Sentence examples for applying the norm from inspiring English sources

Hence, using (8) and applying the norm on (10), we obtain (9), which completes the proof.

Next, we applied the norm (Vert cdot Vert _{lambda}) just for a technical reason to get uniform convergence only under condition (rho E-DP_{o})<1) in the end of the above prho E-DP_{o}

Whatever they may be, the ultimate objective is to consider the Israel-Palestine situation on its own facts and apply the norms of international law to identify three major issues.

Organizations are tools used to apply the norms, rules and regulations needed to create and enforce transactions.

They point out that applying the antidiscrimination norm to disability requires taking account of physical or mental differences among people.

Their model is included in the DG3PD model with parameters L=S=2, μ 1=μ 2=0 and applying the supremum norm to the wavelet coefficients of the oscillating pattern, i.e., ({left |mathcal {W} { cdot }right |}_{ell _{infty }}), instead of the curvelet coefficients ({left | mathcal {C} { cdot }right |}_{ell _{infty }}) as in the DG3PD model.

Zhang et al. experimented with applying the p-norm function instead of max pooling [20].

Hence, in this paper we consider applying the l 1 norm to find the sparsest solution of LCPs, and we obtain the following minimization problem to approximate (1): min x ∈ R n ∥ x ∥ 1 s.t.

Then the error bound would be obtained as follows: E ( x ) ≤ ∥ 2 m ! 4 m 2 m ( k − 1 ) max x ∈ [ 0, 1 ] | u m ( x ) | ∥ 2. Proof Applying the definition of norm in the inner product space, we have ∥ E ( x ) ∥ 2 = ∫ 0 1 [ u ( x ) − C T Ψ ( x ) ] 2 d x.

Some new existence results of at least one positive solution are established by applying the Leggett-Williams norm-type theorem due to O'Regan and Zima [16].

We apply the Frobenius norm ‖S‖F as a criterion for selection of the best amplitudes to use for a more stable and significant angle estimation.