Non-unitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential

A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. To acomplish this, a similar path to the one used in the angular momentum case is employed; hence, the radial eigenfuntions calculated comprise non unitary representations of the algebra. One of the interesting properties of such non unitary representations is that they are not labeled by integer nor by half-integer numbers as happens in the usual angular momentum representation.Comment: 20 pages 1 eps figure in a single zipped file, submitted to J. Math. Phy

Lagrangian Description of the Variational Equations

A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both the original configurations of the system and all the virtual displacements joining any two integral curves. Our main result establishes that both the Euler-Lagrange equations and the corresponding variational equations of the original system can be viewed as the Lagrangian vector field associated with the first prolongation of the original LagrangianAfter discussing certain features of the formulation, we introduce the so-called inherited constants of the motion and relate them to the Noether constants of the extended system

Some rootstocks improve pepper tolerance to mild salinity through ionic regulation

[EN] Grafting has been proposed as an interesting strategy that improves the responses of crops under salinity. In pepper, we reported increased fruit yield of the commercial 'Adige' cultivar under salinity when grafted onto accessions Capsicum chinense Jacq. 'ECU-973' (12) and Capsicum baccatum L. var. pendulum 'BOL-58' (14), whereas no,effect was observed when grafted onto accession Capsicum annuum L var. 'Serrano' (5). We also analysed the physiological and biochemical mechanisms related to the tolerance conferred by these rootstocks. Responses to salinity (40 mM NaCl) were studied in the different plant combinations for 30 days by determining water relations, mineral content, proline accumulation, photosynthetic parameters, nitrate reductase activity and antioxidant capacity. Higher salt tolerance was achieved when the 'Adige' cultivar was grafted onto the 12 genotype, which allowed not only lower Na+ and Cl- accumulation in the scion, but also ion selectivity maintenance, particularly Na+/K+ discrimination. These traits led to a minor negative impact on photosynthesis, nitrate reductase activity and lipid peroxidation in grafted scion leaves. This work suggests that using tolerant pepper rootstocks that maintain the scion's ion homeostasis is a promising strategy to provide salinity tolerance and can consequently improve crop yield.This work has been financed by INIA (Spain) through Project RTA2010-00038-C03-01 and the European Regional Development Fund (ERDF). C.P. is beneficiary of a doctoral fellowship (FPI-INIA) associate with this project.Penella, C.; González Nebauer, S.; Quinones, A.; San Bautista Primo, A.; López Galarza, SV.; Calatayud, A. (2015). Some rootstocks improve pepper tolerance to mild salinity through ionic regulation. Plant Science. 230:12-22. doi:10.1016/j.plantsci.2014.10.007S122223

Symbiotic Plasmid Rearrangement in Rhizobium leguminosarum bv. viciae VF39SM

A rearrangement between the symbiotic plasmid (pRleVF39d) and a nonsymbiotic plasmid (pRleVF39b) in Rhizobium leguminosarum bv. viciae VF39 was observed. The rearranged derivative showed the same plasmid profile as its parent strain, but hybridization to nod, fix, and nif genes indicated that most of the symbiotic genes were now present on a plasmid corresponding in size to pRleVF39b instead of pRleVF39d. On the other hand, some DNA fragments originating from pRleVF39b now hybridized to the plasmid band at the position of pRleVF39d. These results suggest that a reciprocal but unequal DNA exchange between the two plasmids had occurred

Characterization of Rhizobial Isolates of Phaseolus vulgaris by Staircase Electrophoresis of Low-Molecular-Weight RNA

Low-molecular-weight (LMW) RNA molecules were analyzed to characterize rhizobial isolates that nodulate the common bean growing in Spain. Since LMW RNA profiles, determined by staircase electrophoresis, varied across the rhizobial species nodulating beans, we demonstrated that bean isolates recovered from Spanish soils presumptively could be characterized as Rhizobium etli, Rhizobium gallicum, Rhizobium giardinii, Rhizobium leguminosarum bv. viciae and bv. trifolii, and Sinorhizobium fredii