Sentence examples for measured data function from inspiring English sources

Since the data (varphi(r)) is based on (physical) observation, there must be measurement errors, and we assume the measured data function (varphi^{delta}(r)in L^{2}[0,r_{0};r^{2}]), and it satisfies biglVert varphi(cdot -varphi^{delta}(cdot -varphi^{delta}lta, (2) where (delta>0) is the measurable error level.

We assume the measured data function g δ ( x ) ∈ L 2 ( R ).

However, the measured data function g δ ( x ), which is merely in L 2 ( R ), does not posses such a decay property in general.

There will be measured data function g δ ( x ) which is merely in L 2 ( R ) and satisfies ∥ g − g δ ∥ L 2 ( R ) ≤ δ, (1.2).

In applications, input data g ( x ) can only be measured, there will be measured data function g δ ( x ) which is merely in L 2 ( R ), and it satisfies ∥ g − g δ ∥ L 2 ( R ) ≤ δ, (1.2).

But the measured data function (varphi^{delta}(r)) only belongs to (L^{2}[0,r_{0};r^{2}]), we cannot expect it has the same decay rate in (L^{2}[0,r_{0};r^{2}]).

(1.4) where α plays a role of regularization parameter, data (g^{delta}) represents the measured data of function g.

As a consequence, we can fast and accurately estimate the unknown rigidity function and planar inertial function with the help of the first three natural frequencies, and the supplemented measured data of recovered function on two boundaries.

In addition, the calculated chemical potentials or activities of Ni and Al are also in accord with the measured data as a function of temperature using mass spectrometry.

The model was validated against measured data of Modulation Transfer Function (MTF), Noise-Power Spectrum (NPS), and Detective Quantum Efficiency (DQE).

The Weibull parameters are determined based on the wind distribution statistics calculated from the measured data, using the gamma function.