Sentence examples for are defined up from inspiring English sources

We prove for W∗ the classical results of the theory of Dirichlet spaces: the functions in W∗ are defined up to a pluripolar set and the functional capacity associated to W∗ tests the pluripolar sets.

As a result, the signatures are defined up to a scale factor, and thus, the ASC should be replaced with a generalized ASC of the form ∑ j = 1 p ξ j · a j = 1, in which the weights ξ j denote the pixel-dependent scale factors [67].

Such "von-Neumann and Morgenstern" (vNM) utility functions are cardinal, in the strict sense that they are defined up to a positive affine (shape-preserving) transformation [ 4], in contrast to ordinal utility relationships that are only defined up to a monotonic (rank-preserving) transformation [ 2].

For example, Security Groups, the network controls Amazon uses that are defined up front and deployed automatically.

Remember, in physics, the potential is defined up to adding or subtracting a constant.

These are shown to be defined up to an arbitrary rotation.

Procedures are suggested to merge the non-auroral model which is defined up to 60° with the auroral model established with data taken at 70°.

and is defined up to an additive constant [39, 47].

The model provided by HOSVD is defined up to a rotation.

This homeomorphism F is called the lift of the homeomorphism f and is defined up to an integer term.

According to well-known results from frame and graph theory [6, 7], an equiangular frame can be defined up to unitary equivalence by its so called signature matrix.