Sentence examples for a minimal dimension from inspiring English sources

Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy.

Focusing on symmetric cross-ply laminates, an effective minimal dimension reduction is then pursued by expressing both in-plane displacement components and shear angles in terms of transverse displacement and thermal variables via kinematic condensations.

The skew field of quaternions ℍ gives an example of a noncommutative Clifford algebra with minimal dimension.

36 However, there remains the question of whether the mechanical response of a tapered sub-micron pillar that deforms locally at the sample top due to stress concentrations 36 is comparable to that of a larger sample volume with the same minimal dimension.

As we can see, there is a minimal economic dimension of the upgrading project that, in very degraded context, can be relatively high (because the initial real-estate value is very low).

The false nearest neighbors algorithm was adopted to acquire a minimal embedding dimension from the input output data as the system order, and then the eigensystem realization algorithm (ERA) was used to initialize a best-fit state-space representation according to the acquired system order.

The model with arbitrary geometry, inertia distribution and frictions are obtained based on a structured Boltzmann–Hamel d'Alembert formulation, and then the estimation equations are explicitly expressed in terms of a linear form with respect to the base parameters of minimal dimension to be identified.

The same authors have proven that the minimal dimension of data bases is equal to the maximum number of input edges of any black-box node in the network.

In fact, in dimension 2 the condition ( mathcal {P}_E ( frac{1}{2}) < 0 ) is equivalent to the trapped set being filamentary in the sense that ( dim K_E < 2 ), that is the trapped set is below the mean of the maximal dimension 3 and the minimal dimension 1 (direction of the flow).

Atomic force microscopy (AFM) [see Supplemental Material, "Tapping Mode Atomic Force Microscopy (AFM)," pp. 6 7] is another viable option and would be the preferred form of microscopy for plate-like materials or those that tend to orient themselves on surfaces with their minimal dimension oriented upward.

Even though the resulting model was likely to be slightly smaller than the authentic size (Supplementary Figure S2), it provided an estimate of the minimal dimensions of the HEZ 'core' region, showing a cone with flattened top, with a diameter (2 Rb) of 119 nm at its basis and an approximated height (hapex) of 96 nm.