It has been shown that there is a Hamilton cycle in every connected Cayley graph on any group G whose commutator subgroup is cyclic of prime-power order. This note considers connected, vertex-transitive graphs X of order at least 3, such that the automorphism group of X contains a vertex-transitive subgroup G whose commutator subgroup is cyclic of prime-power order. We show that of these graphs...

For smooth domains, Liu et al. (Comm. Pure Appl. Math. 60: 1443-1487, 2007) used optimal estimates for the commutator of the Laplacian and the Leray projection operator to establish well-posedness of an extended Navier-Stokes dynamics. In their work, the pressure is not determined by incompressibility, but rather by a certain formula involving the Laplace-Leray commutator. A key estimate of Liu...

We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The right-hand side can contain partial derivatives in time, space and velocity, as in classical averaging, and f is assumed to have a certain amount of regularity in velocity. The result is that f is also regular in time and space, and this is related to a commutator identity introduced ...

This is a historical survey that includes a progress report on the 1971 seminal paper of Pearcy and Topping and 32 years of subsequent investigations by a number of researchers culminating in a completely general characterization, for arbitrary ideal pairs, of their commutator ideal in terms of arithmetic means. This characterization has applications to the study of generalized traces, linear f...

As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with noncommutative algebra, such as NCAlgebra and NCComAlgebra, one simple method of calculating the commutator in quantum mechanics is put forward and is demonstrated...

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...

Abstract. Non-uniform filtering of the Navier-Stokes equations expresses itself, next to the turbulent stresses, in additional closure terms known as commutator errors. These terms require explicit subgrid modeling if the non-uniformity of the filter is sufficiently pronounced. We derive expressions for the magnitude of the mean flux, the turbulent stress flux and the commutator error for indiv...

RKMK methods and Crouch-Grossman methods are two classes of Lie group methods. The former is using flows and commutators of a Lie algebra of vector fields as a part of the method definition. The latter uses only compositions of flows of such vector fields, but the number of flows which needs to be computed is much higher than in the RKMK methods. We present a new type of methods which avoids th...

We discuss some of the key topological features of a two (1 + 1)-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of superfield formalism. We provide the geometrical interpretation for the Lagrangian density, symmetric energy momentum tensor, topological invariants, etc., by exploiting the on-shell nilpotent BRST-and co-BRST ...