Sentence examples for been defined up to from inspiring English sources
Weyl begins his investigation by noting that, according to his theory, if one asks whether a given function is continuous, the answer is not fixed once and for all, but is, rather, dependent on the extent of the domain of real numbers which have been defined up to the point at which the question is posed.
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.
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°.
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.
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.
Since the modal shape is defined up to a constant, it is allowed to project the complex experimental amplitudes of modal coordinates on the least squares trend line (dashed line in Fig. 14).
Since we have assumed that there are no minimizing abnormal extremals in the problem and ((psi _{lambda },psi ^{0}_{lambda })) is defined up to a multiplicative scalar, we can set (psi ^{0}_{lambda }=-1).
Then, given T > 0, the set D ′ = { ∈ R s × M ˜ : the maximal solution of (2.4) is defined up to T }. is open and the map ∈ D ′ ↦ x T ∈ M ˜, where x is the unique maximal solution of problem (2.4), is continuous.
