Quantum States, Thermodynamic Limits and Entropy in M-Theory

We discuss the matching of the BPS part of the spectrum for (super)membrane, which gives the possibility of getting membrane's results via string calculations. In the small coupling limit of M--theory the entropy of the system coincides with the standard entropy of type IIB string theory (including the logarithmic correction term). The thermodynamic behavior at large coupling constant is computed by considering M--theory on a manifold with topology ${\mathbb T}^2\times{\mathbb R}^9$. We argue that the finite temperature partition functions (brane Laurent series for $p \neq 1$) associated with BPS $p-$brane spectrum can be analytically continued to well--defined functionals. It means that a finite temperature can be introduced in brane theory, which behaves like finite temperature field theory. In the limit $p \to 0$ (point particle limit) it gives rise to the standard behavior of thermodynamic quantities.Comment: 7 pages, no figures, Revtex style. To be published in the Physical Review

Bacterial strains from floodplain soils perform different plant-growth promoting processes and enhance cowpea growth

ABSTRACT Certain nodulating nitrogen-fixing bacteria in legumes and other nodule endophytes perform different plant-growth promoting processes. The objective of this study was to evaluate 26 bacterial strains isolated from cowpea nodules grown in floodplain soils in the Brazilian savannas, regarding performance of plant-growth promoting processes and ability to enhance cowpea growth. We also identified these strains by 16S rRNA sequencing. The following processes were evaluated: free-living biological nitrogen fixation (BNF), solubilization of calcium, aluminum and iron phosphates and production of indole-3-acetic acid (IAA). The abilities to nodulate and promote cowpea growth were evaluated in Leonard jars. Partial sequencing of the 16S rRNA gene identified 60 % of the strains as belonging to genus Paenibacillus. The following four genera were also identified: Bacillus, Bradyrhizobium, Enterobacter and Pseudomonas. None of the strains fixed N2 free-living. Among the strains, 80 % solubilized Ca phosphate and one solubilized Al phosphate and none solubilized Fe phosphate. The highest IAA concentrations (52.37, 51.52 and 51.00 μg mL−1) were obtained in the 79 medium with tryptophan by Enterobacter strains UFPI B5-7A, UFPI B5-4 and UFPI B5-6, respectively. Only eight strains nodulated cowpea, however, all increased production of total dry matter. The fact that the strains evaluated perform different biological processes to promote plant growth indicates that these strains have potential use in agricultural crops to increase production and environmental sustainability