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 ...

Abstract Additive manufacturing (AM) is projected to require 60,000 jobs in the UK by 2025, but there are a series of barriers industrial application. One most problematic non-comprehensive knowledge design for AM (DfAM). This study aims test effect two undergraduate DfAM teaching approaches. A visual and audial approach (design lecture) kinaesthetic, problem-based learning (PBL) (manufacturing...

We introduce the concept of a relative Tutte polynomial. We show that the relative Tutte polynomial can be computed in a way similar to the classical spanning tree expansion used by Tutte in his original paper on this subject. We then apply the relative Tutte polynomial to virtual knot theory. More specifically, we show that the Kauffman bracket polynomial (hence the Jones polynomial) of a virt...

We consider the Gelfand-Dickey (GD) structure defined by the Moyal ⋆-product with parameter κ, which not only defines the bi-Hamiltonian structure for the generalized Moyal KdV hierarchy but also provides a W (κ) n algebra containing the Virasoro algebra as a subalgebra with central charge κ2(n3 − n)/3. The free-field realization of the W (κ) n algebra is given through the Miura transformation ...

We study dynamical effects of introducing noncommutativity on string worldsheets by using a matrix model obtained from the zero-volume limit of four-dimensional SU(N) Yang-Mills theory. Although the dimensionless noncommutativity parameter is of order 1/N , its effect is found to be non-negligible even in the large N limit due to the existence of higher Fourier modes. We find that the Poisson b...

It is well known that any three-manifold can be obtained by surgery on a framed link in S. Lickorish gave an elementary proof for the existence of the three-manifold invariants of Witten using a framed link description of the manifold and the formalisation of the bracket polynomial as the Temperley-Lieb Algebra. Kaul determined three-manifold invariants from link polynomials in SU(2) Chern-Simo...

Noncommutative differential geometry over the Moyal algebra is developed following an algebraic approach. It is then applied to investigate embedded noncommutative spaces. We explicitly construct the projective modules corresponding to the tangent bundles of the noncommutative spaces, and recover from this algebraic formulation the metric, Levi-Civita connection and related curvature introduced...

We show that if a classical knot diagram satisfies a certain combinatorial condition then it is minimal with respect to the number of classical crossings. This statement is proved by using the Kauffman bracket and the construction of atoms and knots.

The aim of the present study was to investigate slot deformation and the equivalent torque capacity of polycarbonate brackets with and without a metal slot in comparison with those of a metal bracket. For this purpose, the expansion characteristics and, in a further investigation, the labial crown torque of an upper central incisor, were measured in a simulated intra-oral clinical situation, us...