Above ground biomass functions with vegetation indices for multiple use systems of two evergreen oaks

Remote sensing is a promising approach for above ground biomass estimation, as forest parameters can be obtained indirectly. The analysis in space and time is quite straight forward due to the flexibility of the method to determine forest crown parameters with remote sensing. It can be used to evaluate and monitoring for example the development of a forest area in time and the impact of disturbances, such as silvicultural practices or deforestation. The vegetation indices, which condense data in a quantitative numeric manner, have been used to estimate several forest parameters, such as the volume, basal area and above ground biomass. The objective of this study was the development of allometric functions to estimate above ground biomass using vegetation indices as independent variables. The vegetation indices used were the Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Simple Ratio (SR) and Soil-Adjusted Vegetation Index (SAVI). QuickBird satellite data, with 0.70 m of spatial resolution, was orthorectified, geometrically and atmospheric corrected, and the digital number were converted to top of atmosphere reflectance (ToA). Forest inventory data and published allometric functions at tree level were used to estimate above ground biomass per plot. Linear functions were fitted for the monospecies and multispecies stands of two evergreen oaks (Quercus suber and Quercus rotundifolia) in multiple use systems, montados. The allometric above ground biomass functions were fitted considering the mean and the median of each vegetation index per grid as independent variable. Species composition as a dummy variable was also considered as an independent variable. The linear functions with better performance are those with mean NDVI or mean SR as independent variable. Noteworthy is that the two better functions for monospecies cork oak stands have median NDVI or median SR as independent variable. When species composition dummy variables are included in the function (with stepwise regression) the best model has median NDVI as independent variable. The vegetation indices with the worse model performance were EVI and SAVI.

Systems of coupled clamped beams equations with full nonlinear terms: Existence and location results

This work gives sufficient conditions for the solvability of the fourth order coupled system┊ u⁽⁴⁾(t)=f(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) v⁽⁴⁾(t)=h(t,u(t),u′(t),u′′(t),u′′′(t),v(t),v′(t),v′′(t),v′′′(t)) with f,h: [0,1]×ℝ⁸→ℝ some L¹- Carathéodory functions, and the boundary conditions {┊ u(0)=u′(0)=u′′(0)=u′′(1)=0 v(0)=v′(0)=v′′(0)=v′′(1)=0. To the best of our knowledge, it is the first time in the literature where two beam equations are considered with full nonlinearities, that is, with dependence on all derivatives of u and v. An application to the study of the bending of two elastic coupled campled beams is considered.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).