It is the intent of this manuscript to provide a general treatment of braiding: past, present, and future. A history and evolution of braiding, braiding machinery, and related engineering developments is provided with emphasis on the design, manufacture, and analysis of braided fabrics and composites. Some recent developments are briefly described, including: 1. a composite braider with axial y...

We complete the realisation by braided subfactors, announced by Ocneanu, of all SU(3)-modular invariant partition functions previously classified by Gannon.

Joyal and Street note in their paper on braided monoidal categories [9] that the 2–category V –Cat of categories enriched over a braided monoidal category V is not itself braided in any way that is based upon the braiding of V . The exception that they mention is the case in which V is symmetric, which leads to V –Cat being symmetric as well. The symmetry in V –Cat is based upon the symmetry of...

In this note, we generalize a result of [4] (see also [9]) and set the isomorphism between the iterated cross product algebra H∨#(H#A) and braided analog of an A-valued matrix algebra H∨⊗A⊗H for a Hopf algebra H in the braided category C and for an H-module algebra A. As a preliminary step, we prove the equivalence between categories of modules over both algebras and category whose objects are ...

The center Z(C) of an autonomous category C is monadic over C (if certain coends exist in C). The notion of Hopf monad naturally arises if one tries to reconstruct the structure of Z(C) in terms of its monad Z: we show that Z is a quasitriangular Hopf monad on C and Z(C) is isomorphic to the braided category ZC of Z-modules. More generally, let T be a Hopf monad on an autonomous category C. We ...

in present study effects of riparian vegetation on morphometric and morphological changes have been investigated in a part of talar river during 58 years. so land use maps produced for 1955 and 2013 by aerial photos. results show during study time riparian vegetation changed extremely and approximately 96% of riparian vegetation removed during 58 years. in additionally, results showed during st...

The anterior cruciate ligament (ACL) is the most commonly injured intra-articular ligament of the knee. The insufficient vascularization of this tissue prevents it from healing completely after extreme tearing or rupture, creating a need for ACL grafts for reconstruction. The limitations of existing grafts have motivated the investigation of tissue-engineered ACL grafts. A successful tissue-eng...

BACKGROUND AND PURPOSE Braided self-expandable stents and flow diverters of uniform construction may develop zones of heterogeneous porosity in vivo. Unwanted stenoses may also occur at the extremities of the device. We studied these phenomena in dedicated benchtop experiments. MATERIALS AND METHODS Five braided devices of decreasing porosity were studied. To simulate discrepancies in diamete...

BACKGROUND Twisting and braiding of four-strand hamstring tendon grafts used for anterior cruciate ligament reconstruction has been proposed, but not proven, as a method of improving tensile properties. HYPOTHESIS Twisting and braiding four-strand human hamstring tendon grafts will have no significant effect on initial graft strength or stiffness. STUDY DESIGN Paired in vitro biomechanical ...

We apply the modern Batalin-Vilkovisky quantization techniques of Costello and Gwilliam to noncommutative field theories in finite-dimensional case fuzzy spaces. further develop a generalization this framework that are equivariant under triangular Hopf algebra symmetry, which particular leads quantizations analogs proposed recently through notion `braided $L_\infty$-algebras'. The illustrated b...