In this paper we consider the optimal structure of double bracket flows and generalisations of these flows to more complex gradient flows. We discuss different notions of optimality and the relationship of the flows to the structure of convex polytopes.

In a Hamiltonian system with first class constraints observables can be defined as elements of a quotient Poisson bracket algebra. In the gauge fixing approach observables form a quotient Dirac bracket algebra. We show that these two algebras are isomorphic. A new realization of the observable algebras through the original Poisson bracket is found.Generators, brackets and pointwise products of ...

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney–Hasegawa–Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced m...

We study the classical current algebra for principal chiral model defined on two dimensional world-sheet with general metric. We develop the Hamiltonian formalism and determine the form of the Poisson brackets between currents. Then we determine the Poisson bracket for Lax connection and we show that this Possion bracket does not depend on the world-sheet metric. We also study the Nambu-Gotto f...

BACKGROUND Technological advances in wire selection and bracket design have led to improved treatment efficiency and allowed longer time intervals between appliance adjustments. The wires remain in the mouth for a longer duration and are subjected to electrochemical reactions, mechanical forces of mastication and generalized wear. These cause different types of corrosion. This study was done to...

In his celebrated proof of Szemerédi’s theorem that a set of integers of positive density contains arbitrarily long arithmetic progressions, W. T. Gowers introduced a certain sequence of norms ‖ · ‖U 2[N ] ≤ ‖ · ‖U 3[N ] ≤ . . . on the space of complex-valued functions on the set [N ]. An important question regarding these norms concerns for which functions they are ‘large’ in a certain sense. ...

A hierarchy of commutative Poisson subalgebras for the Sklyanin bracket is proposed. Each of the subalgebras provides a complete set of integrals in involution with respect to the Sklyanin bracket. Using different representations of the bracket, we find some integrable models and a separation of variables for them. The models obtained are deformations of known integrable systems like the Goryac...

BACKGROUND Torque of the maxillary incisors is crucial to occlusal relationship and esthetics and can be influenced by many factors. The aim of this study was to assess the relative influence of the material of the orthodontic appliance (adhesive, bracket, ligature, and wire) on tooth displacements and developed stresses/strains after torque application. METHODS A three-dimensional upper righ...

Lingual orthodontics has been gaining space around the world due to its particularity to offer a discreet treatment option, “invisible”, in “secret” for the correction of malocclusion, combining biomechanical efficiency and enhancement of the smile during treatment. As the brackets are on the lingual surface, the point of force application is closer to the center of resistance, maximizing the p...

UNLABELLED Aware of the diffusion capacity of bleaching in the dental tissues, many orthodontists are subjecting their patients to dental bleaching during orthodontic treatment for esthetic purposes or to anticipate the exchange of esthetic restorations after the orthodontic treatment. For this purpose specific products have been developed in pre-loaded whitening trays designed to fit over and ...