Geodésicas en Variedades de Riemann

En este trabajo, se hará una introducción a las variedades de Riemann, con el fin de analizar algunas propiedades minimizadoras de las curvas geodésicas en variedades de Riemann.

Environmental taxes and the Double dividend hypothesis

In this End of Degree Dissertation I built a basic economic model, where two perfectly competitive markets interact, as a tool to understand, illustrate and evaluate environmentalfiscal reforms that have already been implemented or have been announced in many developed countries. Thus, in this dissertation I try to explain as simply as possible the theorical aspects of the “double dividend” hyphotesis and provide a numerical example with illustrative purpose.

New symbiotic hypothesis on the origin of eukaryotic flagella

The origin of eukaryotic flagella has long been a mystery. Here we review the possibility that flagella sprouted evolutionarily from the eukaryotic cell proper seems very unlikely because it is hard to imagine what function and benefit in natural selection the flagella would have provided to the cells when they first emerged as simple buds. Lynn Margulis' 1970 spirochete hypothesis, though popular still, has never been confirmed. Moreover, the absence of tubulin and axonemal dynein in the spirochetes and the incapability of the bacterial and eukaryotic membranes' making a continuum now suggest that the hypothesis is outdated. Tubulin genes were recently identified in a new bacteria division, verrucomicrobia, and microtubules have also been found in one of these species, epixenosomes, the defensive ectosymbionts. On the basis of these data, we propose a new symbiotic hypothesis: that the mid-ancestor of eukaryotic cells obtained epixenosomelike verrucomicrobia as defensive ectosymbionts and the ectosymbionts later became endosymbiotic. They still, however, protruded from the surface of their host to play their role. Later, many genes were lost or incorporated into the host genome. Finally, the genome, the bacterial membrane, and the endosymbiotic vesicle membrane were totally lost, and fingerlike protrusions with microtubules formed. As the cells grew larger, the defensive function of the protrusions eventually weakened and then vanished. Some of the protrusions took on a new role in cell movement, which led them to evolve into flagella. The key step in this process was that the dynein obtained from the host evolved into axonemal dyneins, attaching onto the microtubules and forming motile axonemes. Our hypothesis is unproven, but it offers a possible explanation that is consistent with current scientific thought. We hope that our ideas will stimulate additional studies on the origin of eukaryotic flagella and on investigations of verrucomicrobia. Whether such studies confirm, refine, or replace our hypothesis, they should nevertheless further our understanding of the origin of eukaryotic cells.