Aspects of noncanonical Hamiltonian field theory are reviewed. '·1any systems are Hamiltonian in the sense of possessing Poisson bracket structures, yet the equations are not in canonical form. A particular sys tem of thi s type is cons idered, namely reduced magnetohydrodynamics (RllHD) which was derived for tokamak modelling. The notion of a liePoisson bracket is reviewed; these are special P...

When X is an associative H-space, the bar spectral sequence computes the homology of the delooping, H∗(BX). If X is an n-fold loop space for n ≥ 2 this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on H∗(BX), and so it is moreover a spectral sequence of Poisson algebras. Throug...

Relying on the notion of set-valued Lie bracket introduced in an earlier paper, we extend some classical results valid for smooth vector fields to the case when the vector fields are just Lipschitz. In particular, we prove that the flows of two Lipschitz vector fields commute for small times if and only if their Lie bracket vanishes everywhere (i.e., equivalently, if their classical Lie bracket...

First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to KirchhoWs laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using ...

OBJECTIVE The aim of this study was to assess whether repetitive opening and closure of self-ligating bracket clips can cause plastic deformation of the clip. METHODS Three types of active/interactive ceramic self-ligating brackets (n = 20) were tested: In-Ovation C, Quicklear and WOW. A standardized controlled device performed 500 cycles of opening and closure movements of the bracket clip w...

The aim of this study was to compare the static and kinetic frictional forces generated by various contemporary designs of self-ligating brackets (SLBs) and different wire alloys. In total, six different brackets (four passive type SLB, one active SLB, and one conventional bracket) were investigated using stainless steel, nickel-titanium, and titanium-molybdenum alloy archwires of several sizes...

A bracket has been designed to allow a Kowa RC II fundus camera to be mounted firmly on a Haag-Streit goo slit lamp. The bracket provides a steady support which is of particular importance in fluorescein fundus angiography. The bracket consists oftwo parts. The upper part of mild steel and finished in satin chrome fits into the camera shoe and can be locked into place. The lower part is black a...

There is every indication that classical friction controls sliding mechanics below some critical contact angle, theta c. Once that angle is exceeded, however, binding and notching phenomena increasingly restrict sliding mechanics. Using geometric archwire and bracket parameters, the theta c is calculated as the boundary between classical frictional behaviour and binding-related phenomena. What ...