Retraction methods and fixed point free maps with null minimal displacements on unit ball

In this paper we consider the class of H\"older-Lipschitz maps on unit ball $B_X$ of a Banach space $X$, and the question we deal with is whether for any $\alpha\in (0,1)$ and $\lambda>0$ there exists a fixed-point free map $T\colon B_X\to B_X$ such that $\|Tx - Ty\|\leq \lambda\|x - y\|^\alpha$ for all $x, y\in B_X$ and $\mathrm{d}(T,B_X)=0$. We show that if $X$ has a spreading Schauder basis then such a map can always be built, answering a question posed by the first author in \cite{Bar}. In the general case, using a recent approach of R. Medina \cite{M} concerning H\"older retractions of $(r_n)$-flat closed convex sets, we show that for any decreasing null sequence $(r_n)\subset \mathbb{R}$, there exists a fixed-point free mapping $T$ on $B_X$ so that $\|T^nx - T^n y\|\leq r_n(\| x - y\|^\alpha +1)$ for all $x, y\in B_X$ and $n\in\mathbb{N}$. New results related to Lipschitz maps are also obtained.Comment: Comments welcom

Reassessment of exclusion zones of GM cotton in Brazil: the case of Rondônia State.

Cotton (Gossypium hirsutum) was the second crop to received commercial approval to planting GM cultivars in Brazil, in 2005. At that time, the main concern was the possibility of gene flow from GM cottons to affect in situ maintenance of others species sexually compatible ? G. barbadense and G. mustelinum. To avoid this problem, the National Biosafety Technical Commision (CTNBio) conditioned the cultivation of GM cotton to the creation of GM Cotton Exclusion Zones, where just non-GM cultivars could be planted. Cotton cultivation is an important agricultural activity in Brazil and the producers are almost unanimous: fields of GM cultivars yield more, the management is less laborious and the protection against weeds and pests is higher. For these reasons, farmers in the Rondonia, a state included into the exclusion zones, requested CTNBio to remove Rondônia from the exclusion zones. To deliberate, CTNBio asked Embrapa for information. To properly answer, an expedition was performed in 20 of the state?s 52 municipalities, and only one species was found, Gossypium barbadense. Plants were present just in higly anthropized areas, mainly in dooryards of urban and rural houses, and they were maintained as medicinal plants. Plants of G. barbadense were found in 5% to 10% of the houses, protected from gene flow by walls, houses, and trees. There was no signal of interespecifc crossing, even in municipalities were conventional Gossypium hirsutum were planted. The main risk to in situ mainatenance of G. barbadense is the loss of cultural habits resulting from the expansion of the public health care, which increases the use of chemical drugs over medicinal plants. In conclusion, gene flow is not a significant concern to the preservation of Gossypium barbadense in Rondônia, and there is no reason for the state to remain as an exclusion zones

The Copepod Acartia tonsa as live feed for fat snook (Centropomus parallelus) larvae from notochord flexion to advanced metamorphosis.

From early development until the completion of metamorphosis, fat snook (Centropomus parallelus) larvae are commonly fed the rotifers Brachionus spp. and Artemia spp. nauplii. In this study, cultivated copepods Acartia tonsa were evaluated as feed for 15-to 45-day-old larvae. Two experiments were performed using twelve 30-L tanks stocked with 3.3 fat snook larvae L-1. Their initial mean weight and length were 1.35 ± 0.01 mg (mean ± standard deviation) and 3.83 ± 0.33 mm for 15-day-old larvae and 2.79 ± 1.2 mg and 6.99 ± 0.88 mm for 31-day-old larvae. Three dietary treatments were carried out in four replicates, including Rotifer (R), Artemia (A) and/or Copepod (C). Experiment 1 included Diet RA (control), Diet RC and Diet RCA; while experiment 2 included Diet A (control), Diet C and Diet AC. The survival and growth of larvae fed the Diet RCA in experiment 1 were significantly higher than the others. In experiment 2, the inclusion of copepods in the diet did not improve survival and growth, however, larvae fed Diet C had the highest DHA/EPA ratio. We conclude that the copepod Acartia tonsa provides an important nutritional benefit to fat snook larvae undergoing metamorphosis

O futuro do cooperativismo de leite.

bitstream/item/132478/1/Livro-O-futuro-do-cooperativismo.pd

Biodiversity measures in agriculture using DNA.

Introduction; From nature to agriculture: why we need diversity?; Microrganisms and pests associated to plants; Genetic markers and molecular markers; How measures are taken: a brief review on the simplest and most popular tools; Random amplified DNA reveals polymorphism; Repetitive sequences can be especially polymorphic; Sequencing and single nucleotide polymorphism; Markers may help to understand evolution; The gains in plant breeding depends of variance; Conclusion