Sentence examples for compact existence from inspiring English sources

When the life of the Lam family was documented by Thomas Holton, a photographer, from 2003 to 2005, their compact existence within a tiny downtown apartment seemed brimming with optimism and hope.

bIn the real case, when the state space is compact, then the existence follows from the compactness of the set of all probability measures (i.e., Prohorov's Theorem).

We give a necessary and sufficient condition on a positive compact operatorTfor the existence of a singular trace (i.e. a trace vanishing on the finite rank operators) which takes a finite non-zero value onT.

In Section 4, we investigate the asymptotic smoothness of the semi-flow generated by our model and the existence of compact attractor.

We study the existence of compact almost automorphic solutions for a class of integral equations with time-dependent and state-dependent delay.

In Section 4, we state the main results on the existence of compact almost automorphic solutions for Eq. (2) and Eq. (3).

For small initial data with compact support, the global existence problem for timelike minimal hypersurfaces has been considered by Brendle [10] and Lindblad [11].

Now we prove the existence of compact uniform (w.r.t. (hinmathcal {H}(g_{0}))) attractor for the problem (1.1 - 1.3 1.1 - 1.3 external forces (g_{0}in L_{mathrm{C}^^{2}(mathbb{R};H)) in V.

We obtain for H, a closed amenable subgroup of a locally compact group G, the existence of an invariant conditional expectation of CVp G) onto {T∈CVp(G |suppT⊂H}.

Let us also mention that the construction of nontrivial branches of solutions of semilinear equations with exponential nonlinearities allowed Wente to provide counter examples to a conjecture of Hopf [17] concerning the existence of compact (immersed) constant mean curvature surfaces in Euclidean space.

In Section 3, let the forcing term h ( x, t ) satisfy Condition ( C ∗ ); we can prove the existence of compact uniform (w.r.t. σ ∈ H ( σ 0 ), σ 0 ( s ) = ( g 0 ( u, s ), h ( x, s ) ) ) attractor for a non-autonomous suspension bridge equation in E 0. Definition 2.5 ([13]).