Sentence examples for dimensional extension 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.

This is done by employing a method of Putinar and Vasilescu [M. Putinar, F.-H. Vasilescu, Solving moment problems by dimensional extension, Ann. of Math. (2) 1999(3) (1087 1107]–1107] for the corresponding multidimensional moment problem.

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.

He held that space is not a limit but a three-dimensional extension, that it is infinite, and that, contrary to Aristotle, the existence of a vacuum and of more worlds than one is possible.

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

In this section, the PSO algorithm, its multi-dimensional extension, and the FGBF technique are introduced.

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.

For the 3-dimensional extension, the converged Taylor dispersion values increase with decreasing aspect ratios.

Consequently the new multi-dimensional extension can be easily implemented in existing solvers.