For any n ≥ 2 we define an isotopy invariant, 〈Γ〉n , for a certain set of n-valent ribbon graphs Γ in R, including all framed oriented links. We show that our bracket coincides with the Kauffman bracket for n = 2 and with the Kuperberg’s bracket for n = 3. Furthermore, we prove that for any n, our bracket of a link L is equal, up to normalization, to the SUn quantum invariant of L. We show a nu...

INTRODUCTION The aim of this study was to evaluate the differences in quality of life impacts between subjects treated with Invisalign aligners (Align Technology, Santa Clara, Calif) and those with fixed appliances during the first week of orthodontic treatment. METHODS A prospective, longitudinal cohort study involving 60 adult orthodontic patients (33 with Invisalign aligners, 27 with fixed...

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 a...

  Objective: Increased enamel surface roughness following orthodontic bracket debonding leads to increased plaque accumulation and enamel decalcification. Therefore, different methods are employed to achieve smoother enamel surfaces after bracket debonding. This study compared enamel surface roughness following orthodontic bracket debonding and composite resin removal using white stone and tung...

Orthodontic lingual root movement (torque) is an important aspect of treatment biomechanics and is typically achieved by torsion of a rectangular wire within the orthodontic bracket slot which introduces a force couple. The magnitude of the force moment achieved by wire torsion may be influenced by deformation of the orthodontic bracket. A device utilizing an optical image correlation technique...

An in vitro study was conducted to evaluate the accuracy of bracket placement for direct and indirect bonding techniques. Nineteen sets of duplicated Class II malocclusion models were divided into three groups: (1) one set for ideal bracket placement, (2) nine sets for direct bonding on mannequins, and (3) nine sets for indirect bonding. Both direct and indirect bonding were performed on all te...

We will give a generalized framework of derived bracket construction. It will be shown that a deformation differential provides a strong homotopy (sh) Leibniz algebra structure by derived bracket construction. A relationship between the three concepts, homotopy algebra theory, deformation theory and derived bracket construction, will be discussed. We will prove that the derived bracket construc...