Sentence examples for a certain equivalent from inspiring English sources

This work presents one of the averaging procedures leading to equations with constant coefficients, in which the corrugated plates are replaced by a certain equivalent continuous structure with mean stiffness modules that describe the properties of the actual plate.

The basic principle behind modular decomposition is to iteratively identify and contract nodes that are in a certain sense equivalent, until no more equivalent nodes can be found in the graph.

Whenever a core performs a steal, data is fetched from the memory of another core, which is to a certain extent equivalent to a migration.

Then, as Lewis (1979a) points out, believing a property \(F\) is, in a certain sense, equivalent to believing the set of centered worlds \(\langle o, w \rangle\) such that \(o\) has \(F\) in \(w\).

Furthermore, F is contractive in E with respect to a certain strongly equivalent metric in Ω if and only if Lip ( F, E ) < 1 or L ∥ ∥ ( T m, E ) < 1 holds for a positive integer m.

Particularly, we give the result that system (2) is of global exponential stability if and only if T is contractive in R n with a certain strongly equivalent metric.

For the first step, kudzu root starch was liquefied by α-amylase at a certain dextrose equivalent value of 19 21, and β-amylase and pullulanase to saccharify for a certain time, a four-factor nine-level experimental design with nine experiments was performed according to the uniform design table U 9 * (94) to optimize the yield of maltose.

In other words, the two works show that T is contractive in D with a certain strongly equivalent metric if its iterative sequence { x k } exponentially converges to x ∗ for any initial point x 0 ∈ D. The result is helpful to understand the exponential stability of x ∗ from a different view.

Wang et al. [9], Wang and Xu [11] show that system (1) is of exponential stability in D if and only if T is contractive in D with a certain strongly equivalent metric and also present a converse not only to the exponential stability of system (1) different from the Lyapunov function, but also to the Banach contraction theorem different from the ones in Meyers [12], Leader [13], Opoitsev [14].

Combining with other known results, we obtain certain equivalent conditions for two-sided stable-like estimates of the heat kernel.

(3) If M is an (mathcal{A} -equivalent set, then M is contA} -equivalenttain ℬ-equivalent set.  .