GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Relationship between eggplant seed morphology and germination

Structural differences such as abnormalities, damage and free spaces in seeds may affect germination. The aim of this study was to study the relationship between eggplant seed morphology and seed germination. Ten seed lots of the eggplant cultivar Embu were evaluated by X-ray image analysis and the germination test. Seed image analysis was performed by Image Pro Plus® software and the whole seed area and free space between the embryo and endosperm were measured. The internal seed area filled by the embryo and endosperm was calculated from the difference between the whole seed and free space areas. Based on these results and visual seed analysis, seeds were classified into three categories and information on germination was obtained for each one. X-ray image analysis provides a perfect view of the internal seed parts and for seed morphology studies. An increase in seed area filled by the endosperm and embryo does not improve seed germination. Mechanical seed damage and deteriorated tissues can adversely affect seed germination.

Alimentação hospitalar: proposições para a qualificação do Serviço de Alimentação e Nutrição, avaliadas pela comunidade científica

The scope of this paper is to validate proposals used to qualify hospital food by the Brazilian scientific community. An electronic questionnaire was applied to clinical nutrition professionals registered on the Lattes Platform (Brazilian database of institutions and researchers' curricula in the areas of Science and Technology). The questionnaire incorporated a Likert scale and had spaces for comments. The themes dealt with patient participation, the nutritional and sensory quality of hospital diets, and planning and goals of the Hospital Food and Nutrition Service (HFNS). The questionnaire also asked for the top five priorities for a HFNS. Proposals with total or partial adherence equal to or greater than 70% were considered to be approved. All proposals had total adherence equal to or greater than 70%. The proposal that had minimal adherence (70%) was the one that proposed that nutritional intervention must be arranged by mutual agreement with the patient. The proposal that had maximal adherence (93%) was the one advocating that there must be statistical control on diets prescribed by the HFNS. The most cited priorities referred to infrastructure and training of human resources (40%), the quality of hospital food (27%) and the nutritional status of the patient.

Aerial organ anatomy of Smilax syphilitica (Smilacaceae)

Smilax L. in Brazil is represented by 32 taxa and it is a taxonomically difficult genus because the plants are dioecious and show wide phenotypic variation. The analysis and use of leaf anatomy characters is recognized as a frequently successful taxonomic method to distinguish between individual taxon, when floral material is absent or minute differences in flowers and foliage exist such as in Smilax. The aim of this study was to characterize the anatomical features of the aerial organs in Smilax syphilitica collected from the Atlantic Rainforest, in Santa Teresa-ES and the Smilax aff syphilitica from the Amazon Rainforest, in Manaus, Brazil. For this, a total of three samples of Smilax were collected per site. Sample leaves and stems were fixed with FAA 50, embedded in historesin, sectioned on a rotary microtome, stained and mounted in synthetic resin. Additionally, histochemical tests were performed and cuticle ornamentation was analyzed with standard scanning electron microscopy. S. syphilitica and S. aff syphilitica differed in cuticle ornamentation, epidermal cell arrangement and wall thickness, stomata type and orientation, calcium oxalate crystal type, and position of stem thorns. Leaf blades of S. syphilitica from the Amazon Rainforest have a network of rounded ridges on both sides, while in S. aff syphilitica, these ridges are parallel and the spaces between them are filled with numerous membranous platelets. Viewed from the front, the epidermal cells of S. syphilitica have sinuous walls (even more pronounced in samples from the Amazon); while in S. aff syphilitica, these cells are also sinuous but elongated in the cross-section of the blade and arranged in parallel. Stomata of S. syphilitica are paracytic, whereas in S. aff syphilitica, are both paracytic and anisocytic, and their polar axes are directed towards the mid-vein. Calcium oxalate crystals in S. syphilitica are prisms, whereas in S. aff syphilitica, crystal sand. Thorns occur in nodes and internodes in S. syphilitica but only in internodes in S. aff syphilitica. These features have proven to be of diagnostic value and may support a separation into two species, but future studies are needed to confirm that S. aff syphilitica is indeed a new taxon. Rev. Biol. Trop. 60(3): 1137-1148. Epub 2012 September 01.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.