A common debate about the definition of composite materials among composite engineers and materials scientists continues to this day. More recently, biomedical engineers have used the term composite prolifically for newly developed biomaterials, and it might be argued that not every usage of the term composite for a biomaterial would satisfy the traditional composite engineer, who is used to th...

We associate to any braided 2-groupoid with vanishing intermediate homotopy group a principal bundle (or torsor) endowed with a so-called Σ-structure, and show that this is the natural generalization to the 2-category context of the familiar quadratic invariant describing a braided groupoid. The corresponding structures for higher braided n-groupoids are also examined. This leads to the concept...

We associate to any braided 2-groupoid with vanishing intermediate homotopy group a principal bundle (or torsor) endowed with a so-called Σ-structure, and show that this is the natural generalization to the 2-category context of the familiar quadratic invariant describing a braided groupoid. The corresponding structures for higher braided n-groupoids are also examined. This leads to the concept...

When a quantum hyperboloid is realized, as a three parameter algebra Ah,q, in the usual manner, the following problem arises: what is a ”representation theory” of this algebra? We construct the series of all spin representations of Ah,q, and we discuss a braided version of the orbit method, i.e. a correspondence between orbits in g∗ and g-modules. A braided trace and a braided involution are di...

Mechanical properties of hybrid braided composite rebars are evaluated and compared to theoretical predictions which account for specific processing parameters including yarn size, braiding machine setup, and fiber type. Using a combination of high modulus carbon (Thornel P-55S) and aramid (Kevlar 49) fibers bars have been produced of up to 10 mm diameter with a Young's modulus of 200 GPa, a bi...

STATEMENT OF PROBLEM Bioglasses are a series of biocompatible dental materials, which are considered as light conducting inserts in resin composite restorations. Consequently, their chemical stability is more essential when they are used in conjunction with resin composite. OBJECTIVES The aim of this study was to evaluate and compare the chemical stability of Bioglass with dental porcelain an...

The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal bicategory that produces a braided monoidal object from any monoidal object. Some properties and sufficient conditions for existence of the construction are exami...

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzezinski and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. We study the bosonisation of any braided group provides as a trivial principal bundle in three ways.

We construct double biproduct, bicrossproduct, double crossproduct, double bicrossproduct Lie bialgebras from braided Lie bialgebras. The relations between them are found. The main result generalizes Majid’s matched pair of Lie algebras, Drinfeld’s quantum double of Lie bialgebras, and Masuoka’s cross product Lie bialgebras. Some properties of double biproduct Lie bialgebras are given. In the a...