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antisymmetric is no longer valid.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.