We introduce an algebraic theory of integration on quantum planes and other braided spaces. In the one dimensional case we obtain a novel picture of the Jackson q-integral as indefinite integration on the braided group of functions in one variable x. Here x is treated with braid statistics q rather than the usual bosonic or Grassmann ones. We show that the definite integral ∫ x∞ −x∞ can also be...

Braided wire stents demonstrate distinct characteristics compared to welded ones. In this study, both braided and welded wire stents with the same nominal dimensions were crimped inside a sheath and then deployed into a stenosed artery using finite element analysis. The braided wire stent was generated by overlapping wires to form crisscross shape. A welded wire stent was created by welding the...

Braided tensor products have been introduced by the author as a systematic way of making two quantum-group-covariant systems interact in a covariant way, and used in the theory of braided groups. Here we study infinite braided tensor products of the quantum plane (or other constant Zamolodchikov algebra). It turns out that such a structure precisely describes the exchange algebra in 2D quantum ...

A braided n-path is a set of « paths ct(t) in R 3 (i = 1 , . . . , n) satisfying (1) c,(0 = (*,(>), MO, 0> ' i < * < r2, c ^ ) = P„ C/(r2) e { & , . . ,Ô„}(2) The paths do not intersect. Two braided «-paths are regarded as equivalent if and only if it is possible to deform the one configuration into the other respecting conditions (1) and (2) throughout the deformation; note that one does permi...

This paper is motivated by the quest of a non-group irreducible finite index depth 2 maximal subfactor. We compute generic fusion rules Grothendieck ring Rep(PSL(2,q)), q prime-power, applying Verlinde-like formula on character table. then prove that this family rings R_q interpolates to all integers q>=2, providing (when not prime-power) first example infinite non group-like simple integral ri...

Braided subfactors of von Neumann algebras provide a framework for studying two dimensional conformal field theories and their modular invariants. We review this in the context of SU(3) conformal field theories through corresponding SU(3) braided subfactors and various subfactor invariants including spectral measures for the nimrep graphs, A2-planar algebras and almost Calabi-Yau algebras.

We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.

This paper describes a new measuring algorithm for estimating the exterior average braided angle of a three-dimensional (3-D) braided composite material preform] based on image texture. In this project, an advanced filtered algorithm for an image of a 3-D braided composite material preform is developed on the basis of mathematical morphology. Median filter algorithms for mathematical morphology...

The complex eikonal equation in the three space dimensions is considered. We show that apart from the recently found torus knots this equation can also generate other topological configurations with a non-trivial value of the π2(S 2) index: braided open strings as well as hedgehogs. In particular, cylindric strings i.e. string solutions located on a cylinder with a constant radius are found. Mo...