Sentence examples for be defined up from inspiring English sources

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

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.

Of course, the subshock solution will be defined up to an interval, at whose endpoints the derivative (which is infinite) must have the same sign in order for the speed of the subshock to be 0 (via an analogous of the Rankine-Hugoniot condition).

For "hot" transistors (u = 0.2) a LTT can only be defined up to l ~ 10. Figure 5 Calculated drain characteristics for l = 10, v G starting from 0.5 with decrements of 0.1 (solid lines) at the temperature (a) u = 0.1 and (b) u = 0.01.

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°.

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).