Sentence examples for this result relies from inspiring English sources

The proof of this result relies on a characterization of the Schwartz space of a semi-algebraic smooth variety that we give.

This result relies on some preliminaries which may have their own interest: flatness of the sheaf of holomorphic tempered functions and a tempered version of Cartan's Theorem B.

This result relies on data only apart from technical realization of signal acquisition and implementation of identification algorithm, so it is called in the paper optimal abstract design.

This result relies on (1) the standard assumption that the generative distribution is Markov and faithful to some directed acyclic graph (DAG), and (2) a new assumption about the generative distribution that the authors call monotone DAG faithfulness (MDF).

This result relies on a list of assumptions which are described in detail below.

This result relies on the fact that the nonlinearity can guarantee the twist condition of the KAM theorem.

This result relied on data from the Sloan Digital Sky Survey and the ROSAT X-ray satellite's all-sky survey.

Traditional proofs of this result rely on the decomposition of the Markov chain into excursions away from the small set and a careful analysis of the exponential tail of the length of these excursions.

The prediction of this remarkably simple result relies on a steady-state approximation for HO2, as well as steady states for more active radicals during induction.

This intuitively simple result relies on some well-known symmetries in the dynamics of mechanical systems with respect to the group action of SO(3) on solution trajectories of the system.

The proof of this nonuniqueness (but not existence) result relies on an entirely new line of arguments in which the concept of generalized critical value plays a central role.