(A world containing such wonders as Borges's Aleph, where parthood is not antisymmetric, might by contrast be finite and yet atomless.) ❋ Unknown (2009)

Notice that the relation thus defined is asymmetric (rather than antisymmetric): it doesn't permit any object to be existentially dependent upon itself. ❋ Lowe, E. Jonathan (2009)

As already mentioned, however, most contemporary authors are inclined to construe the relation of material constitution as a sui generis, non-mereological relation, or else to treat constitution itself as identity (hence, given (16), as a limit case of an antisymmetric parthood relation; see e.g. Noonan 1993). ❋ Unknown (2009)

The Fock operator (represented as a matrix) also contains some off diagonal elements, corresponding to the fact that you can swap the electrons in any two states without really changing anything (except the overall sign of the wave function), due to the fact that the full multi-electron state must be antisymmetric. ❋ Sean (2008)

For every equation there is a symmetric or antisymmetric equation that link different phenomena. ❋ Unknown (2008)

However any weighted average of a series of numbers, in which the weights are antisymmetric about the central value, gives an estimate of the trend. ❋ Unknown (2007)

The control system went into oscillation 37 myr BP when Antarctica started moving into its present position, the temperature of the ocean and that of the rest of the environment opposing each other in antisymmetric mode. ❋ Unknown (2007)

Back to Wikipedia, this time on fermions: Fermions . . . are particles which form totally-antisymmetric composite quantum states. ❋ Horace Jeffery Hodges (2005)

Fermions have half-integral spin and are described by wavefunctions that are antisymmetric in the exchange of two particles, i.e. the wavefunctions change sign when two particles change places, and they follow what is called ❋ Unknown (1996)

The two particles that are used in this theoretical exploration are in what Christandl calls an "antisymmetric state." ❋ Unknown (2010)

Thus we have seen that by making a measurement which distinguishes between the symmetric and antisymmetric subspaces of our two systems, if we will observe symmetric states half the time and anti-symmetric states the other half the time. ❋ Unknown (2010)

It is tempting to envisage that in human and other vertebrate or invertabrate ghosts with sexual differences a trace of this is carried over, and might be representable by the antisymmetric wave functions characteristic of the Fermi-Dirac statistics. ❋ Unknown (2009)

Order (relation): An irreflexive antisymmetric transitive binary relation on a set. ❋ Unknown (2009)

● Let St and At be the symmetric and antisymmetric products of the total composite system. ❋ Unknown (2009)

A (strict) partial order is which is irreflexive, antisymmetric and transitive. ❋ Unknown (2008)

Order (group theory), the least positive integer (if one exists) such that raising a group element to that power gives the identity Order (relation), an irreflexive antisymmetric transitive binary ❋ Unknown (2008)

Projection operator that projects onto an antisymmetric subspace of a tensor product space of identical linear spaces; in quantum mechanics used to symmetry-adapt fermion wave functions. ❋ Unknown (2008)

y™, and we shall take relation ¤ to be reflexive, antisymmetric and transitive. ❋ Mulligan, Kevin (2007)

(called an antisymmetric tensor of the second order) that combines electricity and magnetism into a single ❋ BANESH HOFFMANN (1968)

The obvious is this: regardless of how one feels about matters of ontology, if ˜part™ stands for the general relation exemplified by (1) - (8) and (12) - (15) above, then it stands for a partial ordering ” a reflexive, transitive, antisymmetric relation: ❋ Unknown (2009)

that pictograph is antisymmetrical ❋ This Guy (2004)