By M.M. Cohen

Cohen M.M. A direction in simple-homotopy thought (Springer, [1973)(ISBN 3540900551)

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Additional info for A course in simple-homotopy theory

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This is the diameter of impenetrable uncharged cylindrical segments of the model chain. The quantitative deﬁnition of Wr /∆Lk is based on the concept of the second virial coeﬃcient [33]. It was shown that approximation of the electrostatic interaction by this hard core potential Fig. 7. Simulation results as function of k, the number of straight segments per Kuhn length of the model chain. 05, eﬀective diameter of the chain equals 5 nm). (b) Probability of trefoil calculated for freely jointed chain, k = 1, (♦) and k = 10 ( ) 32 A.

For a comparison with experimental data, it is convenient to introduce the constant B: NA ∞ p(R)4πr2 dr. 6) B= M 0 This allows us to express P as P = Bc. 7) 28 A. Vologodskii Fig. 4. Probability of linkage between two relaxed DNA molecules 7,000 and 10,000 base pairs in length as a function of the distance between the chains centers of mass, R. The function strongly depends on solution ionic conditions. p(R) shown in the ﬁgure corresponds to near physiological ionic conditions. For each value of R a fraction of conformations of two chains is forbidden because of overlap of one chain with the other.

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