A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/rightcovariant and bicovariant differential structures are introduced and investigated. Furthermore, antipodally covariant calculi are studied. The concept of the *-structure on a multi-braided quantum group is formulated, and in particular the structure of left-c...

Abstract This paper provides an overview of the recent definition, technologies and current trends regarding 3D fabrics. In this a definition fabrics, including spacer is given weaving, braiding, weft warp knitting tailored fiber placement are presented. Furthermore, latest developments in fabrics at Institut für Textiltechnik RWTH Aachen University presented including: large circular knitting,...

Long compact cylindrical rods, which consist of a titanium monoboride-based TiB-30 wt % Ti ceramic composite material, are synthesized during combustion of the initial components (titanium, boron) followed by high-temperature deformation. High-temperature deformation is found to affect the orientation of the hardening titanium monoboride phase in the sample volume and the phase composition of t...

In the last lecture we have learned that the category of modules over a braided Hopf algebra H is a braided monoidal category. A braided Hopf algebra is a rather sophisticated algebraic object, it is not easy to give interesting nontrivial examples. In this text we develop a theory that will lead to a concrete recipe which produces a nontrivial braided Hopf algebra D(A) (called Drinfeld’s quant...

We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that...

The q-Poincaré group of [1] is shown to have the structure of a semidirect product and coproduct B>⊳ ̃ SOq(1, 3) where B is a braided-quantum group structure on the q-Minkowski space of 4-momentum with braided-coproduct ∆p = p⊗ 1+1⊗p. Here the necessary B is not a usual kind of quantum group, but one with braid statistics. Similar braided-vectors and covectors V (R), V (R) exist for a general R...

2014 We present preliminary measurements of the electrical conductivity of a composite made of small conducting rods in an insulating matrix. It constitutes a model material for studying the effect of anisotropy on percolation as a function of particle length to diameter ratio. We can interpret our results, especially the lowering of threshold respective to isotropic systems, by means of a geom...