Discrete Sturm–Liouville problems, Jacobi matrices and Lagrange interpolation series

AbstractThe close relationship between discrete Sturm–Liouville problems belonging to the so-called limit-circle case, the indeterminate Hamburger moment problem and the search of self-adjoint extensions of the associated semi-infinite Jacobi matrix is well known. In this paper, all these important topics are also related with associated sampling expansions involving analytic Lagrange-type interpolation series

Sampling in unitary invariant subspaces associated to LCA groups

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of problems which are interesting in practice, avoiding also cumbersome notation. Along with LCA groups theory, the involved mathematical technique is that of frame theory which meets matrix analysis when appropriate dual frames are computed

A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established

Influencia de la segregación de Ti4+ en la respuesta multiferroica de materiales basados en BiFeO3

Los materiales multiferroicos han cobrado un interés creciente en los últimos años dada la potencialidad de sus aplicaciones prácticas. Los materiales basados en BiFeO3 pueden considerarse los más estudiados hasta la fecha dentro de los pocos multiferroicos conocidos. No obstante, sus propiedades aún no son adecuadas para su empleo en dispositivos pues suelen presentar una elevada conductividad eléctrica y/o una respuesta antiferromagnética. La modificación de estos materiales mediante dopado con Ti4+ puede disminuir las pérdidas dieléctricas y proporcionar un comportamiento ferromagnético. Sin embargo, los cambios producidos en la estructura, microestructura y propiedades de los materiales de BiFeO3 como consecuencia del dopado con Titanio no están claros. En este trabajo se presenta una caracterización detallada de cerámicas de composición nominal BiFe0.95Ti0.05O3 con una elevada resistencia y una respuesta magnética extraordinaria. Los resultados evidencian la formación de una nanoestructura relacionada con la segregación del dopante en borde de grano que es la responsable de los cambios producidos en las propiedades magnetoeléctricas de estos materiales

Quartz crystal microbalance holder design for on-line sensing in liquid applications

In this paper, the design of a QCM sensor for liquid media measurements in vertical position is described. A rugged and low-cost proof holder has been designed, the cost of which is significantly lower than those of traditional commercial holders. The crystal is not replaceable but it can be easily cleaned. Its small volume permits to be used by dipping it in the liquid with the desired location and orientation. The developed design has been experimentally validated by measuring changes in the resonance frequency and resistance of the QCM sensor immersed vertically in different calibrated aqueous glycerol solutions. The obtained results show a great agreement with the Kanazawa theoretical expression. Consequently, the designed QCM sensor would be appropriate for sensing applications in liquids, and might take part of a future on-line multichannel low-cost QCM-based measurement system.Peer ReviewedPostprint (published version

Monitoring leafy vegetables through packaging films with

Fresh-cut or minimally processed fruit and vegetables have been physically modified from its original form (by peeling, trimming, washing and cutting) to obtain a 100% edible product that is subsequently packaged (usually under modified atmosphere packaging –MAP) and kept in refrigerated storage. In fresh-cut products, physiological activity and microbiological spoilage, determine their deterioration and shelf-life. The major preservation techniques applied to delay spoilage are chilling storage and MAP, combined with chemical treatments antimicrobial solutions antibrowning, acidulants, antioxidants, etc.). The industry looks for safer alternatives. Consequently, the sector is asking for innovative, fast, cheap and objective techniques to evaluate the overall quality and safety of fresh-cut products in order to obtain decision tools for implementing new packaging materials and procedures. In recent years, hyperspectral imaging technique has been regarded as a tool for analyses conducted for quality evaluation of food products in research, control and industries. The hyperspectral imaging system allows integrating spectroscopic and imaging techniques to enable direct identification of different components or quality characteristics and their spatial distribution in the tested sample. The objective of this work is to develop hyperspectral image processing methods for the supervision through plastic films of changes related to quality deterioration in packed readyto-use leafy vegetables during shelf life. The evolutions of ready-to-use spinach and watercress samples covered with three different common transparent plastic films were studied. Samples were stored at 4 ºC during the monitoring period (until 21 days). More than 60 hyperspectral images (from 400 to 1000 nm) per species were analyzed using ad hoc routines and commercial toolboxes of MatLab®. Besides common spectral treatments for removing additive and multiplicative effects, additional correction, previously to any other correction, was performed in the images of leaves in order to avoid the modification in their spectra due to the presence of the plastic transparent film. Findings from this study suggest that the developed images analysis system is able to deal with the effects caused in the images by the presence of plastic films in the supervision of shelf-life in leafy vegetables, in which different stages of quality has been identified

