Sentence examples for midpoint function of from inspiring English sources

For a fuzzy number x ˜, we define a function x ˜ M : [ 0, 1 ] → R by assigning the midpoint of each α-level set to x ˜ M for all α ∈ [ 0, 1 ], i.e., x ˜ M = x ˜ L + x ˜ R 2. Then the function x ˜ M : [ 0, 1 ] → R will be called the midpoint function of the fuzzy number  x ˜.

It is natural to define the midpoint function for an equivalence class as follows.

Hence, M 〈 x ˜ 〉 M 〈 y ˜ 〉 is the midpoint function for some fuzzy number equivalence class.

Among applications of the decomposition of a fuzzy interval using a symmetric fuzzy number and a midpoint function is the study of the fuzzy variance of a fuzzy interval [42, 43].

It is interesting to note that the midpoint function x ˜ M is actually a gradual number and all of the gradual numbers form a group structure under addition [40, 41].

For an equivalence class 〈 x ˜ 〉 ∈ F / S, we define a midpoint function M 〈 x ˜ 〉 : [ 0, 1 ] → R by M 〈 x ˜ 〉 = x ˆ M. for all α ∈ [ 0, 1 ], where x ˆ is the Mareš core of 〈 x ˜ 〉.

For any 〈 x ˜ 〉, 〈 y ˜ 〉 ∈ F / S, the midpoint functions M 〈 x ˜ 〉 and M 〈 y ˜ 〉 are continuous from the right at 0 and continuous from the left on [ 0, 1 ], and they are functions of bounded variation on [ 0, 1 ] [33].

We then calculated the density of nucleosome midpoints as a function of distance from an "anchor" nucleosome (treating each nucleosome midpoint within a region as an anchor in turn).

Naphthoquinone has a lower midpoint redox potential than benzoquinone (−70 to −110 mV vs 70 110 mV), demonstrating that kcat values were not simply a function of the midpoint redox potential of each quinone.

Finally, Fig. 7 shows the impact of different IDM implementations on image noise as function of frame midpoint time.

Fig. 7 Mean ± SD of coefficient of variation of voxel values within the white matter volume of interest as function of frame midpoint time for FMZ scans and AD and HC PIB scans.