Sentence examples for arbitrary norm from inspiring English sources

In the sequel, we use (vert wvert _{0}=max_{sin[-h,0]}Vert w(s Vert ), where (Vert cdot Vert ) is an arbitrary norm in X.

On the other hand, the norm is with the property of positive homogeneity, ∥(−1)·w g ∥ any =∥w g ∥ any, where " ∥·∥ any " can be arbitrary norm such as ∥·∥1 and ∥·∥2.

Throughout this section, we assume that the real Euclid space of d dimensions (mathbb{R}^{d}) is endowed with an arbitrary norm (vert cdot vert ), and the space (C mathbb{R}_, mathbb{R}^{d})) is endowed with the family of seminorms begin{aligned} vert xvert _{T}:=sup_{tin[0,T]}biglvert x t) bigrvert,quad T>0.

For arbitrary norm or antinorm ||.||, h A (x)=||x||, and for all (tilde Min mathcal B^{d}cap S), S={x:||x||=1}, O_{S} tilde M =intlimits_{left{vartheta=(x_{1},ldots,x_{d-1}):(vartheta,x_{d} vartheta))^{T}intilde Mright}} h_{K^(N vartheta))dvartheta where K ∗ is the unit ball of the norm ||.||∗ being dual to the norm ||.|| in the first case, and the antipolar set of K={x:||x||≤1} in the second one.

For an arbitrary norm convergent sequence { u n } in ℋ with limit u, start with an arbitrary x 1 = y 1 ∈ H and define two sequences { x n } and { y n } by x n + 1 = a n u + b n J β n B x n + c n J α n A x n + d n e n ; y n + 1 = a n u n + b n J β n B y n + c n J α n A y n + d n v n.

Malocclusion differs from the majority of medical and dental conditions in that it is 'a set of dental deviations' rather than a disease, and orthodontic treatment does not cure a condition but rather corrects variations from an arbitrary norm [ 4].

Recently, Grayver and Kuvshinov (2016) applied arbitrary norms for residual and regularization terms to produce classes of equivalent solutions of smooth or compact models, in which a L 1.5 norm was shown to be most efficient for a stable inversion with sharp boundary.

Now, we give two important examples of multi-norms for an arbitrary normed space E [8].

Now we state two important examples of multi-norms for an arbitrary normed space E; cf. [10].

We use the standard symbol ∥ ⋅ ∥ for an arbitrary vector norm.

We show that (un) has a subsequence (u′n) such that eachu′ncan be expressed as a finite sum (plus a remainder) of translations/dilations of functionsφmand such that the remainder has arbitrary small norm inLq(1/q=(1/p)−(s/d)).