Forgotten giants: Robust climate signal in pollarded trees

Producción CientíficaTree ring records are among the most valuable resources to create high-resolution climate reconstructions. Most climate reconstructions are based on old trees growing in inaccessible mountainous areas with low human activity. Therefore, reconstruction of climate conditions in lowlands is usually based on data from distant mountains. Albeit old trees can be common in humanized areas, they are not used for climate reconstructions. Pollarding was a common traditional management in Europe that enabled trees to maintain great vitality for periods exceeding the longevity of unmanaged trees. We evaluate the potential of pollarded deciduous oaks to record past climate signal. We sampled four pollarded woodlands in Central Spain under continental Mediterranean climate. We hypothesized that pollarded trees have a strong response to water availability during current period without pollarding management, but also in the period under traditional management if pruning was asynchronous among trees. Moreover, we hypothesized that if climate is a regional driver of oak secondary growth, chronologies from different woodlands will be correlated. Pollard oaks age exceeded 500 years with a strong response to Standardized Precipitation-Evapotranspiration Index (SPEI) from 9 to 11 months. Climate signal was exceptionally high in three of the sites (r2 = 0.443–0.655) during low management period (1962–2022). The largest fraction of this climate signal (≈70 %) could be retrieved during the traditional management period (1902–1961) in the three sites where pollarding was asynchronous. Chronologies were significantly correlated since the 19th century for all the studied period, highlighting a shared climate forcing. We identified critical points to optimize pollard tree sampling schema. Our results show the enormous potential of pollarded woodlands to reconstruct hydroclimate conditions in the Mediterranean with a fine spatial grain. Studying pollarded trees is an urgent task, since the temporal window to retrieve the valuable information in pollarded trees is closing as these giants collapse and their wood rots.Junta de Castilla y León-Consejería de Educación [IR2020-1-UVA08; VA171P20]EU LIFE Soria Forest Adapt [LIFE19 CCA/ES/001181]Ministerio de Ciencia e Innovación - AEI (IJC2019-040571-I)Ministerio de Ciencia e Innovación - AEI (PRE2018-084106

Understanding why women don’t choose engineering degrees

Despite the continuous efforts of governments and universities to avoid the underrepresentation of women entering engineering degrees, the trend has not reverted, and this is a general fact all over the world. This fact goes against the tendency of a growing ratio of women in tertiary education, so causes must be investigated. This research examines two main questions: Is it possible to break the invisible barriers that prevent girls from entering in engineering degrees by means of an engineering project or activity? And are there important misconceptions about the role of women in engineering professions and about engineering itself among high school girls? An extensive survey has been carried out between three groups of students: students of the last years of high school (834), students of the first year of engineering degrees (319), and students of the first year of sciences degrees (209). A set of visits to the high schools was developed and a contest of engineering projects was carried out too. The results show that there are important misconceptions in the knowledge that high school students have about engineering degrees and engineering. The visits and the project contest had a good impact that encouraged girls to take engineering activities in their curricula. The main finding is that even though girls see engineering professions as very well valued, they are convinced that engineering is not a profession for women, which suggests that there are educational barriers acquired during earlier stages of their lives

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Frozen spatial chaos induced by boundaries

We show that rather simple but non-trivial boundary conditions could induce the appearance of spatial chaos (that is stationary, stable, but spatially disordered configurations) in extended dynamical systems with very simple dynamics. We exemplify the phenomenon with a nonlinear reaction-diffusion equation in a two-dimensional undulated domain. Concepts from the theory of dynamical systems, and a transverse-single-mode approximation are used to describe the spatially chaotic structures.Comment: 9 pages, 6 figures, submitted for publication; for related work visit http://www.imedea.uib.es/~victo