Luis Leopoldo Silva

Topological invariants and renormalization of Lorenz maps

We prove that the invariants of the topological semiconjugation of Lorenz maps with β-transformations remains constant on the renormalization archipelagoes and analyze how the dynamics on the archipelagoes depends on its structure.

Comparative analysis of main on-farm irrigation systems in Portugal

Abstract Traditional irrigation systems still cover a large area of irrigated lands in Portugal. The needs for competitiveness leads to the gradual abandon of traditional systems, resulting in social and economic impacts. Pressurised on-farm irrigation systems provide labour savings but imply important investments. Surface irrigation does not require expensive equipment and is low energy and low labour consuming, if modern systems are implemented. Flexible-pipe, gated-pipe, surge-flow valve and cablegation are the main equipment issues available to Portuguese farmers for modern surface irrigation practice. Conditions for application of these systems have been studied relative to different soil and topographic conditions. Plane land, either horizontal or sloped and undulated fields can be irrigated by surface systems, if a convenient design is accomplished. The adequacy of the irrigation systems has been evaluated and a cost-benefit study was carried out. A case study of a situation with undulated land, representative of South Portugal, is presented in this paper, comparing surface irrigation issues and a sprinkler system. Conclusions show a particular economic interest on adopting surge-valve, gated-pipe and cablegation.

A UNIFIED RENORMALIZATION SCHEME FOR TWO-PIECEWISE MONOTONOUS MAPS OF THE INTERVAL

In this paper we study the relation between symbolic dynamics and renormalization of maps from the interval to itself, with one discontinuity and two branches of continuity and monotonicity. We introduce a symbolic formalism based on kneading theory that permits us to deal, in a unified way, with the four cases that can occur, at the same time. Using this formalism we also study properties of similarity from the four spaces of kneading invariants.

Differential vineyard fertilizer management based on nutrient,s spatio-temporal variability

Conventionally, vineyard fertilizer management has been based on information from composite soil samples and no account has been taken of the existing spatial variability in soil fertility. This study presents a quantitative analysis of soil phosphorus (P2O5) and potassium (K2O) content as well as pH carried out in an 80 ha vineyard, during 2011 and 2013 in order to identify their spatial variability and temporal stability. Additionally a quantitative analysis of plant P2O5 and K2O content was carried out in 2013 with the objective of evaluating the spatial variability of plant nutrients.In 2013 a contact sensor was used to survey soil apparent electrical conductivity (ECa) and an active optical sensor was used to measure the plant Normalized Difference Vegetation Index (NDVI). The results showed a low potential for implementing site-specific management of phosphorus fertilizer but an interesting potential for implementing site-specific management of potassium fertilizer and pH correction. The concentration of P2O5 and K2O in the plant showed a CV<30%, with adequate values in almost the entire area of the field, in contrast to the concentration of these main macronutrients in the topsoil. These results show that for differential nutrient management of vineyards, plant nutrient concentration is a more stable tool than soil nutrients concentration. The ECa and the NDVI presented weak correlations with soil and plant concentration of, , respectively, P2O5 and K2O, which shows that further development of vegetation operational sensors is needed to support decision making in the vineyard fertilization management.