinear commutator associ...

An autosampler/injector commutator for flow injection analysis (FIA) was constructed with electronic components of used equipments. The apparatus is controlled by commercially available multifunctional interface (PCL711B) connected to a personal computer, and the software was written in Visual Basic language. The system was applied to water analysis and it presented satisfactory results. The lo...

We study heat trace asymptotics for Schrödinger operators using commutator expansions due to Agmon-Kannai and Melin. Closed formulas for coefficients of the scattering phase asymptotics in the short-range case are presented. In the long-range case, following Melin, we consider regularized traces and compute coefficients in their asymptotic expansions. These can be thought of as heat invariants ...

When filtering through a wall with constant averaging radius, in addition to the subfilter scale stresses, a non-closed commutator term arises. We consider a proposal of Das and Moser to close the commutator error term by embedding it in an optimization probem. This report shows that this optimization based closure, with a small modification, leads to a well posed problem showing existence of a...

We revisit the question of microcausality violations in quantum field theory on noncommutative spacetime, taking O(x) =: φ⋆φ : (x) as a sample observable. Using methods of the theory of distributions, we precisely describe the support properties of the commutator [O(x),O(y)] and prove that, in the case of spacespace noncommutativity, it does not vanish at spacelike separation in the noncommutin...

1. All operators will be supposed bounded, linear (everywhere defined) over a Hilbert space. By the commutator, C, of two operators A and B will be meant the operator (1) C = AB BA. A conjecture of Kaplansky, cited in [4], that if A commutes with C, so that (2) AC = CA, then (3) sp(C) = 0 only (sp = spectrum), was recently proved by Kleinecke [6] and Shirokov [9]. Earlier proofs of (3) under th...

We construct a sequence of groups Gn, and explicit sets of generators Yn ⊂ Gn, such that all generating sets have bounded size, and the associated Cayley graphs are all expanders. The group G1 is the alternating group Ad, the set of even permutations on the elements {1, 2, . . . , d}. The group Gn is the group of all even symmetries of the rooted d-regular tree of depth n. Our results hold for ...

this paper is a chronological survey, with no proofs, of a direction in categorical algebra, which is based on categorical galois theory and involves generalized central extensions, commutators, and internal groupoids in barr exact mal’tsev and more general categories. galois theory proposes a notion of central extension, and motivates the study of internal groupoids, which is then used as an a...