Sentence examples for relatively bounded from inspiring English sources

It has three steps: (1) The Kato Rellich theorem which reduces the proof to showing that each (V_{ij}) is relatively bounded for Laplacian on ({mathbb {R}}^3) with relative bound 0.   (2) A proof that any function in (L^2({mathbb {R}}^3)+L^infty ({mathbb {R}}^3)), as an operator on (L^2({mathbb {R}}^3)), is (-Delta )-bounded with relative bound 0. This relies on a simple Sobolev estimate.

Let P be a solid cone of real Banach space E, Ω be a relatively bounded open set of P, (A Pmapsto P) be a completely continuous operator.

Let X be a solid cone of a Banach space E ( X ∘ is nonempty), let Ω be a relatively bounded open subset of X, and let A : X → X be a completely continuous operator.

Then B is relatively form bounded with relative form bound at most (alpha ).

The form t is called relatively form bounded with respect to (mathbf{t}_{A}) ((mathbf{t}_{A} -bounded) if (operA} -boundedm}(mathbf {t}_{A})subset operatorname{Dom}(mathbf{t})) and there are posifive coperatorname{ such that bigl|mathbf{t}[f]bigr|leqslant amathbf{t}_{A}[f]+b| f |_{mathfrak{H} }^{2},quaDominoperatorname{Dom}( mathbf{t}_{A}).

Yes, that's the work I did for the Army Research Office from 2006 to 2009, looking at a proof of concept prototype system as a means to enforcing the international humanitarian law in relatively narrow, bounded circumstances.

The Petitcodiac river valley at Moncton is broad and relatively flat, bounded by a long ridge to the north (Lutes Mountain) and by the rugged Caledonia Highlands to the south.

Another reason: The region is relatively small, and bounded.

Corollary 2.15 A bounded relatively compact subset in a circular metric space is totally bounded.

It is well known that epitaxial films of III-nitrides grow in columnar structures of relatively perfect material bounded by dislocation arrays (the so-called mosaic model) [14 16].

(Basic Estimate) Let (Omega ) be a smoothly bounded relatively compact domain in a Kähler manifold ((X,omega )), and assume the boundary of (Omega ) is (q -positive with respect to (omega ).