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A relation R is antisymmetric if,

for all x and y, x R y and y R x => x == y.

I.e. no two different elements are mutually related.

Partial orders and total orders are antisymmetric. If R is also symmetric, i.e.

x R y => y R x


x R y => x == y

I.e. different elements are not related.
References in periodicals archive ?
Ng, "Influence of stacking sequence on scattering characteristics of the fundamental anti-symmetric Lamb wave at through holes in composite laminates," The Journal of the Acoustical Society of America, vol.
where sinc([theta]) = sin([theta])/[theta], [[mu]] is the anti-symmetric matrix of [mu].
As J is anti-symmetric and R is symmetric positive definite, substitute the controller of (8) into (9) yields
For non-symmetric coefficients, this structure only increases multiplier savings in the filter bank by a factor of two, but for symmetric and anti-symmetric filter coefficients, the savings in multipliers increases further.
where the tensor [u.sup.[mu];v] is a combination of symmetric and anti-symmetric tensors.
Zhang, "The expansion problem of anti-symmetric matrix under a linear constraint and the optimal approximation," Journal of Computational and Applied Mathematics, vol.
We shall write SymCat(Q) for the full sub-2-category of Cat(Q) determined by the symmetric Q-categories (in which the local order is in fact symmetric, but not anti-symmetric).
The normal deviatoric stress acted on viscoelastic fluid is larger than Newtonian fluid, the higher of We about viscoelastic fluid is, the larger normal deviatoric stress is; and the distribution of normal deviatoric stress is different, is anti-symmetric for the Newtonian fluid, but for viscoelastic fluid, with the increase of We, this anti-symmetric decreases gradually, the higher compression on Upstream of oil film is, the lower tension on downstream of oil film is.
Symmetric (S0) and anti-symmetric mode (A0) dispersion curves were drawn for circular plate waveguide of thickness 2 mm and shown in Fig.
Given matrix P [member of] [SOR.sup.n x n], we say that a matrix A [member of] [R.sup.n x n] is generalized centro-symmetric (or generalized central anti-symmetric) with respect to P, if PAP = A (or PAP = - A).

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