Sentence examples for be an open nonempty from inspiring English sources

Now we let G be an open nonempty subset of C ( T ).

Let Ω be an open nonempty bounded subset of (mathbb{R}^{3}) with a Lyapunov boundary ∂Ω.

Let Ω be an open nonempty bounded subset of (mathbb{R}^{3}) with a Lyapunov boundary ∂Ω, (uin H^{alpha}(partialOmega,Cl(V_{3,3}))), (0

where is an open nonempty set of and is the characteristic function of.

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.

We prove the interior approximate controllability for the following reaction-diffusion system with cross-diffusion matrix in, in,, on,,,, where is a bounded domain in,, the diffusion matrix 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.

We study the following reaction-diffusion system with a cross-diffusion matrix and fractional derivatives in, in, on,, in where is a smooth bounded domain,, the diffusion matrix has semisimple and positive eigenvalues,, is an open nonempty set, and is the characteristic function of.

Let ω be an open and nonempty subset of Ω.

Let (omega= a,b)) be an open and nonempty subset of ((0,1)), (chi_{omega}) represent the characteristic function of ω.

Let Ω be an open bounded nonempty subset of (mathbb{R}^{3}) with a Lyapunov boundary ∂Ω, (u(mathbf{x})=sum_{A}e_{A}u_{A}(mathbf{x})), where (u_{A}(mathbf{x})) are real functions.

Let X and Y be two Banach spaces with the norms (Vert cdot Vert _{X}) and (Vert cdot Vert _{Y}) respectively, and (Omega subset X) be an open bounded nonempty set.