Search results for "bracket"
showing 10 items of 99 documents
Practice of lingual orthodontics and practitioners’ opinion and experience with lingual braces in the United States
2020
Background A survey was done on practicing Orthodontists in the United States on their experience with lingual orthodontics. The objectives of this survey study were to assess 1) the satisfaction level with cases treated with lingual orthodontics, 2) factors that influence clinicians' decision to utilize or not utilize lingual braces in their current practices, and 3) intention of using lingual braces in their future practices, if not used currently, in the U.S. Material and methods A survey questionnaire was electronically distributed to 2,200 active U.S. members of the American Association of Orthodontists (AAO). Results 85 orthodontists completed the survey. About 25% of respondents prac…
The Poisson Bracket Structure of the SL(2, R)/U(1) Gauged WZNW Model with Periodic Boundary Conditions
2000
The gauged SL(2, R)/U(1) Wess-Zumino-Novikov-Witten (WZNW) model is classically an integrable conformal field theory. A second-order differential equation of the Gelfand-Dikii type defines the Poisson bracket structure of the theory. For periodic boundary conditions zero modes imply non-local Poisson brackets which, nevertheless, can be represented by canonical free fields.
An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics
2013
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an …
Classical Chern–Simons Mechanics
2001
We are interested in a completely integrable Hamiltonian system \((\mathscr{M}_{2N},\omega,H).\) Local coordinates on the 2N-dimensional phase space \(\mathscr{M}_{2N}\) are denoted by η a = (p, q), a = 1, 2, … 2N and the symplectic 2-form ω is given by
Classical and Quantum Nonultralocal Systems on the Lattice
1997
We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.
Geometric Aspects of Mechanics
2010
In many respects, mechanics carries geometrical structures. This could be felt very clearly at various places in the first four chapters. The most important examples are the structures of the space–time continua that support the dynamics of nonrelativistic and relativistic mechanics, respectively. The formulation of Lagrangian mechanics over the space of generalized coordinates and their time derivatives, as well as of Hamilton–Jacobi canonical mechanics over the phase space, reveals strong geometrical features of these manifolds.
On the Leibniz bracket, the Schouten bracket and the Laplacian
2003
International audience; The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them is obtained. Under some natural conditions, the Leibniz bracket gives rise to a (graded) Lie algebra structure. In particular, those algebras generated by the Leibniz bracket of the divergence and the Laplacian operators on the exterior algebra are considered, and the expression of the Laplacian for the product of two functions is generalized for arbitrary exterior forms.
Closedness of Star Products and Cohomologies
1994
We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called “closed star products” and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.
Remarks on quantum groups
1991
We give a Poisson-bracket realization of SL q (2) in the phase space ℝ2. We then discuss the physical meaning of such a realization in terms of a modified (regularized) toy model, the nonregularized version of which is due to Klauder. Some general remarks and suggestions are also presented in this Letter.
Shear bond strength of ceramic bracket bonded to different surface-treated ceramic materials
2018
Background This study evaluated the effect of ceramic surface treatments on bond strength of ceramic brackets to machine-able ceramics and ceramic veneering metal. Material and Methods Machined ceramic specimens (10x10x1.5 mm) were prepared from Empress® CAD (EP), and e.max® CAD (EM). Ceramic veneering metal specimens (PF) were fabricated from sintered d.Sign® porcelain (1.27 mm thickness) over d.Sign®10 metal (0.23 mm thickness). Each ceramic was divided into 3-groups and treated surface by Er-YAG laser (LE) or etching with 9.6% HF acid for 5 seconds (A5) or 15 seconds (A15). Resin adhesive (Transbond™-XT) was used for attaching ceramic brackets for each group (n=15) and cured with LED (Bl…