Differential resultants of super essential systems of linear OD-polynomials

The sparse differential resultant dres(P) of an overdetermined system P of generic nonhomogeneous ordinary differential polynomials, was formally defined recently by Li, Gao and Yuan (2011). In this note, a differential resultant formula dfres(P) is defined and proved to be nonzero for linear "super essential" systems. In the linear case, dres(P) is proved to be equal, up to a nonzero constant, to dfres(P*) for the supper essential subsystem P* of P.

DERIVE and Linear Algebra

This work describes an experience with a methodology for learning based on competences in Linear Algebra for engineering students. The experience has been based in autonomous team work of students. DERIVE tutorials for Linear Algebra topics are provided to the students. They have to work with the tutorials as their homework. After, worksheets with exercises have been prepared to be solved by the students organized in teams, using DERIVE function previously defined in the tutorials. The students send to the instructor the solution of the proposed exercises and they fill a survey with their impressions about the following items: ease of use of the files, usefulness of the tutorials for understanding the mathematical topics and the time spent in the experience. As a final work, we have designed an activity directed to the interested students. They have to prepare a project, related with a real problem in Science and Engineering. The students are free to choose the topic and to develop it but they have to use DERIVE in the solution. Obviously they are guided by the instructor. Some examples of activities related with Orthogonal Transformations will be presented.

A toolbox with DERIVE: calculus on several variables, Applications of Computer Algebra

A toolbox is a set of procedures taking advantage of the computing power and graphical capacities of a CAS. With these procedures the students can solve math problems, apply mathematics to engineering or simply reinforce the learning of certain mathematical concepts. From the point of view of their construction, we can consider two types of toolboxes: (i) the closed box, built by the teacher, in which the utility files are provided to the students together with the respective tutorials and several worksheets with proposed exercises and problems,

Multi-dimensional classification with super-classes

The multi-dimensional classification problem is a generalisation of the recently-popularised task of multi-label classification, where each data instance is associated with multiple class variables. There has been relatively little research carried out specific to multi-dimensional classification and, although one of the core goals is similar (modelling dependencies among classes), there are important differences; namely a higher number of possible classifications. In this paper we present method for multi-dimensional classification, drawing from the most relevant multi-label research, and combining it with important novel developments. Using a fast method to model the conditional dependence between class variables, we form super-class partitions and use them to build multi-dimensional learners, learning each super-class as an ordinary class, and thus explicitly modelling class dependencies. Additionally, we present a mechanism to deal with the many class values inherent to super-classes, and thus make learning efficient. To investigate the effectiveness of this approach we carry out an empirical evaluation on a range of multi-dimensional datasets, under different evaluation metrics, and in comparison with high-performing existing multi-dimensional approaches from the literature. Analysis of results shows that our approach offers important performance gains over competing methods, while also exhibiting tractable running time.

Experimental evidence of super-resolution better than lambda/105 with positive refraction

Super-resolution (SR) systems surpassing the Abbe diffraction limit have been theoretically and experimentally demonstrated using a number of different approaches and technologies: using materials with a negative refractive index, utilizing optical super-oscillation, using a resonant metalens, etc. However, recently it has been proved theoretically that in the Maxwell fish-eye lens (MFE), a device made of positive refractive index materials, the same phenomenon takes place. Moreover, using a simpler device equivalent to the MFE called the spherical geodesic waveguide (SGW), an SR of up to λ/3000 was simulated in COMSOL. Until now, only one piece of experimental evidence of SR with positive refraction has been reported (up to λ/5) for an MFE prototype working at microwave frequencies. Here, experimental results are presented for an SGW prototype showing an SR of up to λ/105. The SGW prototype consists of two concentric metallic spheres with an air space in between and two coaxial ports acting as an emitter and a receiver. The prototype has been analyzed in the range 1 GHz to 1.3 GHz.

La casa del super-héroe

El culto a los héroes es universal y tiene gran importancia psicológica. Los super-héroes de las películas actuales continúan representando al ser humano completo, una coincidentia oppositorum. Tienen un lado luminoso y otro lado oscuro. Sus casas representan el primero. La cuevas o los sótanos bajo sus casas, el segundo.