Sentence examples for for any given compact from inspiring English sources

Indeed, for any given compact subset, let.

Thus we have lim n → ∞ ∥ K f n ∥ LB = 0. for any given compact operator K on LB.

It follows from (3.4) that, for any given compact set E in the interior of (R^{3}_), there is a positive orbit of (2.2) leaving ultimately E, which will not return to E afterwards.

In this case, for any given compact set E in the interior of (R^{3}_), we can take sufficiently large C such that bigl{ (x,y,z vert V x,y,z) = C bigr} cap E = emptyset, which implies the non-permanence of system (1.5).

Since by a well-known theorem, for any compact operator (widehat{K}:Xto Y), where X and Y are Banach spaces, the weak convergence (x_{n}stackrel{w}{to}x_{0}) implies the norm convergence (widehat{K}x_{n}towidehat{K}x_{0}) [31], we have lim_{jrightarrowinfty}|Kq_{j}|_{H^{infty}_{mu}}=0, (17) for any given compact operator K from (mathcal{B}^{alpha}_{0}) to (H^{infty}_{mu}).

(1) For a given compact set (bar{mathcal{D}}subsetmathcal {R}^{m+n}), let (d=sup{|w-w^{0}||winbar{mathcal{D}}}), where (w^{0}) is the initial iterate.

For a given compact set (bar{mathcal{D}}subsetmathcal {R}^{m+n}), let (d=sup{|w-w^{0}||winbar{mathcal{D}}}), where (w^{0}) is the initial iterate.

This result holds for every initial condition and for every reference signal in a given compact set of the state space; L2 and L∞ transient performance for the output tracking error are guaranteed in the 'learning phase'.

For a given compaction energy, the samples compacted on dry side of optimum have higher strength and bearing capacity in terms of unsoaked CBR value, but have higher expansion and more strength loss when soaked in water.

(i) For any given, since is compact and convex and is continuous on, then by Lemma 2.3, parametric variational inequality has solutions.

Moreover, for any given and for any compact set, for small enough, we have (4.58).