Resumen: Let $X$ be a compact hyperelliptic Riemann surface which admits anti-analytic involutions (also called symmetries or real structures). For instance, a complex projective plane curve of genus two, defined by an equation with real coefficients, gives rise to such a surface, and complex conjugation is such a symmetry. In this memoir, the real structures $\tau$ of
$X$ are classified up to isomorphism (i.e., up to conjugation). This is done as follows: the number of connected components of the set of fixed points of $\tau$ together with the connectedness or disconnectedness of the complementary set in $X$ classifies $\tau$ topologically; they determine the species of $\tau$, which only depends on the conjugacy class of $\tau$ (however, different conjugacy classes may have identical species). On these grounds, for a given genus $g\ge2$, the authors first give a list of all full groups of analytic and anti-analytic automorphisms of genus $g$ compact hyperelliptic Riemann surfaces. For every such group $G$, the authors compute polynomial equations for a surface $X$ having $G$ as full group and then find the number of conjugacy classes containing symmetries; they also compute a representative $\tau$ in every such class. Finally, they compute the species corresponding to such classes. This memoir is an exhaustive piece of work, going through a case-by-case analysis. The problem for general compact Riemann surfaces dates back to 1893, when {\it F. Klein} [Math. Ann. 42, 1--29 (1893)] first studied it. For zero genus, it is easy. For genus one, that is, for elliptic surfaces, it was solved by {\it N. Alling} ["Real elliptic curves" (1981)]. Partial results for hyperelliptic surfaces of genus two were obtained by {\it E. Bujalance} and {\it D. Singerman} [Proc. Lond. Math. Soc. 51, 501--519 (1985)].
Palabras clave: Riemann surface, symmetry, automorphism group, real form, real algebraic curve
Resumen: Subarcsecond spatial resolution images in the [S II] and [N II] + Halpha emission lines of the T Tauri star (TTS) CW Tau are presented. It is shown that CW Tau has a jet that extends up to 2.2'' (300 AU) from the star in the direction P.A. = 144-degrees. The jet emits strongly in [S II], and it is already collimated at 1.3'' (176 AU) from the star. The images also indicate that CW Tau is extended in
the east-west direction and that the jet is slightly shifted to the east. This suggests that CW Tau may be a binary with the two components separated 0.20'' (28 AU). The observations are compared with the theoretical models proposed for the production of forbidden line emission regions (FLERs) and protostellar jets.
Resumen: Using the archival spectrograms, obtained by IUE in 1980s, the line profiles of the CIII, CIV, SiIII, SiIV ions were studied in the spectra of four T Tau-type stars: RU Lup, T Tau, TW Hya, and DR Tau. The lines, reliably detected above the noise level, have asymmetric profiles, redshifted with respect to the laboratory wavelengths. This peculiarity of the profiles
can be explained in the case of disk accretion onto a young star, when the star's global magnetic field stops the accretion disk at some distance from the stellar surface.
Resumen: On every real Banach space X we introduce a locally convex topology tau(p), canonically associated to the weak-polynomial topology w(P). It is proved that tau(p) is the finest locally convex topology on X which is coarser than w(P). Furthermore, the convergence of sequences is considered, and sufficient conditions on X are obtained under which
the convergent sequences for w(P) and for tau(P) either coincide with the weakly convergent sequences (when X has the Dunford-Pettis property) or coincide with the norm-convergent sequences (when X has nontrivial type).
Resumen: An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology tau such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for circle times(tau,delta)(n)(F-1 circle plus F-2) gives a direct proof of a recent result of Diaz and Dineen land generalizes it to other topologies tau) that
the n-fold projective symmetric and the n-fold projective "full" tensor product of a Iocally convex space fare isomorphic if E is isomorphic to its square E-2.
Resumen: Let k be a real field. We show that every non-negative homogeneous quadratic polynomial f (x(1),..., x(n)) with coefficients in the polynomial ring k[t] is a sum of 2n center dot tau(k) squares of linear forms, where tau(k) is the supremum of the levels of the finite non-real field extensions of k. From this result we deduce bounds for the Pythagoras
numbers of affine curves over fields, and of excellent two-dimensional local henselian rings.
