Blanchfield and Seifert algebra in high dimensional knot theory
Novikov [12] initiated the study of the algebraic properties of quadratic forms over polynomial extensions by a far-reaching analogue of the Pontrjagin-Thom transversality construction of a Seifert surface of a knot and the infinite cyclic cover of the knot exterior. In this paper the analogy is applied to explain the relationship between the Seifert forms over a ring with involution A and Blanchfield forms over the Laurent polynomial extension A[z, z]. The rings A and A[z, z] correspond to the two ways of associating algebraic invariants to an n-knot k : S ⊂ S with A = Z : (i) The Z[z, z]-module invariants of the canonical infinite cyclic cover M = pR of the exterior of k M = cl.(S\k(S)×D) ⊂ S with k(S) × D ⊂ S a regular neighbourhood of k(S) in S, p : M → S a map inducing an isomorphism p : H(S) ∼= H(M), and ∂M = S × S. (ii) The Z-module invariants of a codimension 1 submanifold N ⊂ S with boundary ∂N = k(S) ⊂ S ,
The classification theory of high-dimensional – component boundary links involves ‘ Seifert Z – modules
The classification of high-dimensional –component boundary links motivates decomposition theorems for the algebraic K–groups of the group ring AŒF  and the noncommutative Cohn localization † AŒF  , for any > 1 and an arbitrary ring A , with F the free group on generators and † the set of matrices over AŒF  which become invertible over A under the augmentation AŒF ! A . Blanchfield AŒF – modules and Seifert A–modules are abstract algebraic analogues of the exteriors and Seifert surfaces of boundary links. Algebraic transversality for AŒF –module chain complexes is used to establish a long exact sequence relating the algebraic K– groups of the Blanchfield and Seifert modules, and to obtain the decompositions of K .AŒF / and K .† AŒF / subject to a stable flatness condition on † AŒF  for the higher K–groups.
Synthesis of quasi-stationary inhomogeneous impedance body of arbitrary shape
Formulas were obtained for the reflection factors of a plane wave from the inhomogeneous impedance plane, which reflects the incident wave in the given direction. The problem of synthesis of impedance inhomogeneous rotation body was solved for an arbitrary shaped generatrix for the given scattering diagram for co- and cross polarizations. Impedance distributions were obtained in explicit form. Restrictions on the class of implementable scat- terplots were formulated.