On the second moment of the number of crossings by a stationary Gaussian process

Cram\'{e}r and Leadbetter introduced in 1967 the sufficient condition $$\frac{r''(s)-r''(0)}{s}\in L^1([0,\delta],dx),\qquad \delta>0,$$ to have a finite variance of the number of zeros of a centered stationary Gaussian process with twice differentiable covariance function $r$. This condition is known as the Geman condition, since Geman proved in 1972 that it was also a necessary condition. Up to now no such criterion was known for counts of crossings of a level other than the mean. This paper shows that the Geman condition is still sufficient and necessary to have a finite variance of the number of any fixed level crossings. For the generalization to the number of a curve crossings, a condition on the curve has to be added to the Geman condition.Comment: Published at http://dx.doi.org/10.1214/009117906000000142 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Solar Photovoltaic and Thermal Energy Systems: Current Technology and Future Trends

Solar systems have become very competitive solutions for residential, commercial, and industrial applications for both standalone and grid connected operations. This paper presents an overview of the current status and future perspectives of solar energy (mainly photovoltaic) technology and the required conversion systems. The focus in the paper is put on the current technology, installations challenges, and future expectations. Various aspects related to the global solar market, the photovoltaic (PV) modules cost and technology, and the power electronics converter systems are addressed. Research trends and recommendations for each of the PV system sectors are also discussed.Junta de Andalucía P11-TIC-7070Ministerio de Ciencia e Innovación TEC2016-78430-

Rice formulae and Gaussian waves

We use Rice formulae in order to compute the moments of some level functionals which are linked to problems in oceanography and optics: the number of specular points in one and two dimensions, the distribution of the normal angle of level curves and the number of dislocations in random wavefronts. We compute expectations and, in some cases, also second moments of such functionals. Moments of order greater than one are more involved, but one needs them whenever one wants to perform statistical inference on some parameters in the model or to test the model itself. In some cases, we are able to use these computations to obtain a central limit theorem.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ265 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Las construcciones geométricas en torno al lugar geométrico de la parábola influenciado por el Geogebra

El escrito presenta un extracto de algunas de las actividades que estamos elaborando en un trabajo de investigación, acerca de la incidencia de las construcciones geométricas en la génesis instrumental de la parábola. Nuestro trabajo está dirigido a docentes de matemática de una universidad privada de Lima. Los objetivos son analizar cómo la condición geométrica de dicha curva se transforma en instrumento cuando los sujetos dirigen sus acciones a la resolución de los problemas con actividades geométricas y cómo dichas acciones contribuyen al proceso de aprendizaje de algunos contenidos geométricos haciendo uso del Geogebra que movilizan como herramienta mediadora. Las actividades se fundamentan teniendo en cuenta aspectos del Enfoque Instrumental y la Teoría Antropológica de lo Didáctico, para analizar los esquemas y las técnicas que los profesores construyeron o movilizaron durante las tareas propuestas

The Essential Role and the Continuous Evolution of Modulation Techniques for Voltage-Source Inverters in the Past, Present, and Future Power Electronics

The cost reduction of power-electronic devices, the increase in their reliability, efficiency, and power capability, and lower development times, together with more demanding application requirements, has driven the development of several new inverter topologies recently introduced in the industry, particularly medium-voltage converters. New more complex inverter topologies and new application fields come along with additional control challenges, such as voltage imbalances, power-quality issues, higher efficiency needs, and fault-tolerant operation, which necessarily requires the parallel development of modulation schemes. Therefore, recently, there have been significant advances in the field of modulation of dc/ac converters, which conceptually has been dominated during the last several decades almost exclusively by classic pulse-width modulation (PWM) methods. This paper aims to concentrate and discuss the latest developments on this exciting technology, to provide insight on where the state-of-the-art stands today, and analyze the trends and challenges driving its future