Sentence examples for the dimension itself from inspiring English sources

Section IV describes a simulation experiment designed to investigate the effect of different scales of error variability on the accuracy of different methods of dimension estimation (both in estimating the dimension itself and in the impact on Root-Mean-Squared-Error (RMSE)).

Even from the very beginning, when Mandelbrot introduced the fractal geometry, he was aware of the fact that the fractal dimension itself is not sufficient to fully capture the complexity of nondeterministic objects; therefore, he defined the lacunarity as a complementary metric.

The preference for treatment may be related to the prevention-treatment dimension itself, but also to variations on other dimensions that are inherently linked to prevention and treatment (like different efficacy rates and costs per treatment).

"Flatland" challenged the familiar conception of three dimensions; "Flatterland" challenges the familiar conception of dimension itself.

The union, however, is not without an international dimension itself.

This is an increase in scale by increment: the application of the cosmological constant, the incremental expansion of the dimension of space itself, an objective measure, on to subjective space.

Horizontal (d h ), vertical (d v ) distances and height of trapper were varied depending on the size of microparticles, while the dimension of trapper itself was fixed Fig. 3 Numerically simulated streamlines and velocity magnitude contour plots of (a) before and (b) after capturing microparticles.

In each case the quotient of the two quantities of the same dimension is itself a pure number without dimensions.

Interpretation of historical texts by Husserl et al. has played a prominent role in this work, both because the texts are rich and difficult and because the historical dimension is itself part of the practice of continental European philosophy.

The method proposed in this paper provides such POD manifold with a small number of snapshots, comparable to the dimension of the POD manifold itself, which is a crucial step for the computational efficiency of the proposed database generation method.

However, despite the fact that after growth templates removal indicates a diminutive problem and effect on the grown-up nanostructures, this method shows a strict limitation on the reducing of the nanorods or nanotubes diameter as an inadequacy in controlling the dimension of the AAO template itself.