Sentence examples for widely generalized from inspiring English sources

In the Kantorovich's framework, the problem has been widely generalized, with very general cost functions c x, y) instead of the Euclidean distance (|x-y|) and more general measures and spaces.

Because of their widely generalized use in many industries, composites are the subject of many research campaigns.

Because the design of clinical trials is mainly based on demonstrating the efficiency of therapeutic procedures, these studies cannot be widely generalized, especially in complex multifactorial diseases such as vascular disease.

Using Theorem 3.1, we can also show the following fixed point theorem for widely generalized hybrid non-self mappings in a Hilbert space; see Kawasaki and Takahashi [13].

A mapping T from C into H is said to be widely generalized hybrid if there exist α, β, γ, δ, ε, ζ ∈ R such that α ∥ T x − T y ∥ 2 + β ∥ x − T y ∥ 2 + γ ∥ T x − y ∥ 2 + δ ∥ x − y ∥ 2 + max { ε ∥ x − T x ∥ 2, ζ ∥ y − T y ∥ 2 } ≤ 0. for any x, y ∈ C. Such a mapping T is called -widely generalized hybrid.

To confirm whether such results can be more widely generalized, more research needs to be implemented in various environments to assess whether productivity per habitat type is similar or varies in different ecological settings.

Recently, Kawasaki and Takahashi (J. Nonlinear Convex Anal. 14 71-87, 2013) defined a broad class of nonlinear mappings, called widely more generalized hybrid, in a Hilbert space which contains generalized hybrid mappings (Kocourek et al. in Taiwan. J. Math. 14 2497-2511, 2010) and strict pseudo-contractive mappings (Browder and Petryshyn in J. Math. Anal. Appl. 20 197-228, 1967).

They noted that the class of widely more generalized hybrid mappings contains the class of normally generalized hybrid mappings but not of quasi-nonexpansive mappings generally even with having a fixed point.

However, a widely more generalized hybrid mapping is not quasi-nonexpansive in general even if it has a fixed point.

We'll formally test the null hypothesis that the mean expression differs by phenotype with a widely used generalized linear negative binomial model that allows for biological variability among subjects with the same phenotype.

Experimental testing remains the preferred approach to gather insight into the workings of the material and structural elements as the complex behavior of reinforced concrete does not lend itself to widely applicable generalized solutions.