Basic tools in this field (orthogonal polynomials, moduli of smoothness, K-functionals, etc). as well as some selected applications in numerical integration, integral equations, moment-preserving approximation and summation of slowly convergent series are also given.
It is well known that the measure of noncompactness is a very powerful tool to deal with differential equations [17 20], difference equations [21 23], integration equations [24], and differential inclusions [25, 26].
The residuals υ it are assumed to be normally distributed, and white noise is the one-period lagged error correction term derived from the co-integration equation.
According the Table 6, the long-term co-integration equation between the international Brent crude oil prices and influential variables is shown in Eq. (12).
If the linear combination of these non-stationary variables can form a stationary time series, the resulting linear combination is called a co-integration equation, which means these variables exhibit a co-integration relationship.
Figure 1a illustrates the progressive loss of the cellulose crystalline peaks with increasing ballmilling time, leading to the generation of a purely amorphous profile, which was subtracted for crystallinity integrations (equation 3, Methods).
The rates are analyzed in terms of a function f(Z,Qβ) calculated by integration of equation (7) with correction factor F Z,W).
Integration of equation (1) gives ΔS (i.e., SLR) in m relative to pre-industrial times (AD1700): All calculations are performed in m y−1, but we present results in m cy−1 for comparison with previous studies.
Integration of Equation (4) gives: (5).
Integration of Equation 9 allows for the modeling of Phe loss through time.
