By M. Andreis

Content material: Drag relief phenomenon with unique emphasis on homogeneous polymer suggestions / W.-M. Kulicke, M. Kötter, and H. Gräger -- software of NMR to crosslinked polymer platforms / M. Andreis and J.L. Koenig

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9, where a is the polynomial variable. Terms in brackets are referred to as a winding and denoted as (m, n), where m and n are the number of intersections of the windings with a torus meridian and longitude, respectively. 8 Minimal unit cells of woven fabrics: (a) plain weave; (b) 1/2 twill; (c) 2/2 twill; (d) 2/2 hopsack; (e) 5/3 sateen. 9 Minimal unit cells of knitted fabrics: (a) single jersey; (b) 1 × 1 rib; (c) purl; (d) tricot with opened loops; (e) tricot with closed loops. 8 Polynomial invariants of twisted yarns Twist direction Z/S No of strands Polynomial Z 2 ∑ 2k )i a 6k + 2 + 4(( ) + a 2k t 2 i =1 Z 3 Z 4 6k 2( 6k )t a 6k t 3 2k 2∑ ( 1)i a12k 4k 2 4( 4( + ∑ ( 1)i 1) i =1 S 2 2k ∑( )i +1a 1 4k 2 4(( 1) 3( 4k + 2 + 4(( ) − 3( 4k 12k )t 2 + a12k t 4 i =1 2k + 2 + 4( ) + a −2k t 2 i =1 S 3 S 4 −2( −6 6k − 6k )t + a −6k t 3 4k ∑( 2k )i a 12k + 2 + 4( ) i =1 + 2∑ ( )i +1 k k 1 k 4 )t 2 + a −12 t i =1 Note: k is twist level in turns per unit cell.

4 Experimental points in simplex coordinate systems: (a) q = 3, m = 2; (b) q = 3, m = 3; (c) q = 4, m = 2; (d) q = 4, m = 3. 18] A detailed analysis of the approaches and methods used in experiments with mixtures can be found in Cornell (1990). The multivariate statistical methods, such as multivariate hypothesis testing, principal component analysis, cluster analysis, and discriminant analysis are discussed in Dillon and Goldstein (1984). 4 Modelling the geometry of fibre, yarn and fabric Modelling the geometry and structure of textiles is important for the analysis of the mechanical and physical properties of textiles because it provides necessary information on the spatial shapes, orientation, and mutual position of fibres and threads.

A knot invariant is a function of a knot which takes the same value for all equivalent knots. There are numerical, matrix, polynomial, and finite-type invariants. 6 Examples of basic topological objects: (a) knot; (b) link; (c) braid; (d) tangle. considered. The problem of classification of textile structures is important in the context of automatic generation of structures where it is necessary to have a general method that would be able to identify topologically different and physically coherent structures which do not contain closed loops.

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