When the medium bidyadic [[??].sub.m] is not restricted by a dispersion equation, i.e., it satisfies [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for any one-form v, it has a Q-medium solution only when [??] is an antisymmetric
dyadic, i.e., it belongs to case 1 solutions.
We recall that a partially ordered set (poset) P = (A, [less than or equal to]) is a set A endowed with a reflexive, antisymmetric
and transitive binary relation.
Finally, it is plausible that parthood is a partial ordering: reflexive, transitive, and antisymmetric
. These plausible claims cannot all be correct.
Since [THETA] is antisymmetric
with respect to g, we have
We have used in this paper a two-dimensional FDTD code that captures the simulation parameters (spatial discretization step, simulation mode (TE/TM), number of iterations), the injection conditions (injection of a guided mode through a Huygens surface) and the boundary conditions Type (Wall, symmetric or antisymmetric
The four submatrices are real, Su and $22 are symmetric, while [S.sub.12] and [S.sub.21] are antisymmetric
. Moreover, if the distance between any two consecutive [l.sub.k]'s is a constant, then the four submatrices are Toeplitz, but S is not Toeplitz.
We verified also numerically that the current flow at the higher order resonances is not circular and the classification as symmetric or antisymmetric
is no longer valid.
The intense band located at 1 623/cm is characteristic of calcium oxalate and is assigned to the antisymmetric
oxalate COO- stretching mode (Monje & Baran 1996, 1997).
The set of n x n generalized centro-symmetric (or generalized central antisymmetric
) matrices with respect to P is denoted by [CSR.sup.n x n.sub.p] (or [CASR.sup.n x n.sub.P]).
1 are absorption peaks characteristic of Si[O.sub.2], in which absorption peaks at 1105 [cm.sup.-1] and 802 [cm.sup.-1] correspond to the antisymmetric
and symmetric stretching vibration of Si-O respectively.
It is not hard to see that ([??]) acts as and order (antisymmetric
quasi-order) on Dom([phi]); so, it remains as such on M[u].
(2) defines the following symmetry rules: symmetric component of signal [f.sub.S](t)=f(t)+f-t)]/2 creates real component Re[F([omega])] of spectrum that is also symmetric in frequency domain; the antisymmetric
component of signal [f.sub.AS](t)=f(t)-f-t)]/2 creates imaginary component of spectrum Im[F([omega])] that is antisymmetric
in frequency domain.