Due to the topological relation [[pi].sub.3]([S.sup.2]) = Z there is an additional quantum number for the [??]-field, the Hopf number, or Gaufi linking number v of fibres F defined by [[??].sub.F] = const and thus by certain values [[theta].sub.F] and [[phi].sub.F].
For a given [??]-field one can get the linking number in [R.sup.3] by the famous formula of Carl Friedrich Gauss:
Then, the branched [Z.sub.p]-cover [??] defined by [tau] : [[pi].sub.1] (M - L) [right arrow] Z; [for all][[mu].sub.i] [right arrow] 1 is called the total linking number
(or TLN for short) [Z.sub.p]-cover over (M, L).
Link degree is the linking number
of each core node divided by the maximum linking number
in the topology.
and algebra through the distributive law.
3) Average returned linking number
of member search engines;
It is the combination of twists and writhes that impart the supercoiling, and these occur in response to a change in the linking number
. A coiled structure is at a higher energy (less stable).
To resolve the second question we require the notion of the linking number
L([C.sub.1], [C.sub.2]) of two disjoint oriented polygonal knots [C.sub.1] and [C.sub.2] in [R.sup.3].
Arnold, who showed that energy bounds exist for the special case when a quantity called the "linking number
" can be computed for a given tangle of lines.
In the ordinary knot theory, the linking number
is an elementary and important invariant for oriented two-component links.
Claiming to tackle "environmental and digital pollution", it uses numerology - linking numbers
He provides all the necessary prerequisites for graduate students and practitioners, describing Riemann surfaces (including coverings, analytical continuation, and Puiseaux expansion), holomorphic functions of several variables (including analytic sets and analytic set germs as well as regular and singular points of analytic sets), isolated singularities of holomorphic functions (including isolated critical points and the universal unfolding), fundamentals of differential topology (including singular homology groups and linking numbers
), and the topology of singularities (including the Picard-Lefschetz theorem, the Milnor fibration, the Coxeter-Dynkin diagram, the Selfert form and the action of the braid group.