Statistical integrals with an imposed constraint

All the physical quantities of a polymer system can be expressed through the statistical integrals with an imposed constraint. The fixing of several p points relating to the given macromolecules may serve as such a constraint. Each of the point, called a correlation point, is denoted by the index q (1 < q < p). The point with the index q is assumed to relate to the chain jg wjth the area Sg, and the coordinate of the point along the chain is s, (0 < s, < 5,), its spatial position is characterized by the vector r,. The imposed constraint implies that the condition... 

So, the statistical integral with an imposed constraint is designated as... 

As all the physically measured quantities arc derived from the chain statistical integral with an imposed constraint (see section 5.4), this integral is then introduced (Duplantier, 1982) to express the fixing of the chain ends... 

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