Schneps [J. Lie Theory 16 (2006), 19–37] has found surprising links between Ihara brackets and even period polynomials. These results can be recovered and generalized by considering some identities relating Ihara brackets and classical Lie brackets. The period polynomials generated by this method are found to be essentially the Kohnen-Zagier polynomials.

Schneps [J. Lie Theory 16 (2006), 19–37] has found surprising links between Ihara brackets and even period polynomials. These results can be recovered and generalized by considering some identities relating Ihara brackets and classical Lie brackets. The period polynomials generated by this method are found to be essentially the Kohnen-Zagier polynomials.

Introduction: A large number of orthodontists prefer to rebond the failed bonded brackets or use recycled brackets in some instances. The aim of this study was to compare the shear bond strength of rebonding with using recycled brackets on enamel surface. Methods: Bonding of brackets on the surface of extracted first bicuspids was tested in five different groups to compare their shear bond stre...

The aim of this study was to evaluate the frictional force between orthodontic brackets and archwires. The differences in magnitude of the frictional forces generated by ceramic brackets, ceramic brackets with metal reinforced slot, and stainless steel brackets in combination with stainless steel, nickel-titanium, and beta-titanium orthodontic archwires were investigated. Brackets and wire were...

The aim of this study was to assess the effect of bracket type on the labiopalatal forces and moments generated in the sagittal plane. Incognito™ lingual brackets (3M Unitek), STb™ lingual brackets (Light Lingual System; ORMCO), and conventional 0.018 inch slot brackets (Gemini; 3M Unitek) were bonded on three identical maxillary acrylic resin models, with a palatally displaced right lateral in...

Tensile bond strength and failure location were evaluated in vitro for three types of direct bonding cements (unfilled, low filled, and highly filled) with three types of brackets (polycarbonate, stainless steel, and ceramic) using natural teeth and plastic as substrates. An unfilled acrylic cement gave the highest values of bond strength for both the plastic and ceramic brackets, whereas a hig...

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent ∆ operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra, and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie br...