Sentence examples for exists an equivalent from inspiring English sources

Assume that there exists an equivalent metric on such that for every and every, (2.17).

Moreover, there exists an equivalent metric ρ on X that preserve some inequalities.

A Banach space is said to be -smoothable if there exists an equivalent norm under which is -uniformly smooth.

By Theorem 2.8, there exists an equivalent norm on, such that the dual norm satisfies the UKK* property.

We also show a quadratic upper bound: given a cyclic Boolean circuit with m gates, there exists an equivalent acyclic Boolean circuit with m2 gates.

We also consider ANSPs with restricted features, proving the following normal forms: for any ANSP there exists an equivalent ANSP without input filters, and one without output filters.

As the harmonic analysis associated with the Weinstein operator has known remarkable development, it is a natural question whether there exist an equivalent of the theory of localization operators and new uncertainty principles for the continuous wavelet transform relating to this harmonic analysis.

Due to the noncontinuous of feasible set, generally can only find a set P ε, such that Φ∈ ε,1]. It is nontrivial to find out the Pareto-optimal front of set P ε. The question becomes if there exist a equivalent function F such that ( ρ ∗, p ∗ ) = arg max F if and only if ( ρ ∗, p ∗ ) = arg ( max ∑ k = 1 K R k & max Φ ).

According to the revelation principle [15], for any feasible contract of incomplete information, there exists a payoff-equivalent revelation mechanism that enables the sources to truthfully report their types.

This assumption necessarily requires that (1) for each Chinese emotion word, there exists a precise translation equivalent in English, and (2) each pair of Chinese and English translation equivalent emotion words are perceived (by native speakers of Chinese and English, respectively) with the same emotion type and equivalent emotion intensity.

Then by the Löwenheim-Skolem-Tarski Theorem, there exists a model elementarily equivalent to the model generated by the Completeness Theorem that is of the same size as the world (since by Löwenheim-Skolem-Tarski Theorem T will have models of every infinite size).