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The symmetry operation (x,y,z)->(-x,-y,-z). When used in conjunction with a rotation, it becomes an improper rotation.

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

A relation R on a set S is irreflexive provided that no element is related to itself; in other words, xRx for no x in S.

A vector field v for which the curl vanishes, del xv=0.

An integral of motion which restricts the phase space available to a dynamical system.

A map which is monotone increasing and therefore order-preserving.

To rearrange without cutting or pasting.

J_(nualphabeta)^mu=J_(nubetaalpha)^mu=1/2(R_(alphanubeta)^mu+R_(betanualpha)^mu), where R is the Riemann tensor.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

The jerk j is defined as the time derivative of the vector acceleration a, j=(da)/(dt).