We obtain an R-matrix or matrix representation of the Artin braid group acting in a canonical way on the vector space of every (super)-Lie algebra or braided-Lie algebra. The same result applies for every (super)-Hopf algebra or braided-Hopf algebra. We recover some known representations such as those associated to racks. We also obtain new representations such as a non-trivial one on the ring ...

In order to effectively differentiate all kinds of defects inside the composites, this paper carries out testing on the internal defects of three-dimensional (3d) braided composites by use of acoustic emission nondestructive detecting technology. It puts forward the processing method for acoustic emission signals for the internal defects of three-dimensional braided composites based on wavelet ...

Braiding is a versatile and cost-effective approach to generating various composite structures for mechanical, sports, biomedical engineering applications, which are different from each other. For example, stent braided structure blood penetration in it essential as much the right function. Predicting tensile responses prerequisite success of implementation structures, usually performed via des...

Abstract Conventional carbon fibre laminates are known to be moderately electrically conductive in-plane, but have a poor through-thickness conductivity. This poses problem for functionality aspects that of increasing importance industry, such as sensing, current collection, inductive/resistive heating, electromagnetic interference (EMI) shielding, etc. restriction is course more pronounced non...

Braided composites have seen substantial industrial uptake for structural applications in the past decade. The dependence of their properties on braid angle provides opportunities lightweighting through structure-specific optimisation. This paper presents an integrated approach, combining finite element (FE) simulations and a genetic algorithm (GA) to optimise braided beam structures spaceframe...

On November 5, 1993, the City of Calgary completed the construction of the first smart prestressed concrete highway bridge built in Canada. A total of six pretensioned girders of a continuous two span skew highway bridge were prestressed using carbon fibre composite cables (CrCC) developed by Tokyo Rope, and Leadline rods produced by Mitsubishi Kasei, Japan. This paper describes the constructio...

We interpret a recent formula for counting orbits of GL(d, Fq) in terms of counting fixed points as addition in the affine braided line. The theory of such braided groups (or Hopf algebras in braided categories) allows us to obtain the inverse relationship, which turns out to be the same formula but with q and q interchanged (a perfect duality between counting orbits and counting fixed points)....

The main aim of this paper is to investigate the structure of primitively generated connected braided bialgebras A with respect to the braided vector space P consisting of their primitive elements. When the Nichols algebra of P is obtained dividing out the tensor algebra T (P ) by the two-sided ideal generated by its primitive elements of degree at least two, we show that A can be recovered as ...