Algunas consideraciones en torno a la dolarización

La Historia nos muestra que la existencia de crisis periódicas es algo inherente al desarrollo de las economías de libre mercado. Después de la caída del socialismo real y dada la evolución del capitalismo hacia la globalización tenemos que las crisis son un problema mundial. Sin embargo, las crisis no son iguales y la que se produjo en el sureste asiático en 1997 presenta características que antes no existían: rapidez y tamaño del contagio o la enorme diferencia entre las causas desencadenantes y su extensión. Esta situación ha vuelto a poner en candelero el antiguo debate entre los partidarios de los tipos de cambio fijos y los que piensan que estos deben ser flexibles o de libre flotación. Los modelos que explicaban las crisis cambiarias, desarrollados a finales de los setenta, no sirven para comprender lo sucedido en 1997 ya que ponían el énfasis en las incompatibilidades entre políticas monetaria y fiscal y política de tipo de cambio, mientras que los desarrollados en la década de los noventa nos dicen que no sólo se trata de diferencias en los parámetros fundamentales sino de expectativas dentro de un sistema financiero mundializado. La evidencia empírica nos muestra que la mayoría de los países no han podido mantener la confianza en las políticas adoptadas en compatibilidad con los tipos de cambio. A lo que se tiende es al tipo de cambio fijo optando por una de las tres fórmulas de las que se puede disponer: moneda única (Unión Monetaria Europea), junta monetaria (Argentina en 1991, Hong Kong) o la dolarización (Panamá, Ecuador, El Salvador, Argentina). El análisis de estas posibilidades será el objeto de nuestro trabajo

Various applications of discontinuous Petrov-Galerkin (DPG) finite element methods

Discontinuous Petrov-Galerkin (DPG) finite element methods have garnered significant attention since they were originally introduced. They discretize variational formulations with broken (discontinuous) test spaces and are crafted to be numerically stable by implicitly computing a near-optimal discrete test space as a function of a discrete trial space. Moreover, they are completely general in the sense that they can be applied to a variety of variational formulations, including non-conventional ones that involve non-symmetric functional settings, such as ultraweak variational formulations. In most cases, these properties have been harnessed to develop numerical methods that provide robust control of relevant equation parameters, like in convection-diffusion problems and other singularly perturbed problems. In this work, other features of DPG methods are systematically exploited and applied to different problems. More specifically, the versatility of DPG methods is elucidated by utilizing the underlying methodology to discretize four distinct variational formulations of the equations of linear elasticity. By taking advantage of interface variables inherent to DPG discretizations, an approach to coupling different variational formulations within the same domain is described and used to solve interesting problems. Moreover, the convenient algebraic structure in DPG methods is harnessed to develop a new family of numerical methods called discrete least-squares (DLS) finite element methods. These involve solving, with improved conditioning properties, a discrete least-squares problem associated with an overdetermined rectangular system of equations, instead of directly solving the usual square systems. Their utility is demonstrated with illustrative examples. Additionally, high-order polygonal DPG (PolyDPG) methods are devised by using the intrinsic discontinuities present in ultraweak formulations. The resulting methods can handle heavily distorted non-convex polygonal elements and discontinuous material properties. A polygonal adaptive strategy was also proposed and compared with standard techniques. Lastly, the natural high-order residual-based a posteriori error estimator ingrained within DPG methods was further applied to problems of physical relevance, like the validation of dynamic mechanical analysis (DMA) calibration experiments of viscoelastic materials, and the modeling of form-wound medium-voltage stator coils sitting inside large electric machinery.Computational Science, Engineering, and Mathematic

Global minimization of polynomial integral functionals

We describe a `discretize-then-relax' strategy to globally minimize integral functionals over functions $u$ in a Sobolev space satisfying prescribed Dirichlet boundary conditions. The strategy applies whenever the integral functional depends polynomially on $u$ and its derivatives, even if it is nonconvex. The `discretize' step uses a bounded finite-element scheme to approximate the integral minimization problem with a convergent hierarchy of polynomial optimization problems over a compact feasible set, indexed by the decreasing size $h$ of the finite-element mesh. The `relax' step employs sparse moment-SOS relaxations to approximate each polynomial optimization problem with a hierarchy of convex semidefinite programs, indexed by an increasing relaxation order $\omega$. We prove that, as $\omega\to\infty$ and $h\to 0$, solutions of such semidefinite programs provide approximate minimizers that converge in $L^p$ to the global minimizer of the original integral functional if this is unique. We also report computational experiments that show our numerical strategy works well even when technical conditions required by our theoretical analysis are not satisfied.Comment: 22 pages, 9 figure

Global stability of fluid flows despite transient growth of energy

Verifying nonlinear stability of a laminar fluid flow against all perturbations is a central challenge in fluid dynamics. Past results rely on monotonic decrease of a perturbation energy or a similar quadratic generalized energy. None show stability for the many flows that seem to be stable despite these energies growing transiently. Here a broadly applicable method to verify global stability of such flows is presented. It uses polynomial optimization computations to construct non-quadratic Lyapunov functions that decrease monotonically. The method is used to verify global stability of 2D plane Couette flow at Reynolds numbers above the energy stability threshold found by Orr in 1907. This is the first global stability result for any flow that surpasses the generalized energy method.Comment: 6 pages + 3-page supplement, 2 figure

Apreciación del valor de marca en una empresa de internet por parte del consumidor

El valor de las marcas varía dependiendo de los sectores de la economía de que se trate y puede variar también dentro del mismo sector económico. Según un reciente informe1 sobre empresas realizado en varias economías desarrolladas, el valor de la marca representa en el sector industrial poco más del 10% del valor total de la empresa, alrededor del 40% en el sector de los servicios financieros y del automóvil y del 70 al 90% en el sector de la alimentación y el de los productos de lujo. En términos absolutos el valor de una marca, excluyendo el valor de sus otros activos de propiedad intelectual e intangibles, puede ser enorme, y más aún para una empresa virtual en la que la búsqueda de la rentabilidad y la necesidad de ser eficaces en la comunicación cobra una especial relevancia