Sentence examples for mathematical properties have from inspiring English sources

Its mathematical properties have been studied further in many works [6 10, 27, 28].

Although the Lorentz metamaterial model has been used by physicists and electrical engineers, its mathematical properties have not been investigated yet.

As mentioned earlier, numerous network information measures [11], [14], [22] have been developed, but their mathematical properties have yet to be studied in detail.

SSEM-Lasso's mathematical properties have been fully characterized [ 12].

Then, copula functions have been extensively studied and a comprehensive discussion of their mathematical properties has been presented [11, 12].

Due to their appealing mathematical properties, they have been extensively applied in a great variety of topics in computer graphics, such as the modelling of BRDFs [24], early work on image-based rendering and re-lighting [25, 26], BRDF shading [27], irradiance environment maps [28], precomputed radiance transfer [29, 30], distant lighting [31, 32] and lighting-invariant object recognition [33].

It is shown that these mathematical properties, which have been discussed for fuzzy variables and rough variables by Liu [3] as well as for fuzzy random variables by Yang and Liu [19], are also valid for fuzzy rough variables in a similar way.

Our examples provide only a few among many ways in which the mathematical properties we have obtained for FST can be used to interpret its behavior in the analysis of empirical data.

Such properties have been predicted by mathematical modelling to play an important role in the adaptive processes of yeast cells (Schaber et al., 2010).

In other words: Of all the measures of location, the mean is the most commonly used because it is easily understood and has useful mathematical properties that make it convenient for use in many statistical contexts.

The first step that natural numbers have only structural properties—has recently been defended by a variety of mathematical structuralists (Parsons 1990, Resnik 1997, and Shapiro 1997).