WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

Bouncing Cosmologies in Palatini f(R)f(R) Gravity

We consider the early time cosmology of f(R) theories in Palatini formalism and study the conditions that guarantee the existence of homogeneous and isotropic models that avoid the Big Bang singularity. We show that for such models the Big Bang singularity can be replaced by a cosmic bounce without violating any energy condition. In fact, the bounce is possible even for pressureless dust. We give a characterization of such models and discuss their dynamics in the region near the bounce. We also find that power-law lagrangians with a finite number of terms may lead to non-singular universes, which contrasts with the infinite-series Palatini f(R) lagrangian that one needs to fully capture the effective dynamics of Loop Quantum Cosmology. We argue that these models could also avoid the formation of singularities during stellar gravitational collapse.Comment: 8 pages, 4 figures; added references and a short comment in sec.I

Efficient functional built-in test for RF systems using two-tone response envelope analysis

Trabajo presentado al AFRICON celebrado en Nairobi del 23 al 25 de septiembre de 2009.This paper presents a novel and low-cost methodology that can be used for testing RF blocks embedded in complex SoCs. It is based on the detection and spectral analysis of the two-tone response envelope of the block under test. The main non-linearity specifications of the block under test can be easily extracted from the envelope signal. The analytical basis of the proposed methodology is demonstrated, and a proposal for its implementation as a built-in test core is discussed. Finally, practical simulation examples show the feasibility of the approach.This work has been partially supported by the Spanish Ministry of Innovation through project TEST (TEC2007-68072/MIC) and CATRENE's project TOETS.Peer Reviewe

Regulatory Design for RES-E Support Mechanisms: Learning Curves, Market Structure, and Burden-Sharing

Drawing from relevant experiences in power systems around the world, this paper offers a critical review of existing policy support mechanisms for RES-E (renewable energy sources for electricity), with a detailed analysis of their regulatory implications. While recent studies provide an account of current RES-E support systems, in this paper we focus on the impacts these mechanisms have on the overall energy market structure and its performance in the short and long term. Given the rising importance of RES-E in systems everywhere, these impacts can no longer be overlooked.Massachusetts Institute of Technology. Center for Energy and Environmental Policy Researc

Articulando las actividades de conjeturar y probar de los matemáticos profesionales desde la teoría de Peirce

“La formulación de conjeturas y el desarrollo de pruebas son dos aspectos fundamentales del trabajo de un matemático profesional” (Alibert y Thomas, 1991, p. 215). La investigación que estamos llevando a cabo pretende proponer un modelo, desde la educación matemática, que describa y explique cómo los matemáticos profesionales desarrollan las actividades de conjeturar y probar. Concretamente, y debido al carácter sociocultural de la investigación en matemáticas, los participantes considerados en este trabajo son investigadores en matemáticas que tienen al menos una publicación en “JCR science edition”

Ecuaciones de resistencia al flujo para ríos de montaña

Three models of flow resistance (a Keulegan-type logarithmic law and two models developed for large-scale roughness conditions: the full logarithmic law and a model based on an inflectional velocity profile) were calibrated, validated and compared using an extensive database (N = 1,533) from rivers and flumes, representative of a wide hydraulic and geomorphologic range in the field of gravel-bed and mountain channels. It is preferable to apply the model based on an inflectional velocity profile in the relative submergence (y/d90) interval between 0.5 and 15, while the full logarithmic law is preferable for values below 0.5. For high relative submergence, above 15, either the logarithmic law or the full logarithmic law can be applied. The models fitted to the coarser percentiles are preferable to those fitted to the median diameter, owing to the higher explanatory power achieved by setting a model, the smaller difference in the goodness-of-fit between the different models and the lower influence of the origin of the data (river or flume).Se han calibrado, validado y comparado tres modelos de resistencia al flujo (una ley logarítmica tipo Keulegan y dos modelos desarrollados para condiciones de alta rugosidad: la ley logarítmica completa y un modelo basado en un perfil de velocidad inflexional) empleando para ello una extensa base de datos (N = 1,533) de río y de laboratorio, representativa de un amplio intervalo hidráulico y geomorfológico en el ámbito de cauces de grava y de montaña. El modelo basado en un perfil de velocidad inflexional es preferible para su aplicación en el intervalo de sumersión relativa (y/d90) comprendido entre 0,5 y 15, mientras que la ley logarítmica completa es preferible para valores inferiores a 0,5. Para sumersión relativa alta, por encima de 15, es posible aplicar indistintamente la ley logarítmica y la ley logarítmica completa. Son preferibles los modelos ajustados con los percentiles más gruesos que los ajustados con el diámetro mediano, debido a: la mayor capacidad explicativa alcanzada fijado un modelo, la menor diferencia en la bondad de ajuste entre los diferentes modelos y la menor influencia del origen de los datos (río o laboratorio)

Improving the accuracy of RF alternate test using multi-VDD conditions: application to envelope-based test of LNAs

Trabajo presentado al "20 Asina Test Symposium" celebrado en Nueva Delhi (India) del 20 al 23 de Noviembre del 2011.-- Reprinted from (relevant publication info). This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the products or services of CSIC Spanish National Research Council, Digital.CSIC. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This work demonstrates that multi-VDD conditions may be used to improve the accuracy of machine learning mod- els, significantly decreasing the prediction error. The proposed technique has been successfully applied to a previous alternate test strategy for LNAs based on response envelope detection. A prototype has been developed to show its feasibility. The prototype consists of a low-power 2.4GHz LNA and a simple envelope detector, integrated in a 90nm CMOS technology. Post- layout simulation results are provided to verify the functionality of the approach. Copyright © 2011 IEEE.This work has been partially funded by a CSIC JAE-Doc contract (cofinanced by FSE), a Spanish MAE-AECID grant and projects: SR2 - Short Range Radio (Catrene European project 2A105SR2 and Avanza I+D Spanish project TSI-020400-2010-55, cofinanced with FEDER program), Auto-calibración y auto-test en circuitos analógicos, mixtos y de radio frecuencia (Andalusian Government project P09-TIC-5386, cofinanced with FEDER program), and Catrene project TOETS (CT 302).Peer reviewe