Square knot

Fig. 2. Illustrations of (a) a three-throw sliding knot, and (b) a three-throw flat square knot.

Splices in primacord are best made with a square knot (see Figure 5). It may be a good precaution to tape or tie the knot to prevent loosening, particularly if the cord is stiff or slippery. 

The knots in Figure 21 are all prime knots because they cannot be divided (factored) into smaller, nontrivial knots. Prime knots are the building blocks of composite knots and of links. Like prime numbers, which yield composite numbers upon multiplication, or like atoms in chemistry, which yield molecules upon combination, prime knots are the elementary units of knot theory. Composite knots are exemplified by the topologically achiral square knot and the topologically chiral granny knot (Figure 22). In each of these knots, a plane perpendicular to the... 

This study is designed to compare the effect of ftie gel-former selected in Section 13.3.4.2 on POA wifti a size 6-0 silk suture/saline, HA, and C-TA as basic barrier and positive controls, respectively. The adhesion formation was studied using a rat sidewall model. The abdominal cavity was entered into in female Sprague-Dawley rats through a small midline incision. A 1-cm2 area of peritoneal sidewall was excised wifti a scalpel blade. The 6-0 silk was then sutured aroimd the perimeter of ftie excised area with a square knot at each corner. Aliquots of either the gel-former (100 pL) or the controls (1 mL) were injected on tiie excised site. One week postoperative, the adhesion prevention score was recorded for the different formulations on a scale of 0 to 10. A score of 10 represents maximum adhesion whereas 0 reflects the absence of any adhesions. Adhesion rating criteria were based on the work by Bums et al. ... 

It should be noted that in contrast to the mentioned trefoil knot, the square knot (Scheme 1) is achiral. Like the classical mesoform of tartaric acid, the square knot bears a mirror plane and. consequently, shows that symmetry considerations are important. For more complex... 

Scheme I Molecular formulae and molecular graphs of a [2]catenane and a trefoil knot. Bottom Graph of a square knot.

While we re on the subject, here is another winch refinement. An adjustable winch coupler, made of a short cord with knotted ends (3), allows milling closer to the winch at the end of the cut. This can replace the former cross-over system (shown in photo 1). Wrap the coupler around the winch ropes a few times and tie it with a square knot (4) or three or four half-hitches. Then attach the winch rope to the riser post for a direct pull (5). 

Solv=MeOH, EtOH and PrOH), and l,4-bis(4-pyridyl-butadiyne) (bpb, n= 0.5, Solv=MeOH). Like the btr derivative, compressed [FeN6] pseudo-octahedral sites define the knots of the square- or rhombus-shaped windows, which constitute the layered grid structure of the three compounds. Stacking of these layers in the crystal defines their most important structural differences, which are determined by the ligand size and crystal packing efficiency. In principle, the 2D grids are organised in a fashion similar to that described for the [Fe(btr)2(NCX)2]-H20 system the parallel layers are alternated so that the iron atoms of one layer lie vertically above and below the centres of the squares formed by the iron atoms of the adjacent layers. 

The square root of the monodromy matrix gives rise to the so-called braiding matrix responsible for a proper form of skein relations, yielding knot or link invariants. 

Figure 11. Antijunctions and mesojunctions. (a) A 949 knot drawn in a DNA context. Each of the nodes of this knot is shown to be formed from a half-turn of double helical DNA. The polarity of the knot is indicated by the arrowheads passing along it. Various enclosed areas contain symbols indicating the condensation of nodes to form figures. The curved double-headed arrow indicates the condensation of two half-turns into a full turn, the solid triangle indicates a three-arm branched junction, the empty square indicates a 4-strand antijunction, and the shaded square is a four-strand mesojunction. (b) Schematic drawings of 3-strand and 4-strand junctions, antijunctions, and mesojunctions shown as the helical arrangements that can flank a triangle or a square. Each polygon is formed from strands of DNA that extend beyond the vertices in each direction. The arrowheads indicate the 3 ends of the strands. The vertices correspond to the nodes formed by a half-turn of double helical DNA. Base pairs are represented by lines between antiparallel strands. Thin double-headed arrows perpendicular to the base pairs represent the axis of each helical half-turn. The lines perpendicular to the helix axes terminating in ellipses represent the central dyad axes of the helical half-turns. The complexes 33 and 44 correspond to conventional branched junctions. The complex 40 is a 4-strand antijunction. The complexes on the bottom row are mesojunctions, which contain a mix of the two orientations of helix axes.

The spline surface S(x,y) consists of a set of bicubic polynomials, one in each panel, joined together with continuity up to the second derivative across the panel boundaries. Because each B-spline only extends over four adjacent knot intervals, the functions B.(x)C.(y) are each non-zero only over a rectangle composed of 16 adjacent panels in a 4 x 4 arrangement. The amount of calculation required to evaluate the coefficients y may be reduced by making use of this property. As before, least-squares methods may be used if the number of data exceeds (h+4)(jJ+4), which is usually the case. 

Figure 22. Diagrams of composite knots with c(K) = 6. (a) Square, or reef knot, (b) and (c) Enantiomorphs of the granny knot.

Figure 27(c)]. It remains to be noted that Borromean links composed of metric circles are impossible,108 that Borromean links composed of three triangles or three squares have inspired sculptures by John Robinson,109 and that this link, in the form of three interlocked triangles, was known to the ancient Scandinavians as Odin s triangle or the Walknot (meaning knot of the slain ).110... 

Figure 10.8. The loss in strength due to knots is a function of their size and location. The equations here are from an appendix in ASTM D245 (ASTM, 2005b). In essence, the strength ratio for a timber with a knot on the edge/margin of the wide face is deemed to be equivalent to the square of the strength ratio of a timber with an identical knot that lies at the centre of that face.

These compounds enjoy a number of advantages over their organic counterparts, in particular, one-pot reactions, high yields, spectroscopic, electronic, and magnetic properties, which are inaccessible with organic species [20,21], Furthermore, the use of transition metal coordination has been explored by Lehn and co-workers and many others. The new strategy was successfully used for the construction of molecular racks [1,22], ladders [1,11,23], grids [1,11,24,25], squares [7,26,27], cylinders [11,28], molecular boxes [29], catenanes [13,15,30], rotaxanes [31], knots... 

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