Adaptive strategies of two Portuguese grapevines varieties (Aragonês. syn. Tempranillo and Trincadeira) face drought: physiological and structural responses.

At Mediterranean regions and particularly in southern Portugal, it is imperative to identify grape varieties more adapted to warm and dry climates in order to overcome future climatic changes. Two Vitis vinifera genotypes, Aragonez (syn. Tempranillo) and Trincadeira, were selected to assess their physiological responses to soil water stress. Vines were subjected to four irrigation regimes: irrigated during all phenological cycle, non-irrigated during all phenological cycle, non irrigated until veraison, irrigated after veraison. Predawn leaf water potential was much higher in Trincadeira than Aragonez in non- irrigated plants. This result is in accordance with its higher stomatal control efficiency in this variety (Trincadeira). Photosynthetic capacity (Amax at saturating light intensity) decreased due to stomatal and biochemical limitations under water stress. However, recovery capacity of leaf water status after irrigation was faster in Trincadeira. Yield and yield x Brix increased when irrigation occurred after veraison, particularly in Trincadeira. These results show that Trincadeira presents a drought adaptation than Aragonez. Ratio of variable to maximum fluorescence Fv/Fm and total leaf chlorophyll related with leaf water potential for both species. Reflectance Normalized Difference Vegetation Index (NDVI705), Red Edge Inflexion Point Index and Photochemical Reflectance Index were related with irrigation treatment. Relative water content and specific leaf area were similar between varieties. In conclusion, we suggested that there is variation among the genotypes and the main physiological parameters for variety selection, for drought, were leaf water potential, stomatal conductance and reflectance indexes.

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).