Sentence examples for dimensional extension of from inspiring English sources

The formal infinite dimensional extension of the Sard inequality,μ TA)⩽∫A |Lambda;| dμ,is shown to hold and applications to absolute continuity on Wiener space are presented.

Our approach is a direct infinite dimensional extension of the finite-dimensional feedback linearization/backstepping approaches and employs spatial Volterra series nonlinear operators both in the transformation to a stable linear PDE and in the feedback law.

In this paper, we implement for the first time a two dimensional extension of the spring-block model, applying it to structured surfaces and investigating by means of numerical simulations the frictional behaviour of a surface in the presence of features like cavities, pillars or complex anisotropic structures.

We call the operators ˜A symplectic dimensional extensions of A. In this paper we study the relation between A and ˜A in detail, in particular their regularity, invertibility and spectral properties.

Then, we summarize our multi-dimensional extension of AIC and MDL.

The proposed model is a three-dimensional extension of the nine-unit soil landscape model.

We also introduce a multi-dimensional extension of the multi-overlap algorithm.

(3) (mathbb {K}_mathrm {u}(X)) is not a finite-dimensional extension of a properly infinite (mathbb {K} -algebra.  .

(mathbb {K}_mathrm {u}(X)) is not a finite-dimensional extension of a properly infinite (mathbb {K} -algebra.

(3) (Rightarrow ) (1): Assume that (mathbb {K}_mathrm {u}(X)) is not a finite-dimensional extension of a properly infinite (mathbb {K} -algebra.

To derive the proposed multi-dimensional extension of the M-EFT algorithm, namely the R-D EFT, we start by looking at an R-dimensional noise-only case.