Sentence examples for dimensional case and from inspiring English sources

The approach has the advantages of being able to handle the high dimensional case and produce affine discrete state space models, readily usable in control engineering applications.

Now we attack this problem by deriving a specialized optimization algorithm based on two ingredients: first, a recently found necessary condition for the quasiconvexity of fourth-degree polynomials that distinguishes between both classes in the three dimensional case, and secondly, upon a characterization of rank-one convex fourth-degree polynomials in terms of infinitely many constraints.

2.2 we consider the boundary rigidity in the two dimensional case and in Sect.

We generalize some of our results to higher dimensional cases and use integral approximation formulas obtained to design numerical schemes for detecting fractional dimensional edges in signal processing.

The general two-dimensional non-separable case poses several challenges which do not exist in the one-dimensional case and the separable two-dimensional case.

This paper presents some theoretical results, first in a two-dimensional case and then extended to a three-dimensional context.

This is computationally demanding in a realistic three-dimensional case and the computational cost needs to be minimized.

We present the one-dimensional case and extend it to two-dimensional problems on tensor-product meshes.

Ray-based devices cannot achieve patterns with high resolution, coherent holographic devices cannot achieve certain intensity patterns, even in the two-dimensional case, and volumetric devices cannot simulate occlusions and suffer from out-of-focus blur.

The stability study is performed using an amplification matrix analysis on a one-dimensional case and allows the determination and optimization of coupling parameters.

These equations are first derived for three-dimensional case and then reduced to the two-dimensional case by expanding mechanical displacement and electric potential as power series.