After 20 months of clinical testing and more than 600 bonded arches, brief interim conclusions can be drawn on treatment with a new lingual bracket system, one that differs fundamentally from conventional appliances in both design and manufacture. The demand for maximum individuality is met by using state-of-the-art computer-aided design/computer-aided manufacturing technology to fuse the 2 nor...

A new method to derive presentations of skein modules is developed. For the case of homotopy skein modules it will be shown how the topology of a 3-manifold is reflected in the structure of the module. The freeness problem for q-homotopy skein modules is solved, and a natural skein module related to linking numbers is computed.

We study the Bäcklund symmetry for the Moyal Korteweg-de Vries (KdV) hierarchy based on the Kuperschmidt-Wilson Theorem associated with second Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes the result of Adler for the ordinary KdV. PACS: 02.30.Ik, 11.10.Ef

Working within the Moyal algebra, we define an index for Laurent series of smooth complex matrix-valued functions of 2d real variables. For d = 1, we prove that the index of a Laurent series is equal to a multiple of the winding number of its initial term’s determinant. For d > 1, under certain conditions, we prove that the index of a Laurent series depends only upon its initial term’s behaviou...

We build a differential calculus for subalgebras of the Moyal algebra on R4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to realize the complex of forms as a tensor product of the noncommutative subalgebras with the external algebra Λ. MSC: 46L87;

2 Preliminaries 5 2.1 The ring R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The algebra A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Algebra A and (1+1)-dimensional cobordisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Kauffman bracket . . . . . . . . . . . . . . . . . . . ...

We extend the quasi-tree expansion of A. Champanerkar, I. Kofman, and N. Stoltzfus to not necessarily orientable ribbon graphs. We study the duality properties of the Bollobás-Riordan polynomial in terms of this expansion. As a corollary, we get a “connected state” expansion of the Kauffman bracket of virtual link diagrams. Our proofs use extensively the partial duality of S. Chmutov.

BACKGROUND This study aims to compare the 'Nuvola®' system with 'Fantasmino®' system, examine their material properties, and define the indications for use of the aligners. METHODS Two groups of patients were selected and were respectively treated with Nuvola® aligner and Fantasmino® system. RESULTS The goal of treatment has been achieved with the two systems. CONCLUSIONS The two types of...

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.