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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.
Although ambient exposures are measured with some imprecision, these exposure measurement errors are nondifferential with respect to either true ambient exposure or the clinical measurements.
In our specific case the source of uncertainty we address is measurement error in the dependent variable, childlessness, which is measured with some noise in the ACS sample.
Rainwater and river flows can be measured with some accuracy.
The idea that suffering and its alleviation can be measured with some precision is characteristic of the foundation's technocratic, optimistic thinking.
Similar(42)
Slow winds and colder temperatures have been blamed for a surge in airborne pollutants beyond what instruments in the city could measure with some recording an Air Quality Index (AQI) maximum of 999.
So we can measure with some certainty the distance from which Dejan Stankovic scored one of the fastest, and most memorable, of goals in the history of that august stadium.
The quakes' effect on residents' emotional and psychological wellbeing is more difficult to measure, with some seriously traumatised by them at the time and others less so.
Peanuts which are used in this research are measured with respect to some physical properties.
Also, hourly blood glucose measurements were most frequently obtained by fingerstick capillary measures, with some venous and arterial sampling using point-of-care glucose meter, blood gas analyzer and central laboratory measurements.
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