Sentence examples for spaces variable from inspiring English sources

It is well known that Musielak-Orlicz spaces include many spaces as special spaces, such as Lebesgue spaces, weighted Lebesgue spaces, variable Lebesgue spaces and Orlicz spaces; see [1].

Each state-space variable was modeled as follows: (3).

PCA [16] is applied for reduction of the descriptor space (variable space).

The transformed solutions are obtained using the Fourier transform on the space variable.

Thus, we propose a minimal state-space variable representation that prevents this shortcoming.

The functions F, G, and Σ are locally Lipschitz continuous in the space variable z.

Especially, the nonlinearity f permits the singularity on the space variable.

Problem P does not admit any non-trivial solution independent of the space variable x.

In the first step, let us use the discretization in the space variable x.

F x u denotes the Fourier transformation of u with respect to its space variable.

Step 3: Discretize the space variable X in the bilinear equations (15) and (16).