Symplectic matrices with predetermined left eigenvalues

We prove that given four arbitrary quaternion numbers of norm 1 there always exists a $2\times 2$ symplectic matrix for which those numbers are left eigenvalues. The proof is constructive. An application to the LS category of Lie groups is given.Comment: 7 page

Spherically Symmetric Solutions in M\o ller's Tetrad Theory of Gravitation

The general solution of M\o ller's field equations in case of spherical symmetry is derived. The previously obtained solutions are verified as special cases of the general solution.Comment: LaTeX2e with AMS-LaTeX 1.2, 8 page

Actividad de AIA oxidasa en estacas de especies del género Nothofagus

There is variation in rooting capacity among the different species of Nothofagus. Lenga cuttings (N. pumilio) present an almost null answer to rooting, compared to raulí (N. alpina) and roble (N. obliqua). According to antecedents compiled in literature, the endogenous levels of indole acetic acid (IAA), hormone responsible for the formation of adventitious roots, vary depending on the levels of IAA oxidase activity. Based on these observations, the IAA oxidase activity was comparativily analyzed in cuttings from these three Nothofagus species. To quantify the enzymatic activity, a spectrophotometric test was carried out, measuring at 535 nm. The residual amount of IAA was determined by reference to a calibration curve. The enzymatic activity was expressed in IAA mM mg protein-1 hours-1. The results show that lenga presents a greater IAA oxidase enzymatic activity when compared to the other analyzed species (P&lt; 0.05). These results would support at least partially the differences in the rootting capacity in Nothofagus species studys.Entre las distintas especies de Nothofagus existe variación en la capacidad de enraizamiento. Las estacas de lenga (N. pumilio) presentan una respuesta casi nula al enraizamiento, comparada con raulí (N. alpina) y roble (N. obliqua). Según antecedentes recopilados en literatura, los niveles endógenos de ácido indol acético (AIA), hormona responsable de la formación de raíces adventicias, varían según los niveles de actividad de AIA oxidasa (AIA-O). Basados en estas observaciones, la actividad de AIA-O fue comparativamente analizada en estacas de estas tres especies de Nothofagus. Para cuantificar la actividad enzimática se realizó un ensayo de espectrofotometría, midiendo a 535 nm λ. La cantidad residual de AIA se estimó por referencia a una curva de calibración. La actividad enzimática fue expresada en mM de AIA mg de proteína-1 h-1. Los resultados muestran que N. pumilio presenta una mayor actividad enzimática de AIA oxidasa en comparación con las otras especies analizadas (P < 0,05). Estos resultados respaldarían, al menos parcialmente, las diferencias en la capacidad de rizogénesis en las especies de Nothofagus estudiadas

Improved time-resolved acousto-optic technique for optical fiber analysis of axial non-uniformities by using edge interrogation

The time-resolved acousto-optic technique demonstrated recently to be a very useful method for the analysis of fiber axial non-uniformities, able to detect variations of fiber diameter in the nanometric scale with a spatial resolution of few cm. An edge interrogation approach is proposed to improve further the performance of this technique. The detection of subnanometer fiber diameter changes or sub-ppm changes of the core refractive index is demonstrated