Sentence examples for given two functions from inspiring English sources

end{aligned} The function θ is quadratic, vanishes at (x=c) and (x=d), and is negative in (]c,d[). Given two functions (phileqpsi) in ([c,d]), let us denote by ([phi,psi]) the functional interval [phi,psi]=bigl{ V in W^{2,1}bigl [c,d]bigr) : phi(x) le V x) le psi(x) mbox{ for all }x in[c,d]bigr}.

Given two functions, the equality (3.13).

This work discusses the following problem: given two functions f1∈Vf and f2∈Vg, compute f1 + f2.

Given two functions and, which are analytic in, the function is said to be subordinate to, written as (1.11).

Furthermore, given two functions (f,g : varPi rightarrowmathbb{R}), the expected value (6) induces an inner product langle f, g rangle:=mathbb{E} ( f g ) (7) on the Hilbert space (L^{2} varOmega ) = { f : mathbb{E}[ f^{2} ] < infty}).

Given two functions f 1, f 2 in L 1 ( D ) we define the convolution ∗ by: ( f 1 ∗ f 2 ) ( z ) = ∫ G f 1 ( g ⋅ O ) f 2 ( g − 1 ⋅ z ) d g.

We give five functions distributed on interval ([-5,5]).

Given two smooth functions and μ defined on such that in, on, the corresponding variational inequality is as follows: (3.17).

Given two window functions {w}_1(n)={w}_1(n),kern0.5em -nlele nle N/2-1 (14) {w}_2(n)={w}_2(n),kern0.5em -nlele nle N/2-1 (15)where the two window functions can be chosen separately such as rectangle, hamming, and triangle.

According to Schellekens [27], p.540, given two complexity functions f and g, the numerical value (d_{mathcal{C}}(f,g)) (the complexity distance from f to g) can be interpreted as the relative progress made in lowering the complexity by replacing any program P with complexity function f by any program Q with complexity function g.

Let be given two bi-functions satisfying for all and.