Geometric Algebra in Nonsinusoidal Power Systems: A Case of Study for Passive Compensation

New-generation power networks, such as microgrids, are being affected by the proliferation of nonlinear electronic systems, resulting in harmonic disturbances both in voltage and current that affect the symmetry of the system. This paper presents a method based on the application of geometric algebra (GA) to the resolution of power flow in nonsinusoidal single-phase electrical systems for the correct determination of its components to achieve passive compensation of true quadrature current. It is demonstrated that traditional techniques based on the concepts of Budeanu, Fryze or IEEE1459 fail to determine the interaction between voltage and current and therefore, are not suitable for being used as a basis for the compensation of nonactive power components. An example is included that demonstrates the superiority of GA method and is compared to previous work where GA approaches and traditional methods have also been used

Non-Equilibrium Random Matrix Theory : Transition Probabilities

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.Comment: REVTeX, 5 pages, 2 figure

Professional partnership between universities and schools: the use of a diagnostic tool to support development of student teachers’ professional skills

This paper describes a case study concerning a student teacher at risk of failing a teaching placement, who was supported by colleagues and university tutors through the use of a diagnostic tool in the form of a checklist. The checklist comprised a number of categories relating to aspects of teaching and learning within the classroom and was used consistently by staff to provide feedback to the student and as a basis for discussion and evaluation of his lessons. Scrutiny of the checklists, completed over a four week period, staff questionnaires and staff and student interviews indicate that the student and teaching staff found the tool user friendly and helpful in identifying areas of good practice and those requiring development. Other benefits for the student included the development of a pro-active approach to planning lessons and reflection on practice. The tool may be useful as a means of providing formative feedback and initiating dialogue relating to practice, particularly at an early stage of a teaching career

About the Infinite Repetition of Histories in Space

This paper analyzes two different proposals, one by Ellis and Brundrit, based on classical relativistic cosmology, the other by Garriga and Vilenkin, based on the DH interpretation of quantum mechanics, both of which conclude that, in an infinite universe, planets and living beings must be repeated an infinite number of times. We point to some possible shortcomings in the arguments of these authors. We conclude that the idea of an infinite repetition of histories in space cannot be considered strictly speaking a consequence of current physics and cosmology. Such ideas should be seen rather as examples of {\guillemotleft}ironic science{\guillemotright} in the terminology of John Horgan.Comment: 14 pages, no figures. Accepted for publication in slightly different form at THEORIA (http://www.ehu.es/ojs/index.php/THEORIA

Hierarchical Axion Inflation

We propose a new field theory mechanism for generating an effective trans-Planckian decay constant from sub-Planckian ones. Using the minimal two axions and a hierarchy between two axion decay constants is sufficient for realizing inflation through non-perturbative effects only and with minimal tuning. The inflationary motion is kept entirely within a sub-Planckian domain. We outline possible strategies of embedding the model in a string theory setup.Comment: REVTeX, 5 pages, 2 figures, added refs, changed the numerical parameter values of the stringy example, removed ED1's from the superpotentia

Dark Energy-Dark Matter Interaction from the Abell Cluster A586

We find that deviation from the virial equilibrium of the Abell Cluster A586 yields evidence of the interaction between dark matter and dark energy. We argue that this interaction might imply a violation of the Equivalence Principle. Our analysis show that evidence is found in the context of two different models of dark energy-dark matter interaction.Comment: Talk presented by O.B. at Encuentros Relativistas Espanoles 2007, Puerto de la Cruz, Tenerife, Spain, 10-14 September 2007. 6 pages, 3 figures and style fil

Contextualizando la investigación en pensamiento numérico en España

Con la intención de contextualizar las investigaciones realizadas en España dentro del marco de las realizadas a nivel mundial, busqué algún trabajo sobre el estado de la cuestión en pensamiento numérico. No he encontrado ninguno realizado en los últimos años pero sí uno realizado por Verschaffel, Greer y Torbeyns en 2006 que a su vez hacía referencia a otro anterior de Bergeron y Herscovics de 1990. Teniendo en cuenta que las primeras tesis en didáctica de la matemática están en este periodo de años, me ha parecido oportuno centrarme en estos trabajos para contextualizar a nivel mundial, por un lado, el punto de partida de las investigaciones en pensamiento numérico en nuestro país y, por otro, el nivel que se llega a alcanzar al final de este periodo. Así, he organizado este texto de réplica en tres partes, la primera dedicada a la revisión realizada por Bergeron y Herscovics (1990), la segunda al estudio realizado por Verschaffel et al. (2006) y la tercera dedicada a sacar conclusiones sobre los trabajos anteriores y el presentado aquí por el profesor González Mari