Abstract We compare two associative algebras which encode the “quantum topology” of Legendrian curves in contact threefolds product type $$S\times {\mathbb {R}}$$ S × R . The first is skein algebra graded links and second Hall Fukaya category S construc...

Silica exists in Rice husk, an agriculture waste, as a naturally occurring phase. In first step, acidic pre-treatment and calcination of the rice husk were performed to obtain nano-silica, in which various sizes of the nano-silica, totally with sizes under 80 nm, were achieved. Second, to reduce nano-silica to elemental Si and subsequently formation of the composite, Mg used as the reducing age...

We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the construction of quantum invariants and modular categories. In particular, an elementary proof of the Wenzl formula for quantum dimensions is given. This proof does not use the representation theory of quantum groups and the...

Nanosized spherical LiFePO4/C composite was synthesized from nanosized spherical FePO4 ·2H2O, Li2C2O4, aluminum oxide, titanium oxide, oxalic acid, and sucrose by binary sintering process. The phases and morphologies of LiFePO4/C were characterized using SEM, TEM, CV, EIS, EDS, and EDX as well as charging and discharging measurements. The results showed that the as-prepared LiFePO4/C composite ...

For a surface F , the Kauffman bracket skein module of F × [0, 1], denoted K(F ), admits a natural multiplication which makes it an algebra. When specialized at a complex number t, nonzero and not a root of unity, we have Kt(F ), a vector space over C. In this paper, we will use the product-to-sum formula of Frohman and Gelca to show that the vector space Kt(T ) has five distinct traces. One tr...