We define Gerstenhaber’s graded Lie bracket directly on complexes other than the bar complex, under some conditions, resulting in a practical technique for explicit computations. The Koszul complex of a Koszul algebra in particular satisfies our conditions. As examples we recover the Schouten-Nijenhuis bracket for a polynomial ring and the Gerstenhaber bracket for a group algebra of a cyclic gr...

We will give a generalized framework of derived bracket construction. The derived bracket construction provides a method of constructing homotopies. We will prove that a deformation derivation of dg Leibniz algebra (or called dg Loday algebra) induces a strong homotopy Leibniz algebra by the derived bracket method.

A knot diagram has an associated looped interlacement graph, obtained from the intersection graph of the Gauss diagram by attaching loops to the vertices that correspond to negative crossings. This construction suggests an extension of the Kauffman bracket to an invariant of looped graphs, and an extension of Reidemeister equivalence to an equivalence relation on looped graphs. The graph bracke...

OBJECTIVE To evaluate the clinical performance of APC™II Victory Series™ (3M Unitek) brackets in direct orthodontic bonding with and without the use of primer. DESIGN A single-operator, two-centre prospective, non-inferiority randomized controlled clinical trial. SETTING The Orthodontic departments at the Leeds Dental Institute and St Luke's Hospital, Bradford, UK. ETHICAL APPROVAL Ethica...

introduction: any decrease in friction between orthodontic wire and bracket can accelerate tooth movement in the sliding technique and result in better control of anchorage. the present study was carried out to decrease this friction by coating of zinc oxide nanoparticles (zno) on orthodontic wires and porcelain brackets. materials and methods: in this in vitro study, a combination of 120 0.019...

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 streng...

Let A be one of the following commutative associative algebras: the algebra of all smooth functions on the plane: A = C(R), or the algebra of polynomials A = C[p, q] over R or C. There exists a non-trivial formal associative deformation of A called the Moyal ⋆-product (or the standard ⋆-product). It is defined as an associative operation A → A[[h̄]] where h̄ is a formal variable. The explicit for...

We introduce diagrams and Reidemeister moves for links in F ×S, where F is an orientable surface. Using these diagrams we compute (in a new way) the Kauffman Bracket Skein Modules (KBSM ) for D × S and A× S, where D is a disk and A is an annulus. Moreover, we also find the KBSM for the F0,3 × S , where F0,3 denotes a disk with two holes, and thus show that the module is free.

In any 2-category C with zeros (for example the topological 2-category T op∗ of based spaces, based maps and track classes of homotopies) box bracket operations have been defined and studied by Hardie-Marcum-Oda [4]. These are secondary homotopy operations and if (as we will suppose) C admits a suspension functor Σ (see [3]) they take values in morphism groups HC(ΣW,X), here denoted π(ΣW,X), of...

Background. Any decrease in friction between orthodontic wire and bracket can accelerate tooth movement in the sliding technique and result in better control of anchorage. This study was carried out to evaluate frictional forces by coating orthodontic wires and porcelain brackets with zinc oxide nanoparticles (ZnO). Methods . In this in vitro study, we evaluated a combination of 120 samples of ...