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.
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.
Although such quantities are somewhat abstract, recent scientometric analyses have shown that they may be measured with some degree of accuracy, such as Jones' [19] quantification of an individual's lifetime innovation potential, and the decrease in this potential over the last century due to longer training periods (see Figure 2B).
T4 tails are stable for years, large enough to be measured with some certainty, and small enough to be numerous in a field.
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.
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.
Although some approaches have been recently proposed to solve this classical problem [35], most available HRTF databases have been measured with some practical resolution.
Inevitably, diet was measured with some error, although this would most likely result in nondifferential misclassification with respect to disease status and likely underestimation of risk.
To test the in vitro inhibition of lipid peroxidation by the extracts, lipid peroxidation induced by Fe2+/ascorbate system in mouse liver homogenate was used and thiobarbituric acid-reactive substances (TBARS) were measured with some modifications [ 20].
