"Linking numbers and nucleosomes"

Date:
1972-1977
Reference:
PP/CRI/H/6/12/2
Catalogue details

Licence: In copyright

Credit: "Linking numbers and nucleosomes". Source: Wellcome Collection.

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    how the writhing number of a curve depends ox th2 curve 1333 For the T 0 -component of TT : w -T 0 = f oî' all t ; hence |TF(6)- T 0 (b) ¡< ¡T 0 (6) - T ¿b) j. For the C 0 -component of IF : - ?J] +(?.••£ T.jt hence ! — (IF- Z7 0 )! < (LiL il 4-1— T.lllT« — T I I di j \|d< °| |df . |j ll ' Integrating the above inequality and using W(a) = 0 we obtain : |W(6).l7o(Ä)|< J = J*+ j^- ü|)|*. - T.lòt. For the F 0 -component of TF : ±0r-rj = ^..(r, _ + ( Fo .|. Hence, reasoning as before, | W(b)-V 0 (b)\ < I. Since |TF(6)¡ is no greater than the sum of the absolute values of its components, we have W)l< \T 0 (b) - ^(6)! +2/. ■>ul)stituting |1F(Z>)[ = \U 0 (b) — Z7 X (6)| into inequality (3) we find: I sin Tz(Wr(X 0 ) - TFr(Xi))!<|- I T 0 (b) - T x {b)\ + 21. This inequality must hold if the right-hand side is replaced by T 0 (j>) — T t (p) I -f 21 for any p in the interval [a, è] ; by averaging •ver p the inequality of the theorem is obtained. Received May 3, 1072 California Institute of Technology Pasadena, California USA
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