  We prove the following: Let $2p + 1$ be no less than 5 and $p$ be a natural
number. Let $K$ and $J$ be closed, oriented, $(2p+1)$-dimensional connected,
$(p-1)$-connected, simple submanifolds of the standard $(2p+3)$-sphere. Then
$K$ is equivalent to $J$ if and only if a Seifert matrix associated with a
simple Seifert hypersurface for $K$ is $(-1)^p$-$S$-equivalent to that for $J$.
  We also discuss the $2p+1=3$ case. This result implies one of our main
results: Let $\mu$ be a natural number. A 1-link $A$ is pass-move equivalent to
a 1-link $B$ if and only if the knot product of $A$ and $\mu$ copies of the
Hopf link is $(2\mu+1, 2\mu+1)$-pass-move equivalent to that of B and $\mu$
copies of the Hopf link.
  It also implies the other of them: Two-fold cyclic suspension commutes with
the performance of the twist move for spherical $(2k+1)$-knots ($2k+1>4$).
  Furthemroe we prove the following: Let $2p+1$ be no less than 5 and p be a
natural number. Let $K$ be a closed oriented $(2p+1)$-dimensionalsubmanifold of
the standard $(2p+3)$-sphere. Then $K$ is a Brieskorn submanifold if and only
if $K$ is connected, $(p-1)$-connected, simple and has a $(p+1)$-Seifert matrix
associated with a simple Seifert hypersurface that is $(-1)^p$-$S$-equivalent
to a Kauffman-Neumann-type, or a KN-type (See the body of the paper for a
definition.) We also discuss the $2p+1=3$ case.
