Invariant

He refers to the hyperbolic angle as an invariant measure with respect to the squeeze mapping just as circular angle is invariant under rotation.

He thinks the absolute/relative distinction should be recast in terms of an invariant/variant distinction, where there are many things a proposition can be invariant with regard to or vary with.

In analogy to the characterizations of the outerplanar and planar graphs as being the graphs with Colin de Verdière graph invariant at most two or three, the linklessly embeddable graphs are the graphs that have Colin de Verdière invariant at most four.

In invariant-theoretic conditional inference, the sampling distribution is conditioned on an invariant of the group of transformations (with respect to which the Haar measure is defined).

In this discussion, an invariant metric is simply one that is invariant under rotations of the circle.

In this way he demonstrated that the laws of physics remained invariant as they had with the Galilean transformation, but that light was now invariant as well.

Normal subgroup main A subgroup of H that is invariant under all inner automorphisms is called normal ; also, an invariant subgroup.

The adiabatic principle allowed Wien to conclude that for each mode, the adiabatic invariant energy/frequency is only a function of the other adiabatic invariant, the frequency/temperature.

The impulse response h completely characterizes any linear time-invariant (or shift-invariant in the discrete-time case) filter.

The stem cells will produce invariant natural killer T cells, which can be multiplied and then frozen for use in treatments for future cancer patients.

A basic assumption of relativity is that coordinate transformations must leave spacetime intervals invariant.

A construction on Lie groups On an n-dimensional Lie group, Haar measure can be constructed easily as the measure induced by a left-invariant n-form.

Again, the difference in length and time scales is such that the speed of light is invariant.

Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces.

All forms of energy are believed to interact at least gravitationally, and many authors state that superluminal propagation in Lorentz invariant theories always leads to causal paradoxes.

A loop invariant is an assertion which must be true before the first loop iteration and remain true after each iteration.

Also length of a unit vector (of dimension length, not length/force, etc.) has no coordinate-system-invariant significance.

Another approach is given in the work of Dürr et al. citation in which they use Bohm-Dirac models and a Lorentz-invariant foliation of space-time.

Any of the above may be applied to each dimension of multi-dimensional data, but the results may not be invariant to rotations of the multi-dimensional space.

Arnold Sommerfeld identified this adiabatic invariant as the action variable of classical mechanics.