Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

Studies of aberrant phyllotaxy1 Mutants of Maize Indicate Complex Interactions between Auxin and Cytokinin Signaling in the Shoot Apical Meristem

One of the most fascinating aspects of plant morphology is the regular geometric arrangement of leaves and flowers, called phyllotaxy. The shoot apical meristem (SAM) determines these patterns, which vary depending on species and developmental stage. Auxin acts as an instructive signal in leaf initiation, and its transport has been implicated in phyllotaxy regulation in Arabidopsis (Arabidopsis thaliana). Altered phyllotactic patterns are observed in a maize (Zea mays) mutant, aberrant phyllotaxy1 (abph1, also known as abphyl1), and ABPH1 encodes a cytokinin-inducible type A response regulator, suggesting that cytokinin signals are also involved in the mechanism by which phyllotactic patterns are established. Therefore, we investigated the interaction between auxin and cytokinin signaling in phyllotaxy. Treatment of maize shoots with a polar auxin transport inhibitor, 1-naphthylphthalamic acid, strongly reduced ABPH1 expression, suggesting that auxin or its polar transport is required for ABPH1 expression. Immunolocalization of the PINFORMED1 (PIN1) polar auxin transporter revealed that PIN1 expression marks leaf primordia in maize, similarly to Arabidopsis. Interestingly, maize PIN1 expression at the incipient leaf primordium was greatly reduced in abph1 mutants. Consistently, auxin levels were reduced in abph1, and the maize PIN1 homolog was induced not only by auxin but also by cytokinin treatments. Our results indicate distinct roles for ABPH1 as a negative regulator of SAM size and a positive regulator of PIN1 expression. These studies highlight a complex interaction between auxin and cytokinin signaling in the specification of phyllotactic patterns and suggest an alternative model for the generation of altered phyllotactic patterns in abph1 mutants. We propose that reduced auxin levels and PIN1 expression in abph1 mutant SAMs delay leaf initiation, contributing to the enlarged SAM and altered phyllotaxy of these mutants.

THE SPECTRAL EVOLUTION AND EJECTA OF RECURRENT NOVA U Sco IN THE 2010 OUTBURST

Synoptic spectroscopic observations of the U Sco 2010 outburst from maximum light to quiescence as well as a contemporaneous X-ray observation are presented and analyzed. The X-ray spectrum 52 days after outburst indicates a hot source ( kT(bb) similar to 70 eV). Narrow-line components from the irradiated companion atmosphere were observed in hydrogen and helium optical recombination lines. The formation of a nebular spectrum is seen for the first time in this class of recurrent novae, allowing a detailed study of the ejecta using photoionization models. Unusual [O III] auroral-to-nebular line ratios were found and possible scenarios of their origin are discussed. The modeling of the emission line spectrum suggests highly heterogeneous ejecta with masses around or above 3 x 10(-6) M(sun).

Phytomass production and nitrogen accumulation in maize cultivated with different doses of (15)N-urea

This work aimed to study the possible alterations in production, accumulation of the vegetative phytomass and nitrogen efficiency use of the maize crop, in different doses of N applied in the fertilization, by using the technique of isotopic dilution of (15)N. The completely randomized block experimental design was adopted, with 5 treatments and 4 replicates. The following treatments were constituted in the doses in covering: 0, 50, 100, 150 and 200 kg ha(-1) of N, with fertilization of N-urea, respectively. Comparisons among the treatments had been run for crop productivity; nitrogen accumulation for the plant, and use of the nitrogen of the urea-(15)N for the crop. The increase of the dose of N-fertilizer resulted in increase of the dry matter mass, of the dry matter yield crop tax, of the productivity and accumulation of N in the maize plants.

Localization of Pantoea ananatis inside lesions of maize White Spot Disease using transmission electron microscopy and molecular techniques

The etiological agent of maize white spot (MWS) disease has been a subject of controversy and discussion. Initially the disease was described as Phaeosphaeria leaf spot caused by Phaeosphaeria maydis. Other authors have Suggested the existence of different fungal species causing similar symptoms. Recently, a bacterium, Pantoea ananatis, was described as the causal agent of this disease. The purpose of this Study was to offer additional information on the correct etiology of this disease by providing visual evidence of the presence of the bacterium in the interior of the MWS lesions by using transmission electron microscopy (TEM) and molecular techniques. The TEM allowed Visualization of a large amount of bacteria in the intercellular spaces of lesions collected from both artificially and naturally infected plants. Fungal structures were not visualized in young lesions. Bacterial primers for the 16S rRNA and rpoB genes were used in PCR reactions to amplify DNA extracted from water-soaked (young) and necrotic lesions. The universal fungal oligonucleotide ITS4 was also included to identity the possible presence of fungal structures inside lesions. Positive PCR products from water-soaked lesions, both from naturally and artificially inoculated plants, were produced with bacterial primers, whereas no amplification was observed when ITS4 oligonucleotide was used. On the other hand, DNA amplification with ITS4 primer was observed when DNA was isolated from necrotic (old) lesions. These results reinforced previous report of P. ananatis as the primary pathogen and the hypothesis that fungal species may colonize lesions pre-established by P. ananatis.

Identification by computer-simulated RFLP of phytoplasmas associated with eggplant giant calyx representative of two subgroups, a lineage of 16SrIII-J and the new subgroup 16SrIII-U

Symptoms resembling giant calyx, a graft-transmissible disease, were observed on 1-5% of eggplant (aubergine; Solanum melongena L.) plants in production fields in Sao Paulo state, Brazil. Phytoplasmas were detected in 1 2 of 1 2 samples from symptomatic plants that were analysed by a nested PCR assay employing 16S rRNA gene primers R16mF2/R16mR1 followed by R16F2n/R16R2. RFLP analysis of the resulting rRNA gene products (1.2 kb) indicated that all plants contained similar phytoplasmas, each closely resembling strains previously classified as members of RFLP group 16SrIII (X-disease group). Virtual RFLP and phylogenetic analyses of sequences derived from PCR products identified phytoplasmas infecting eggplant crops grown in Piracicaba as a lineage of the subgroup 16SrIII-J, whereas phytoplasmas detected in plants grown in Braganca Paulista were tentatively classified as members of a novel subgroup 16SrIII-U. These findings confirm eggplant as a new host of group 16SrIII-J phytoplasmas and extend the known diversity of strains belonging to this group in Brazil.

Oviposition by a moth suppresses constitutive and herbivore-induced plant volatiles in maize

Plant volatiles function as important signals for herbivores, parasitoids, predators, and neighboring plants. Herbivore attack can dramatically increase plant volatile emissions in many species. However, plants do not only react to herbivore-inflicted damage, but also already start adjusting their metabolism upon egg deposition by insects. Several studies have found evidence that egg deposition itself can induce the release of volatiles, but little is known about the effects of oviposition on the volatiles released in response to subsequent herbivory. To study this we measured the effect of oviposition by Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) moths on constitutive and herbivore-induced volatiles in maize (Zea mays L.). Results demonstrate that egg deposition reduces the constitutive emission of volatiles and suppresses the typical burst of inducible volatiles following mechanical damage and application of caterpillar regurgitant, a treatment that mimics herbivory. We discuss the possible mechanisms responsible for reducing the plant`s signaling capacity triggered by S. frugiperda oviposition and how suppression of volatile organic compounds can influence the interaction between the plant, the herbivore, and other organisms in its environment. Future studies should consider oviposition as a potential modulator of plant responses to insect herbivores.