Sentence examples for a norm function from inspiring English sources

Since we have constraints 2 and 3, we can induce a norm function p(x)=d(x−0) which satisfies the norm definition.

By denoting (rho xi,e)) simply by (rho xi)), we define a norm function (rho xi) in C^{infty}(Gbackslash{e}) cap C(G)) such that (1) (rho xi) = 0) if and only if (xi= e);   (2) (rho xi) = rho xi^{ - 1}));   (3) (rho(delta_{lambda}(xi)) = lambdarho xi)), (lambda > 0).

If the function f corresponds to a norm function, such as that used to order the Gaussian integers above, then the domain is known as norm-Euclidean.

Converse is not true because the norm function of a HL integrable mapping is not necessarily HL integrable or HK integrable.

where |. | in Equation 7 represents the norm function of a vector, and θ and φ are the angles between the vector c and vectors (x* − x I ) and (x o − x I ), respectively.

The norm function for a 70yr old crystalline lens is calculated following Eq. (3).

They consider three Hamiltonians on (L^2({mathbb {R}}^2,d^2 x)): begin{aligned} H_0=-frac{partial ^2}{partial x_1^2}-frac{partial ^2}{partial x_2^2}; quad H_1=H_0+V(x_2);quad H=H_1+K end{aligned} (13.15 where (V in L^1({mathbb {R}} cap L^2({mathbb {R}})) and K is a rank 1 operator, (Ku = clangle varphi,u rangle varphi ) with (varphi ) a norm 1 function in (L^2({mathbb {R}}^2)) and c is a constant.

The norm function captures the 'size' of the signals.

GF: the final norm function evaluations (p(x)) when the program is stopped.

An example of this mapping is the norm function used to order the Gaussian integers above.

The failure criterion of a spot weld as a function of the axial load and the shear load is expressed as a different function from an elliptic function, which was proposed in previous researches: the different function is called a β-norm function in this paper.