Sentence examples for by choosing the function from inspiring English sources

By choosing the function φ, we can obtain a lot of important linear operators, and in consequence new and also well-known classes of functions.

In [38 40], the authors illustrated their main results with a list of several corollaries by choosing the function α in different ways.

A sufficient condition to ensure the nonnegativity of the numbers ( K 2 n + 1 ( f Ω ) ) n ∈ N 0 is provided by choosing the function f in Theorem 5.4 additionally as symmetric.

Then T has a unique fixed point in ⋂ j = 1 m A j. Proof The proof is obvious by choosing the function ϕ, ψ in Corollary 2.4 as ϕ ( t ) = ( 1 − k ) t and ψ ( t ) = t.

One can check this by choosing the function (u(x)=ln (ln frac{4R}{vert x-x_{0} vert })) for some (R>0), where (x_{0}) is a fixed point in Ω.

Vukicevic et al. [6] presented another degree-based topological index, called the geometric-arithmetic (GA) index, which is defined from (1) by choosing the function (F(d_{p},d_{q})=2sqrt{d_{p}cdot d_{q}}/(d_{p}+d_{q})).

Then T has a unique fixed point in ⋂ j = 1 m A j. Proof The proof is obvious by choosing the functions ϕ, ψ in Theorem 2.1 as ϕ ( t ) = ( 1 − k ) t and ψ ( t ) = t.

Robustness is achieved by choosing the objective function according to the error probability density function, as in robust system identification.

A more general approach is to assume, in the population, a GLM, with binomial errors and arbitrary link function g: For example, the "liability threshold" model widely used in genetics can be represented in the above form by choosing the link function, the inverse of the Gaussian probability distribution function.

So you can so by choosing the mean function, you're basically just that by choosing the mean function to be zero, you're basically just modeling the covariance of these different data points on this function.

Robustness can be achieved by choosing the objective function according to the error's p. d. f. assumption, which is the same fashion as in robust identification.