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A classical theorem of braid theory, dating back to Artin's work, says that two closed braids in a solid torus are ambient isotopic if and only if they represent the same conjugacy class of the braid group. This theorem can be reformulated in the framework of link theory without referring to the group structure. A link in a surface bundle over the circle is transversal whenever it covers the circle. In this terminology, Artin's theorem states that in a solid torus trivially fibered over the circle transversal links are ambient isotopic if and only if they are isotopic in the class of transversal links. We generalize this result by proving that (in the piecewise linear category) transversal links in an arbitrary compact orientable -manifold fibered over the circle with a compact fiber are ambient isotopic if and only if they are isotopic in the class of transversal links. [ABSTRACT FROM AUTHOR]

Let n, m ∈ ℕ, n ≥ 3 and n ≥ m ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid UVSBmn and group UVSGmn. These properties emerged by studying the analogous properties of the unrestricted virtual singular pseudosymmetric braid of braid monoid and group. These mathematical objects are submonoids and subgroups of the virtual singular braid group VSGn. For many of these quotients, we have obtained reduced presentations. [ABSTRACT FROM AUTHOR]

This study investigated the effects of different braid materials (polyethylene terephthalate, nylon 6, and their hybrid), weaving frequencies of the braids (7, 9, 11, 13 Hz), and concentrations of polyether sulfone solution (15% and 18 wt%) on braid angles, braid thickness, and bursting resistance. The results showed that for all types of single and hybrid braids, the braid angle decreases with increasing spinning frequency. When spinning frequency was increased from 7 to 13 Hz, the average wall thickness of polyethylene terephthalate, nylon 6, and the hybrid braids increased by approximately 50%, 65%, and 60%, respectively. The bursting pressure results were obtained in the range of 9.3 to 20.2 bars. The Fourier transform infrared spectroscopy results revealed no chemical bond between the braids and the polyether sulfone layer. Optical and electron microscope analyses revealed formation of uniform thickness of the polyether sulfone layers on the surface of the braids, as well as the penetration of polyether sulfone into the gaps between the filaments. The analyses also showed macroscopic adhesion of polyether sulfone to the braids and provided information on the amount and size of the pores in the polymer layers. The results showed that the selection of appropriate weaving frequency, braid materials, and polyether sulfone layer concentration are important as controllable parameters for producing polymeric hollow fiber composites with excellent burst pressure resistance. [ABSTRACT FROM AUTHOR]