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Textile fibers, threads, yarns and fabrics are measured in a multiplicity of units.. A fiber, a single filament of natural material, such as cotton, linen or wool, or artificial material such as nylon, polyester, metal or mineral fiber, or human-made cellulosic fibre like viscose, Modal, Lyocell or other rayon fiber is measured in terms of linear mass density, the weight of a given length of ...
A braid. A braid (also referred to as a plait; / p l æ t /) is a complex structure or pattern formed by interlacing three or more strands of flexible material such as textile yarns, wire, or hair. [1] The simplest and most common version is a flat, solid, three-stranded structure.
Braids, Links, and Mapping Class Groups is a mathematical monograph on braid groups and their applications in low-dimensional topology.It was written by Joan Birman, based on lecture notes by James W. Cannon, [1] and published in 1974 by the Princeton University Press and University of Tokyo Press, as volume 82 of the book series Annals of Mathematics Studies.
1925 braiding machine in action The smallest braiding machine consists of two horn gears and three bobbins. This produces a flat, 3-strand braid. A braiding machine is a device that interlaces three or more strands of yarn or wire to create a variety of materials, including rope, reinforced hose, covered power cords, and some types of lace.
The composition of the braids σ and τ is written as στ.. The set of all braids on four strands is denoted by .The above composition of braids is indeed a group operation. . The identity element is the braid consisting of four parallel horizontal strands, and the inverse of a braid consists of that braid which "undoes" whatever the first braid did, which is obtained by flipping a diagram ...
Braided lines often have 1/3 to 1/4 the diameter of mono or fluorocarbon lines at a given test breaking strength. Therefore, it is easy to fit much longer braided line on a spool than monofilament or fluorocarbon line for the same strength. This is very important for deep sea fishing, since reels don't have to be very big to accommodate long lines.
In mathematics and theoretical physics, braid statistics is a generalization of the spin statistics of bosons and fermions based on the concept of braid group.While for fermions (bosons) the corresponding statistics is associated to a phase gain of () under the exchange of identical particles, a particle with braid statistics leads to a rational fraction of under such exchange [1] [2] or even ...
The degree of polymerization, or DP, is the number of monomeric units in a macromolecule or polymer or oligomer molecule. [1] [2] [3]For a homopolymer, there is only one type of monomeric unit and the number-average degree of polymerization is given by ¯ ¯ = ¯, where ¯ is the number-average molecular weight and is the molecular weight of the monomer unit.