Sentence examples for with some measurement from inspiring English sources

In reality, they can only be measured with some measurement errors, and we would actually have noisy data: φ ϵ ( x ) = ∑ p = 1 ∞ φ p ϵ sin p x, g ϵ ( x ) = ∑ p = 1 ∞ g p ϵ sin p x. for which ∥ φ ϵ − φ ∥ ≤ ϵ, ∥ g ϵ − g ∥ ≤ ϵ.

Physically, φ can only be measured with some measurement errors, and we would actually have a disturbed data function φ ϵ ( x, y ) = ∑ p, q = 1 ∞ φ p q ϵ sin p x sin q y ∈ L 2 , g ϵ ( x, y ) = ∑ p, q = 1 ∞ g p q ϵ sin p x sin q y ∈ L 2. for which ∥ φ ϵ − φ ∥ ≤ ϵ, ∥ g ϵ − g ∥ ≤ ϵ, where the constant ϵ > 0 represents a bound on the measurement error, ∥ ⋅ ∥ denotes the L 2 -norm.

There was a borderline statistically significant median 10-degree difference in flexion at 2 years in favor of the Ti implants; however, these measurements were encumbered with some measurement uncertainty (as they were measured with plastic protractors) that we believe would overshadow the importance of the clinical difference.

With the aid of computer simulation based on a simple heat conduction model together with some measurement results, this work presents a rapid evaluating tool for predicting the peak temperature of a heatsink by using the concept of effective heat conductivity.

Some of the existing no-reference perceptual quality assessment methods are composed of a set of spatial features combined with some measurement of artifacts.

The success of the ordering can be evaluated not only with code coverage and model coverage, but also with some measurement methods such as APFD [14] and APXC [11].

The authors would like to thank M. Nicotra, Y. Zhang and M. Allan for assistance with some measurements.

The KPIX structure is presented along with some measurements characterizing its performance.

The determination of the optimal setting of oven temperature and the DC gradient in the spin-filter will be presented and illustrated with some measurements.

Simulation results of the entire behavior of the circuit before submission are presented along with some measurements of the actual chip response.

The estimated stretch rate at x/D = 53.5 is about 50 10 s-1, while at x/D = 107 the stretch rate is about 10 s-1 with some measurements at adiabatic equilibrium.