We show that the Chebyshev polynomials form a basic block of any positive basis of the Kauffman bracket skein algebras of surfaces.

Unusual scattering effects from tiny spherical particles may be obtained when concentric shells are designed by pairing together "complementary" double-negative, single-negative, and/or standard double-positive materials. By embedding these highly polarizable scatterers in a host medium one can achieve a bulk medium with interesting effective parameters. Some physical insights and justification...

The lubrication performance of journal bearings with different sorts of uniformly distributed micro-spherical textures are studied in this paper. Geometries and dynamic models of journal bearings with pure concave/convex textures are developed. The validity of the proposed models is verified against the oil film pressure distribution from the literature. The effects of geometry parameters (the ...

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physic...

1 2 In this study, the hydrothermal carbonation of calcium hydroxide under high CO 2-Ar pressure 3 (90 bar) and high temperature (90 °C) coupled with a complex selenocystine fragmentation 4 was carried out by using a batch system in order to synthesize an elemental selenium 5 (Se 0)/calcite composite. Under O 2-poor conditions, the composite was mainly characterized 6 by red spherical selenium ...

Let M be an oriented 3-manifold. For any commutative ring R with a specified invertible element A one can assign an R-module S2,∞(M ;R,A) called the Kauffman bracket skein module of M. This invariant of 3-manifolds was introduced by the first author in [P-1]. This paper gives insight into broad and intriguing connections between two apparently unrelated theories: the theory of skein modules of ...

We study the algebraic and geometric properties of stated skein algebras surfaces with punctured boundary. prove that algebra bigon is isomorphic to quantum group $\mathcal{O}{{q^2}}(\operatorname{SL}(2))$ thus providing a topological interpretation for its structure morphisms. also show lifts in suitable sense Reshetikhin–Turaev functor, particular, we recover dual $R$-matrix $\mathcal{O}{{q^2...

Let k be a subring of the field of rational functions in x, v, s which contains x, v, s. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) xL+ − xL− = (s − s)L0; (2) L with a positive twist = (xv)L; (3) L ⊔ O = ( v−v −1 s−s−1 )...

We report a feasible approach to the preparation of monodispersed metal-shell composite microspheres based on a combination of surface reaction and surface seeding techniques. The method was implemented for coating polystyrene (PS) spheres with silver shell having a variable thickness by controlling the amount of reagents in the reaction procedure. These composite spherical particles in dimensi...