Sentence examples similar to multi dimensional case from inspiring English sources

In the multi-dimensional case, we consider only radial eigenpairs.

In Section 2, we present two generalizations of Theorem 1.1 to multi-dimensional case.

The results for the multi-dimensional case will be given in the next subsection.

In multi-dimensional case, we dispose of estimations of mode signs for each mode couple option.

In this section, we shall establish two generalizations of Theorem 1.1 to multi-dimensional case.

However, limited results have been obtained about the multi-dimensional case.

The extension of the proposed technique to a multi-dimensional case is straightforward.

In the multi-dimensional case, the radial distance-time section is represented in the frequency-wavenumber plane.

For simplicity of presentation, suppose d=m=1, the multi-dimensional case can be treated with the same method.

(2.1) The extension to a general multi-dimensional case will be presented at the end of this section.

The optimization of activated carburizing for industrial application presented here involved improvement of multi-dimensional case uniformity.