Sentence examples for basis of the singular from inspiring English sources

The second, Theorem 18.1.1, applies to square symmetric matrices and is the basis of the singular value decomposition described in Theorem 18.2.

Then, an integrated fault detection and fault-tolerant control architecture of actuators and sensors is taken into account in the implementation of the infinite-dimensional system on the basis of the singular perturbation formulation.

Numerical results of the mode mixity predicted by the present closed-form formulations correlate well with those numerically calibrated on the basis of the singular field and crack-tip force models.

Secondly, the general updating equations for the analytical model are obtained on the basis of the singular-value decomposition results, the eigenequation, and the modal orthogonality relations.

On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illustrated, and the existence of the relaxation oscillation with a rapid movement process alternating with a slow movement process is proved.

Since these affixes cannot be predicted by phonological or semantic factors, all nouns have to be assigned to classes on the basis of their singular and plural forms.

In the case of the amtB-glnK operon (import of ammonia) it was formerly concluded that it is not repressed by GlnR on the basis of a singular observation.

We do not trust, on the basis of sad experience, the singular perspective of the "business community" or Wall Street, or ideologically narrow politicians who have only their own, donation-driven special interests in mind.

However, by decomposition techniques on the basis of singular perturbation analysis or batch phase analysis one is able to reduce the dimension of the augmented state vector.

The Fed keeps the minimum balances of the various, not-so-numerous, banks throughout the country and strives to set the total amount of money available on the basis of its own singular judgment.

From an ensemble of complex signals, a complex correlation matrix is formed, and its complex eigensolution is the basis of the decomposition (like a complex singular value decomposition).