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...

A Clifford algebra has three major multiplications: inner product, outer product and geometric product. Accordingly, the same Clifford algebra has three versions: Clifford vector algebra, which features on inner products and outer products of multivectors; Clifford bracket algebra, which features on pseudoscalars and inner products of vectors; Clifford geometric algebra, which features on geome...

AIM The aim of the study is to investigate the galvanic corrosion potential of metal injection molding (MIM) brackets to that of conventional brackets under similar in vitro conditions with nickel-titanium and copper nickel-titanium archwires. MATERIALS AND METHODS Twenty-five maxillary premolar MIM stainless steel brackets and 25 conventional stainless steel brackets and archwires, 0.16 inch...

We investigate a generalization of Brockett’s celebrated double bracket flow that is closely related to matrix Riccati differential equations. Using known results on the classification of transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility of the generalized double bracket flow on Grassmann manifolds are derived. This leads to sufficient Lie...

Given a simple Lie algebra g, we consider the orbits in g * which are of R-matrix type, i.e., which possess a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an algebra quantizing the latter bracket a quantum orbit of R-matrix type. We describe some orbits of this type explicitly and we construct a quantization of the whole Poisson pe...

The objective of this study was to investigate the influence of different conditioning procedures on various ceramic microstructures and bracket adhesion. Ceramic specimens (feldspathic, leucite, leucite-free, and fluorapatite) were mechanically conditioned (n = 20 per ceramic type) with conventional hydrofluoric acid (5 per cent HF; 60/30 seconds), buffered hydrofluoric acid (9.6 per cent BHF;...