In a companion paper, we introduced a notion of multi-Dirac structures, a graded version of Dirac structures, and we discussed their relevance for classical field theories. In the current paper we focus on the geometry of multi-Dirac structures. After recalling the basic definitions, we introduce a gradedmultiplication and amulti-Courant bracket on the space of sections of a multi-Dirac structu...

The conservation of the Hamiltonian structures in Whitham's method of averaging. Abstract The work is devoted to the proof of the conservation of local field-theoretical Hamiltonian structures in Whitham's method of averaging. The consideration is based on the procedure of averaging of local Pois-son bracket, proposed by B.A.Dubrovin and S.P.Novikov. Using the Dirac procedure of restriction of ...

We construct a differential and a Lie bracket on the space {Hom(A, A)},k,l≥0 for any associative algebra A. The restriction of this bracket to the space {Hom(A, A)},k≥0 is exactly the Gerstenhaber bracket. We discuss some formality conjecture related with this construction. We also discuss some applications to deformation theory. 0. There exists a well-known way (due to Jim Stasheff) to define ...

We first extend the Peierls algebra of gauge invariant functions from the space S of classical solutions to the space H of histories used in path integration and some studies of decoherence. We then show that it may be generalized in a number of ways to act on gauge dependent functions on H. These generalizations (referred to as class I) depend on the choice of an “invariance breaking term,” wh...

The aim of this in vitro study was to investigate both shear bond strength (SBS) by shear testing of indirectly bonded brackets, and the accuracy of a new transfer method, the Aptus bonding device (ABD). For comparison, the SBS of directly bonded brackets in two experimental arrangements was also measured. The precision of the positioning of the indirect bracket transfer was assessed by photogr...

A paradigm for describing dynamical systems that have both Hamiltonian and dissipative parts is presented. Features of generalized Hamiltonian systems and metric systems are combined to produce what are called metriplectic systems. The phase space for metriplectic systems is equipped with a bracket operator that has an antisymmetric Poisson bracket part and a symmetric dissipative part. Flows a...

In this paper we show that the moduli space of twisted polygons in G/P , where G is semisimple and P parabolic, and where g has two coordinated gradations, has a natural Poisson bracket that is directly linked to G-invariant evolutions of polygons. This structure is obtained by reducing the quotient twisted bracket on GN defined in [23] to the moduli space GN/PN . We prove that any Hamiltonian ...

introduction: the aim of this study was to assess the galvanic behavior of different bracket and archwire combinations that are commonly used in orthodontic treatments. methods: three types of orthodontic archwires with a diameter of 0.016×0.022 inch and 80 standard edgewise maxillary central incisor brackets were selected. three groups consisted of different wire-bracket couples and one group ...