On closures of discrete sets

The depth of a topological space X (g(X)) is defined as the supremum of the cardinalities of closures of discrete subsets of X. Solving a problem of Martínez-Ruiz, Ramírez-Páramo and Romero-Morales, we prove that the cardinal inequality |X|≤g(X)L(X)⋅F(X) holds for every Hausdorff space X, where L(X) is the Lindelöf number of X and F(X) is the supremum of the cardinalities of the free sequences in X

Stellar footprints of a variable G

Theories with varying gravitational constant $G$ have been studied since long time ago. Among them, the most promising candidates as alternatives of the standard General Relativity are known as scalar-tensor theories. They provide consistent descriptions of the observed universe and arise as the low energy limit of several pictures of unified interactions. Therefore, an increasing interest on the astrophysical consequences of such theories has been sparked over the last few years. In this essay we comment on two methodological approaches to study evolution of astrophysical objects within a varying-$G$ theory, and the particular results we have obtained for boson and white dwarf stars.Comment: This essay received Honorable Mention in the 1999 Essay Competition of the Gravity Research Foundatio

Stability of bubbles in a Hele–Shaw cell

The linear stability of steadily moving bubbles in a Hele–Shaw cell is investigated. It is shown analytically that without the effect of surface tension, the bubbles are linearly unstable with the stability operator having a continuous spectrum. For small bubbles that are circular, analytical calculations also show that any amount of surface tension stabilizes a bubble. Numerical calculations suggest that the branch of bubble solutions that, in the limit of large area, corresponds to the McLean–Saffman finger is stable for any nonzero surface tension. However, the decay rate of disturbances on the McLean–Saffman branch depends appreciably on the bubble size even for large bubbles. This suggests that the stability results on this branch cannot be immediately extrapolated to the McLean–Saffman fingers. For another branch of bubble solution, which in the limit or large area corresponds to the first of the Romero–Vanden-Broeck finger solutions, numerical evidence suggests that it is unstable to one symmetric and one antisymmetric mode for any surface tension. The symmetric unstable mode tends to break the tip of the bubble and the growth rate of this mode is unaffected by further increase in bubble size, once the bubble is large enough. This suggests that there is an analogous instability for the finger, and this agrees with the numerical findings of Kessler and Levine [Phys. Rev. A 33, 2632 (1986)]. Agreement is noted in the quantitative comparison of the growth rate with the predictions [Tanveer, Phys. Fluids 30, 2318 (1987)] on the limiting growth rate for the symmetric unstable mode for the first Romero–Vanden-Broeck branch of finger solution

Discussion required for correct interpretation

Thank you for the opportunity to comment on the editorial by Romero and colleagues [1], which raises a number of important and interesting questions. Such discussion is mandatory if results of scientific techniques such as gene array are to be correctly interpreted and used as the basis for future improvements in patient care

Análisis didáctico en la práctica de la formación de profesores de matemáticas

Este es un libro sobre formación de profesores de matemáticas. Su público objetivo son profesores de matemáticas (en formación y en ejercicio) y formadores de profesores de matemáticas. Su propósito es contribuir con un modelo de formación de profesores de matemáticas que se pueda llevar a la práctica en programas de formación y que contribuya a las prácticas pedagógicas de los profesores. El centro de atención del libro son las oportunidades que el profesor puede proporcionar a sus estudiantes en clase para que ellos puedan avanzar en su aprendizaje de los temas de las matemáticas escolares. Para ello, el libro ofrece un conjunto estructurado de conceptos y técnicas con las que el profesor puede analizar un tema concreto de las matemáticas escolares, producir información sobre el tema para diseñar una unidad didáctica, llevarla a la práctica y evaluar su diseño e implementación

Basic properties of Gamma-ray loud blazars

In this paper, a method is proposed to determine the basic properties of $\gamma$-ray loud blazars, among them the central black hole mass, M, the Doppler factor, $\delta$, the propagation angle of the $\gamma$-rays with respect to the symmetric axis of a two-temperature accretion disk, $\Phi$, and the distance (i.e. the height above the accretion disk), d at which the $\gamma$-rays are created, for seven $\gamma$-ray loud blazars with available GeV variability timescales and in which the absorption effect of a $\gamma$-ray and the beaming effect have been taken into account. Our results indicate that, if we take the intrinsic $\gamma$-ray luminosity to be $\lambda$ times the Eddington luminosity, $L_{\gamma}^{in} = \lambda L_{Edd.}$, the masses of the blazars are in the range of $(4 \sim 131)\times 10^{7}M_{\odot}$, the Doppler factors ($\delta$) lie in the range of 0.57 to 5.33 the angle ($\Phi$) is in the range of $13^{\circ}$ to 43$^{\circ}$ and the distance (d) is in the range of 26R_{g} to 411R_{g}. Our model results are independent of $\gamma$-ray emission mechanisms but they do depend on the X-ray emission mechanism of the accretion disk.Comment: 14 pages, 3 tables, A&A accepte

The infection biology of pig-associated Salmonella

Through the use of an establishe dline of porcine intestinal epithelial cells, known as IPEC-1, this in vitro work examines the initial adhesion, invasion and persistence abilities of different Salmonella serovars and phage types, including multiresistant and monophasic S. typhimurium DT193 isolates. The resultant innate immune response of the porcine cells to the isolates is assessed through determination of interleukin (IL)-6 and IL-8 concentrations present in cell culture supernatants