Sentence examples for be the open subset from inspiring English sources

Following the idea of Katriel [16], we take U to be the open subset of D given by U=Bigl{ (S,I in D bigm| min_{tin[0,T]}S t)< deltaBigr}, (2.3) where (deltain 0,1)) is to be fixed.

end{aligned} (4.2)In the case of an even dimension N, the domain of definition of this formula is a complex torus (T^+ := T_1 times T_0^+) where (T_1 = (mathbb {C}^times )^n) and (T_0^+ subset (mathbb {C}^times )^n) is the open subset determined by the conditions (|t_{0,j} | = mathrm {e}^{ mathfrak {Re}, phi _j} > 1) for all (j,).

The most familiar example, of course, is that in which O, C are the open and closed subsets, respectively, of a topological space.

For K ∈ K o n, let σ ( K ) ⊂ S n − 1 denote the compact set that is the support of the i th surface area measure S i ( K, ⋅ ) of K; i.e., ω = S n − 1 ∖ σ ( K ) is the largest open subset of S n − 1 for which S i ( K, ω ) = 0. Let v ( K ) ⊂ S n − 1 denote the set of extreme normal directions of ∂K.

Let be Banach space, be a bounded open subset of, and be a completely continuous operator.

Let be an open subset of the real line or of the complex plane.

To formulate the problem, let M be an open subset of H in which the parameter λ takes values.

Let be a bounded open subset of, be proper and satisfy (3.11), (3.12).

Let U be an open subset of g.

Let be an open subset of,, and.

Let Γ ⊆ ∂ M be an open subset.