Assessment of rubber tree panels under crowns resistant to South American leaf blight

The objective of this work was to assess the performance of panel clones under crowns resistant to South American leaf blight (Microcyclus ulei). The experiment was carried out with 18 panel clones crown-budded with Hevea pauciflora x H. guianensis, in a Xanthic Ferralsol (Oxisol) in Manaus, AM, Brazil. The following parameters were evaluated: dry rubber yield, plant nutritional status, and anatomical and physiological characteristics of the latex vessels. In the first three years of evaluation, the panel clones IAN 2878, IAN 2903, CNS AM 7905, CNS AM 7905 P1, and PB 28/59 showed the highest dry rubber yield potential, while the clones IAN 6158, IAN 6590, and IAN 6515 should not be recommended for crown budding. Higher potassium and copper foliar content in panel clones were associated to an increase in dry rubber yield. The simultaneous evaluation of anatomical and physiological characteristics of latex is fundamental for the selection of panel clones in the Amazon region. Crown budding is an efficient technology for South American leaf blight management in endemic regions

A Fresh Variational-Analysis Look at the Positive Semidefinite Matrices World

International audienceEngineering sciences and applications of mathematics show unambiguously that positive semidefiniteness of matrices is the most important generalization of non-negative real num- bers. This notion of non-negativity for matrices has been well-studied in the literature; it has been the subject of review papers and entire chapters of books. This paper reviews some of the nice, useful properties of positive (semi)definite matrices, and insists in particular on (i) characterizations of positive (semi)definiteness and (ii) the geometrical properties of the set of positive semidefinite matrices. Some properties that turn out to be less well-known have here a special treatment. The use of these properties in optimization, as well as various references to applications, are spread all the way through. The "raison d'être" of this paper is essentially pedagogical; it adopts the viewpoint of variational analysis, shedding new light on the topic. Important, fruitful, and subtle, the positive semidefinite world is a good place to start with this domain of applied mathematics