We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N -soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space noncommutativity. The noncommutativity of coordinates is shown to obstruct the general construction of a τ function for these solitons. We investigate the two-soliton s...

In this article we extend evaluations of the Kauffman bracket on regular isotopy classes of knots and links to a variety of functors defined on the category FrT ang of framed tangles. We show that many such functors exist, and that they correspond up to equivalence to bilinear forms on free, finitely-generated modules over commutative rings R.

We show that the Kauffman bracket skein modules of certain manifolds obtained from integral surgery on a (2, 2b) torus link are finitely generated, and list the generators for select examples.

This in vitro study investigated the influence of using different combinations of bracket, adhesive, and light-curing source on the tensile bond strength to porcelain and on failure patterns at debonding. Tensile tests were performed using: one ceramic bracket versus one metal bracket, two orthodontic composites; type bisphenol A-glycidyldimethacrylate and urethane dimethacrylate (UDMA), and fo...

o bjectives: the purpose of this study was to evaluate the effect of salivary ph on the shear bond strength (sbs) of orthodontic brackets to tooth surface. materials and methods: eighty intact premolars were randomly divided into four groups of 20.  after bonding a bracket on each tooth, the groups one to four were stored in artificial saliva at a ph of 3.8, 4.8, 5.8, and 6.8, respectively for ...

The purpose of this study was to analyze the relationship between the critical contact angle and the torque angle in an orthodontic bracket and archwire assembly in 3 dimensions. Three-dimensional mathematical models were created with geometric bracket-archwire parameters that included 2 slot sizes, 3 bracket widths, and 3 to 4 wire sizes. From this, 3-dimensional mathematical equations (3DMEs)...

We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac’s procedure for incorporating constraints. First, the Poisson bracket of moments of the u...

We extend the Nambu bracket to 1-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplica-tive Nambu structure. A Lie group G with a Nambu structure P is a Nambu-Lie group iff P = 0 at the unit, and the Nambu bracket of left (right) invariant forms is left (right) invariant. We define a corresponding notion of a Nambu-Lie algebra. We give several...

The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are ...