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;...

It is shown that the dual of the double compactified D=11 Supermembrane and a suitable compactified D=10 Super 4D-brane with nontrivial wrapping on the target space may be formulated as noncommutative gauge theories. The Poisson bracket over the world-volume is intrinsically defined in terms of the minima of the hamiltonian of the theory, which may be expressed in terms of a non degenerate 2-fo...

The change in the bisphenol A (BPA) content in a polycarbonate (PC) orthodontic bracket and its leaching characteristics were studied by immersing the bracket in water because BPA has been the matter of controversy in dentistry due to its estrogenic potential. PC brackets were placed in water at 37 degrees C and 60 degrees C and the BPA content in the bracket and the amount of BPA released into...

In this paper we introduce a new invariant of virtual knots and links that is non-trivial for many virtuals, but is trivial on classical knots and links. The invariant will initially be expressed in terms of a relative of the bracket polynomial [4], and then extracted from this polynomial in terms of its exponents, particularly for the case of knots. The analog of the bracket polynomial will be...

JCO/DECEMBER 2005 T lingual technique is considered to be one of the most difficult, requiring extended treatment times and often achieving less-than-satisfactory results. Firstand third-order tooth movements are complicated by the variable lingual tooth anatomy.1 Torque control is also more problematic; with the reduced interbracket distance, even small variations in bracket height can have a ...