Knot

The mass spectra [17] give a grossly simplified picture of the complex mixture which can result from a ring-opening polymerization. Knotted isomers can have almost identical mass spectra, dominated by the parent ion. With the reversibility of metathesis, the polyolefin mixture near equilibrium is expected to contain a large variety of knotted and linked species. 

This sparse set of choices becomes richer with larger rings. With more crossings, n, die number of possible knots increases exponentially [21]. There are 21 for n = 8, 165 for n= 10, and 2176 for n=12 [22]. Models indicate that many 12-fold knots should be stable in a cycloalkane of C20o- The rapid increase in the number of possible knots between Ci0o ( 5) and C2oo (-3000) results from the dependence of allowed values of n on ring size. 

There are 106 knots for n = 16 [23] and by extrapolation there will be 107 for n=18. Thus a ring of -300 carbon atoms has the potential for tens of millions of knotted isomers, most of which will be chiral. The laboratory tests of these conjectures are left as an exercise for the reader. 

Barash performed the Herculean labor of preparing the catenane, 3. Drs A.M. Trozzolo and H.L. Frisch were always willing to engage in thought-provoking conversation. More recently, discussion with Professors D.W. Sumners, S.G. Whittington, and J. Simon familiarized me with recent mathematical advances relevant to chemical topology. 

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T. Schlick and W. K. Olson. Trefoil knotting revealed by molecular dynamics simulations of supercoiled DNA. Science, 257 1110-1115, 1992. 

Fig. 11.40 Distribution of strain energy is two knotted polymer chains containing 35 (left) and 28 (right) carbon atoms. The strain energy is localised and most of the bonds immediately outside the entrance point to the knot. (Figure redrawn from Saitta A M, P D Sooper, E Wasserman and M L Klein 1999. Influence of a knot on the strenght of a polymer strand. Nature 399 46-48.)...

Saitta A M, P D Sooper, E Wasserman and M L Klein 1999. Influence of a Knot on the Strength of Pol5 ner Strand. Nature 399 46-48. 

Knots nd Ca.tena.nes, Closed-circular DNA hehces can cross over one another three or more times to form topological knots. These stmctures are not common, but have been found to occur naturally in some bacteriophage DNAs. 

Both catenanes and knots can bring together remote DNA sequences and may be important in transcription regulation and genetic recombination... 

The wide range of types of paper products results in a variety of sludges. SoHd wastes result from several sources within the mill, eg, bark, sawdust, dirt, knots, pulpwood rejects, flyash, cinders, slag, and sludges. Sludges often are disposed of in combination with residuals from other sources. Approximately 300 kg of soHd waste per ton of finished product is generated by the pulp and paper industry. 

Definitions of the commonly measured tensile properties are as follows Unear density (tex) is the weight in grams of 1000 m of yam. Tenacity is the tensile stress at break and is expressed in force-per-unit linear density of unstrained specimen, N /tex. Knot tenacity is the tensile stress required to mpture a single strand of yam with an overhand knot tied in the segment of sample between the testing clamps. It is expressed as force-per-unit linear density and is an approximate measure of the britdeness of the yam. Toop tenacity is the tensile stress required to mpture yam when one strand of yam is looped through... 

This process uses coUated signatures that ate sewn on special machines which pass thread through the folds of each signature and ate knotted at the back Glue is appHed to the spine and hard covets ate attached. Finished books ate then dried in special hydraulic presses. 

Resistance to axial compressive deformation is another interesting property of the silk fibers. Based on microscopic evaluations of knotted single fibers, no evidence of kink-band failure on the compressive side of a knot curve has been observed (33,35). Synthetic high performance fibers fail by this mode even at relatively low strain levels. This is a principal limitation of synthetic fibers in some stmctural appHcations. 

Although the USP defines the knot-pull tensile strength test in terms of a surgeon s knot, most surgeons use a variety of other knots depending on... 

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