Sentence examples for respective norms from inspiring English sources

Thus, and are, respectively, the supremum norms on for vector and matrix functions of domains in respectively, in defined from their pointwise respective norms for each. is the n th identity matrix.

Evidently, and are Banach spaces with respective norms (1.3).

It is clear that and are Banach spaces with respective norms.

The respective norms can be defined as (lVert urVert=sup{vert u(t) vert :0leq tleq1 }) and (lVert vrVert=sup{vert v t) vert :0leq tleq1 }).

Note that P C ( J ) and P C 1 ( J ) are Banach spaces with the respective norms ∥ x ∥ ∞ = sup { | x ( t ) | : t ∈ J }, ∥ x ∥ = max { ∥ x ∥ ∞, ∥ x ′ ∥ ∞ }.

The convergence rates for q and p are (1+gamma+frac{beta}{2}) under the respective norms, which are almost close to the prediction of Theorem 4.1.

X 1, X 2, and H are completion spaces of X under the respective norm.

It is shown that the space (J) of test white noise functionals has an analytic version A∞ which is an algebra as well as a topological linear space topologized by the projective limit of a sequence {Ap:pϵN} of Banach spaces with respective norm given by ∥ƒ∥Ap=supZϵCJ−p{|ƒ z)|exp[−2−1∥z∥]p2]}, where SJ−p denotes the complexification of J−p.

Can't Fabio see that, underneath it all, when you strip off the outer epidermis, and correct for facial structure, height, musculature and respective ethnographic norms of penis-size, we're all the same?

Let T : X 0 → Y 0 be a linear operator with T (X 1 ) ⊆ Y 1. Assume that T : X 0 → Y 0 as well as T : X 1 → Y 1 are continuous, i.e., (35) ‖ Tx ‖ Y 0 ≤ C 1 ‖ x ‖ X 0 for all x ∈ X 0, ‖ Tx ‖ Y 1 ≤ C 2 ‖ x ‖ X 1 for all x ∈ X 1, with the respective operator norms C 1, C 2 > 0. Let 0 < s < 1 and X s = [ X 0 ; X 1 ] s and Y s = [ Y 0 ; Y 1 ] s.

The innovation vector can be considered as an indicator of the amount of information introduced in the system by the actual measurements and the respective normalized norm can be used again as the measurement quality indicator.