Sentence examples for be an arbitrary open from inspiring English sources

Let L be a second order elliptic differential operator and let D be an arbitrary open subset of Rd.

Let D be an arbitrary open subset of Rd and let U D), V(D) and H D) stand for the sets of all positive solutions in D for three equations mentioned above.

Let be an arbitrary open set, and.

Let be an arbitrary open subset of, and let.

To complete the proof, let be an arbitrary open subset of.

Now let U ( x, c ) be an arbitrary open ball in the cone metric space ( X, d ).

(3.2). in (3.2) is an arbitrary open subset of.

For instance, if Ω is an arbitrary open subset of R n and p ∈ ] n / 2, + ∞ [, a bound of type (1.2) and a consequent uniqueness result can be found in [2].

Let be an open subset and be an arbitrary local homeomorphism with.

Let be an arbitrary graph.

where is a bounded domain in,, the diffusion matrix (1.2). has semisimple and positive eigenvalues, is an arbitrary constant, is an open nonempty subset of, denotes the characteristic function of the set, and the distributed controls.