Sentence examples for obtain a criterion from inspiring English sources

On the positive side, we obtain a criterion for Riemann integrability of quasi-Banach valued maps based on an approximation method by polynomial functions.

In order to obtain a criterion flexible enough to validate interesting programs using higher-order primitives, we introduce a notion of polynomial quasi-interpretations, coupled with a simple termination criterion based on linear types and path-like orders.

We obtain a criterion for the boundedness and compactness of the products of differentiation and composition operators C φ D m on the logarithmic Bloch space in terms of the sequence { z n }.

As application we obtain a criterion for the operator-norm convergence of the Trotter product formula on Banach spaces with error estimate n−1 log n, provided one of the generators has a bounded H∞ functional calculus.

Consequently, in order to obtain a criterion (Equation 16) that results in a good approximation of the entropy (29), a more reasonable choice of κ j + 1 ( o ) will be as follows: κ j + 1 ( o ) = 1 α j + 1 ( o ).

Mao and Xia [5] obtained a criterion for spectral gap by hitting times for jump processes via decomposition method.

Starting from the data obtained, a criterion is refined for estimating the FRV coefficient based on car technical features.

For systems with disturbance but without delay, by using Lyapunov stability theory, we obtained a criterion for exponentially practical stability of a general discrete time system and a linear discrete time singular system, respectively.

We would also like to mention here that an exact formula for the repetitive function of an l-Grigorchuk subshift has been obtained, independently, in [32], and hence they have also obtained a criterion similar to ours for an l-Grigorchuk subshift to be (alpha )-repetitive.

They investigated local well-posedness and blow-up solutions of (1.2) by means of Kato's semigroup approach to nonlinear hyperbolic evolution equation and obtained a criterion and condition on the initial data guaranteeing the development of singularities in finite time for strong solutions of (1.2) by energy estimates.

If for each pair of functions f and g in F, f and g share the value 0 and f n f' and g n g' share a nonzero value a in D, then F is normal in D. In 2008, Zhang [10] obtained a criterion for normality of F in terms of the multiplicities of the zeros and poles of the functions in F and use it to improve Theorem 1.2 as follows.