BACKGROUND AND OBJECTIVES The purpose of this in vitro study was to evaluate the bond strength of the laser-etched base bracket, site of bond failure, and evaluate for enamel remnants on the bracket base after debonding, when compared to foil mesh base bracket. MATERIALS AND METHODS Sixty noncarious, human premolar extracted for the orthodontic treatment were used for this study. The teeth we...

We show that the skew-symmetrized product on every Leibniz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative multiplication on E which, when E is a Lie algebra, is derived from the integrated adjoint representation. We apply this construction to realize the bracket operations on the sections of Courant algebroid...

Orthodontic torque expression is the result of axial rotation of rectangular archwires within a rectangular bracket slot. This study investigates the effect of bracket material on torque expression. Torque exerted by a rotating archwire on each bracket will be measured as well as the relative deformation of each bracket slot. A total of 60 tests were performed where archwires were rotated withi...

Based on the presentation of Kauffman bracket skein algebra thickened torus given by third author in previous work [4], Frohman and Gelca established a complete description multiplicative operation leading to famous product-to-sum formula. In this paper, we study structure four-holed sphere. We present an algorithm compute product any two elements algebra, give explicit formula for some familie...

After decades of machine literacy research, image recognition, position discovery, bracket, product, audio natural language processing, and others remain unsolved. Deep literacy's most fundamental study direction is categorization. concurrently, intelligent computer picture technology allows progressive enhancement in response to transnational links the development progress multiple disciplines...

Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In this paper, we construct two non-trivial virtual knot diagrams, K D and K m , t...

We introduce the notion of a Poisson symmetric space and the associated infinitesimal object, a symmetric Lie bialgebra. They generalize corresponding notions for Lie groups due to V. G. Drinfel’d. We use them to give some geometric insight to certain Poisson brackets that have appeared before in the literature. 1 Motivation Let us recall briefly the best-known examples of Poisson manifolds. Th...

Various aspects of the Nahm equations in 3 and 7 dimensions are investigated. The residues of the variables at simple poles in the 7dimensional case form an algebra. A large class of matrix representations of this algebra is constructed. The large N limit of these equations is taken by replacing the commutators by Moyal Brackets, and a set of non trivial solutions in a generalised form of Wigne...