Sentence examples for applies to the function from inspiring English sources

where the subscript x by the operator L1 indicates that the operator L1 applies to the function of x.

An important example of our result will be the case that for a function finmathcal{F}bigl epsilon,gamma epsilon),rho,cbigr) cap operatorname{PAP}bigl(X^{1+epsilon}, X^{gamma epsilon)}bigr) there exists (lambda_{0}>0) such that for any (0lelambdalelambda _{0}), and Theorem 3.1 applies to the function λf.

For any fixed (x_{i} in[a,b]), put psi_{i}^{m}(x)=mathbb{L}^R_{x_{i}}^{m}(x)= mathbb {L}_{y}R_{y}^{m}(x)|_{y=x_{i}}, (10) where (mathbb{L}^) is the adjoint operator of (mathbb{L}) and the subscript y in the operator (mathbb{L}) indicates that the operator (mathbb{L}) applies to the function y.

Spline interpolations are applied to the functions of day of year, geomagnetic latitude and solar local time, and linear interpolation is applied to the function of F10.7.

(a) This follows directly from Banach's fixed-point theorem applied to the function Ψ.

Then by (1.2), applying to the function, we can see that (1.8).

The radial basis function (RBF) neural network is widely applied to the function approximation and pattern classification.

The proposed method has been applied to the function of Linux to demonstrate the information leakage risk propagation.

With the help of (97) applied to the function v n, the Hoelder and Young inequalities as well as (95), we get (100).

The differentiability with respect to R follows from the implicit function theorem applied to the function F w,R =w"+ n-1 frac{S'(t+ n-1 frac{} w' + w^{p} and the radial non-degeneracy of (tilde{u}_{R}).

However, for historical reasons, a special syntax applies to the trigonometric functions: a positive exponent applied to the function's abbreviation means that the result is raised to that power, while an exponent of −1 denotes the inverse function.