After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear time-varying systems, the problem is formulated for first-order systems. Finally, explicit necessary and sufficient conditions for the commutativity of first-or...

A ring satisfying x = x is necessarily commutative. We consider a variety of weaker forms of this condition and show that many but not all of them imply commutativity. We also present a variety of elementary proofs of the fact that x = x implies commutativity.

We obtain a criterion on the commutativity of polynomials in the enveloping algebra of a Lie algebra in terms of an involution condition with respect to the Berezin bracket. As an application, it is shown that the commutativity requirement of missing label operators for reduction chains in the missing label problem can be solved analytically. PACS numbers: 02.20Sv, 21.60Fw

This research paper aims to investigate if oxidative stress biomarkers increase after a painful procedure in term newborns and if nonpharmacological approaches, or sex, influence pain degree, and the subsequent OS. 83 healthy term newborns were enrolled to receive 10% oral glucose or sensorial saturation (SS) for analgesia during heel prick (HP). The ABC scale was used to score the pain. Advanc...

We examine magnetic and electric near horizon regions of maximally supersymmetric D– brane and NS5–brane bound states and find transformations between near horizon regions with worldvolume dual magnetic and electric fluxes. These point to dual formulations of NCYM, NCOS and ODp theories in the limit of weak coupling and large spatial or temporal non-commutativity length scale in terms of weakly...

In this paper we study the structure and the commutativity of a ring R, in which for each x,y ? R, there exist two integers depending on x,y such that [x,y]k equals x n or y n.

We need to perform arithmetic in Fp(z)12 to use Ate pairing on a Barreto-Naehrig (BN) curve, where p(z) is a prime given by p(z) = 36z + 36z + 24z + 6z+ 1 with an integer z. In many implementations of Ate pairing, Fp(z)12 has been regarded as the 6-th extension of Fp(z)2 , and it has been constructed as Fp(z)12 = Fp(z)2 [v]/(v−ξ) for an element ξ ∈ Fp(z)2 such that v − ξ is irreducible in Fp(z)...

Abstract The notion of commutativity two normal states on a von Neumann algebra was defined some time ago by means the Pedersen–Takesaki theorem. In this note, we aim at generalising to an arbitrary number states, and obtaining results so joint commutativity. Also relations between broadcastability are investigated.

We calculate the long-range Vanderwaals force and the photoelectric cross section in a noncommutative set up. While we argue that non-commutativity effects could not be discerned for the Vanderwaals interactions, the result for the photoelectric effect shows deviation from the usual commutative one, which in principle can be used to put bounds on the space-space non-commutativity parameter.

We provide here a simple, yet very general framework that allows us to explain several constraint propagation algorithms in a systematic way. In particular, using the notions commutativity and semi-commutativity, we show how the well-known AC-3, PC-2, DAC and DPC algorithms are instances of a single generic algorithm. The work reported here extends and simplifies that of Apt [1].