Sentence examples for use the norm from inspiring English sources

Hence we will use the norm ∥ u ∥ = | ∇ u | p ( x ) for all u ∈ W 0 1, p ( x ).

In this paper, we use the norm defined in (2.3), which is an equivalent norm in E p × p with norm (2.4).

We first present a credit evolution model to quantify the expected credit variation of each node in WMN, then use the norm of the expected credits variation to quantify the credit disparity.

Finally, one can use the norm to define a metric (or distance function) on C 0 ( [ a, b ] ) by d h ( f, g ) = ∥ f − g ∥ h = var h ( f − g ).

We also use the norm (|mathbf{z}|_{mathbf{H}(operatorname{div},Omega)}=(| mathbf{z}|^{2}+|operatorname{div}mathbf{z}|^{2})^{frac{1}{2}}) of the space (mathbf{H}(operatorname{div},Omega)).

Then (2.2) and (2.3) show that ∥ ⋅ ∥ and ∥ ⋅ ∥ H are two equivalent norms on E. Henceforth we use the norm ∥ ⋅ ∥ as the norm for E. And the spaces M, N are mutually orthogonal with respect to the associated inner product.

For, we use the norms and and denote the norm in by.

Using the norm as comparative level is useful and easy.

Using the norm bound given by small gain theorem SGT), robustness of the proposed control system is evaluated.

One of the most important results for solving (1.1) using the norm topology is the following result due to Dhage [12].

We give stability criteria by establishing the desired inequalities via using the norm estimation of the delayed matrix cosine and sine of polynomial degree.