Using the unitemporal MODIS data (1a), burn scars are divided among the second and third components.
According to PCA, the environmental factors accept LA and AL, mainly contributed to the second and third components.
The optimization procedure previously described has shown a serious problem: the objective function is heavily dependent on the fleet dimension (first component of s) and slightly dependent on threshold values (second and third components of s).
The function f : ( 0, 1 ] × [ 0, ∞ ) × [ 0, ∞ ) → [ 0, ∞ ) is continuous, lim t → 0 + f ( t, ⋅, ⋅ ) = ∞ for all t ∈ ( 0, 1 ], and nondecreasing with respect to the first component, decreasing with respect to its second and third components.
The first and third components exhibit a shearing-type behaviour inclined at 45 ° from the horizontal and 90 ° from one another; the second again shows a similar shearing-type behaviour but now roughly parallel to the fast-scan (horizontal) direction.
where α ∈ R such that 3 < α ≤ 4, D 0 + α is the Riemann-Liouville fractional derivative and f : ( 0, 1 ] × [ 0, ∞ ) × [ 0, ∞ ) → [ 0, ∞ ) is continuous, lim t → 0 + f ( t, ⋅, ⋅ ) = + ∞ (f is singular at t = 0 ) for all t ∈ ( 0, 1 ], f ( t, ⋅, ⋅ ) is nondecreasing with respect to the first component and decreasing with respect to its second and third components.
