Sentence examples for a generalization version of from inspiring English sources

In this work, a generalization version of El Haddad Topper Smith's equation is used to evaluate the behavior of cracks emanating from circular holes and semi-elliptical notches.

Applying a generalization version of Ekeland's variational principle due to Lin and Du (see, for instance, [26, 28]), there exists v ∈ Y such that εp v, x) >f v) - f(x) for all x ∈ Y with x ≠ v. Hence (a) holds from v ∈ Y.

The second one is a generalization of the version of the MEFM proposed for the analysis of the perfect periodic particulate composites and based on the choice of a comparison medium coinciding with the matrix.

Now, we show that Theorem 3.9 is a generalization of the following version of Nadler's fixed point theorem in b-metric spaces.

The switching strategies are based on a generalization of a recent extended version of the small gain theorem and do not require any assumption on the continuity of the delay and its time-variation rate.

In this paper, it is presented an improved version of a generalization of the Bateman equation that allows performing analysis at equilibrium for a large number of systems.

The ((Ce)^_{c}) condition is a version of the ((PS ^_{c}) condition and a generalization of the ((Ce)) condition of [18], and it can ensure a deformation lemma.

In 2007, Huang and Zhang [1] introduced the concept of cone metric spaces, as a generalization of metric spaces, and gave the version of the Banach contraction principle and other basic theorems in the setting of cone metric spaces.

The model represents an enhanced version and a generalization of another model previously proposed by the authors.

In Section 2, we give general solutions of a discrete version of the Riemann-Weber generalization of Euler differential equation and decide an oscillation constant for the discrete equation.

Our generalization will include a multidimensional version of the Hilbert-type inequality in the whole plane.