Sentence examples for demonstrated by equation from inspiring English sources

The standard morphological gradient (G m) is the full difference between the dilated and eroded image demonstrated by Equation 3. G m f = δ B f − ϵ B f (3).

Among these three methods, the jackknife test is deemed the most objective and rigorous one that can exclude the memory effects during the entire testing process and can always yield a unique result for a given benchmark dataset, as elucidated in [ 59] and demonstrated by Equation  50 of Chou and Shen [ 60].

Accuracy of the method for meteorological computations are demonstrated by solving Helmholtz equation and non-divergent barotropic vorticity equation on the sphere.

The large value of F indicates that most of the variation in the response can be demonstrated by the regression equation in the Eq. (18).

The relationship between empty body gain (EBG) and average daily gain (ADG) was demonstrated by the following equation: EBG = (0.934 ± 0.0111) × ADG.

The principle of surface wettability can usually be demonstrated by the Young equation, as follows (Wang et al. 2015): cos theta = frac{{gamma_{text{sv}} - gamma_{text{sl}} }}{{gamma_{text{lv}} }} (3)where γsv, γsl and γlv are the interfacial free energy of solid/vapor, solid/liquid, and liquid/vapor, respectively; and θ is the contact angle.

Some typical cases for problems in acoustics, as well as fluid mechanics, have been studied here and potential use in large eddy simulations (LES) has been demonstrated by solving Navier Stokes equation for lid driven cavity.

The applicability of the cusp catastrophe is demonstrated by applying the equations to the Mentougou coal mine.

For a given benchmark dataset, the jackknife test generates a unique outcome and is deemed as the most objective one compared to other two methods, as elucidated in [ 28, 29] and demonstrated by [ 30, equations (28)–(32)] in.

If so, the differential equation can be solved simply as a quadratic equation as demonstrated by the subsequent steps: Check to see if the differential equation satisfies the form shown in equation (1) in Figure 6.

Validity of this impedance up to the typical working cell currents on the order of several hundred mA cm−2 is demonstrated by fitting the model equation to numerical impedance spectra calculated from the full system of conservation equations.