Sentence examples for small norms from inspiring English sources

Meyer's decomposition framework models the various components of the decomposition as having small norms in different Banach spaces, i.e. complete normed vector spaces.

It is assumed that the matrices defining the delayed dynamics have sufficiently small norms and that the norm of the error matrix of the delay-free dynamics with respect to its limiting value is also sufficiently small.

However, according to [2, 24], "oscillatory components do not have small norms in L 2 or L 1." In our case, we use the Banach ({left |{mathcal {C}}{ cdot }right |}) which is more suitable than the Banach space (E = B^{-1}_{infty, infty }) in equation (1.3) [3] for measuring small-scale objects, e.g., noise.

we look for solutions y 1 ( t ), y 2 ( t ) : R → R 2 of F ( y 1 ) + ε H 1 ( y 1, y 2, η, ε ) = 0, F ( y 2 ) + ε H 2 ( y 1, y 2, η, ε ) = 0 (35). in the Banach space of C 1 -functions on ℝ, bounded together with their derivatives and with small norms.

However, we can conjecture that the variation vector has small norm for a random complex matrix.

More importantly, the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices.

If the variation vector has a small norm, then the new detection order will be nearly the same as the optimal detection order.

We establish Lp-solvability for 1small 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)).

In the case of regression, the objective is to find a hyperplane with small norm while simultaneously minimize the sum of the distances from the data points to the hyperplane.

More precisely we will prove the existence of a function u defined on Σ and of small norm such that its normal graph S u over Σ has vanishing mean curvature and the scalar product of the unit normal vectors, ( N S u ) i ⋅ ν i, equals ψ i at each point of the i th component of ∂ S u, with i ∈ { 1, 2, 3 }.