Electrostatic models for zeros of Laguerre-Sobolev polynomials

Let {$\{S_n\}_{n\geqslant 0}$} be the sequence of orthogonal polynomials with respect to the Laguerre-Sobolev inner product $$\langle f,g\rangle_S =\!\int_{0}^{+\infty}\! f(x) g(x)x^{\alpha}e^{-x}dx+\sum_{j=1}^{N}\sum_{k=0}^{d_j}\lambda_{j,k} f^{(k)}(c_j)g^{(k)}(c_j),$$ where $\lambda_{j,k}\geqslant 0$, $\alpha >-1$ and $c_i \in (-\infty, 0)$ for $i=1,2,\dots,N$. We provide a formula that relates the Laguerre-Sobolev polynomials $S_n$ to the standard Laguerre orthogonal polynomials. We find the ladder operators for the polynomial sequence $\{S_n\}_{n\geqslant 0}$ and a second-order differential equation with polynomial coefficients for $\{S_n\}_{n\geqslant 0}$. We establish a sufficient condition for an electrostatic model of the zeros of orthogonal Laguerre-Sobolev polynomials. Some examples are given where this condition is either satisfied or not.Comment: arXiv admin note: substantial text overlap with arXiv:2308.0617

Asymptotic zero distribution for a class of extremal polynomials

We consider extremal polynomials with respect to a Sobolev-type p-norm, with 1and measures supported on compact subsets of the real line. For a wide class of such extremal polynomials with respect to mutually singular measures (i.e. supported on disjoint subsets of the real line), it is proved that their critical points are simple and contained in the interior of the convex hull of the support of the measures involved and the asymptotic critical point distribution is studied. We also find the nth root asymptotic behavior of the corresponding sequence of Sobolev extremal polynomials and their derivatives.A.D.G. was supported by the Research Fellowship Program, Ministerio de Economía, Industria y Competitividad of Spain, under grant BES-2016-076613. The authors G.L.L. and H.P.C. were supported by the Ministerio de Economía, Industria y Competitividad of Spain, under grant MTM2015-65888-C4-2-P

Polynomials of least deviation from zero in Sobolev p-Norm

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm (1<p<∞) for the case p=1. Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least n−d∗ zeros on the convex hull of the support of the measure, where d∗ denotes the number of terms in the discrete part.The research of H. Pijeira-Cabrera was partially supported by Ministry of Science, Innovation and Universities of Spain, under grant PGC2018-096504-B-C33. Funding Open Access funding provided by Universidad Carlos III de Madrid thanks to the CRUE-CSIC 2021 agreement with Springer Nature

Discrete-continuous Jacobi-Sobolev spaces and Fourier series

Let p≥1,ℓ∈N,α,β>−1 and ϖ=(ω0,ω1,…,ωℓ−1)∈Rℓ. Given a suitable function f, we define the discrete–continuous Jacobi–Sobolev norm of f as: ∥f∥s,p:=(∑k=0ℓ−1∣∣f(k)(ωk)∣∣p+∫1−1∣∣f(ℓ)(x)∣∣pdμα,β(x))1p, where dμα,β(x)=(1−x)α(1+x)βdx. Obviously, ∥⋅∥s,2=⟨⋅,⋅⟩s−−−−√, where ⟨⋅,⋅⟩s is the inner product ⟨f,g⟩s:=∑k=0ℓ−1f(k)(ωk)g(k)(ωk)+∫1−1f(ℓ)(x)g(ℓ)(x)dμα,β(x). In this paper, we summarize the main advances on the convergence of the Fourier–Sobolev series, in norms of type Lp, in the continuous and discrete cases, respectively. Additionally, we study the completeness of the Sobolev space of functions associated with the norm ∥⋅∥s,p and the denseness of the polynomials. Furthermore, we obtain the conditions for the convergence in ∥⋅∥s,p norm of the partial sum of the Fourier–Sobolev series of orthogonal polynomials with respect to ⟨⋅,⋅⟩s.Authors thank the valuable comments by the referees. Their suggestions have contributed to improve the presentation of this manuscript. The research of F. Marcellán and H. Pijeira-Cabrera was partially supported by Spanish State Research Agency, under Grant PGC2018-096504-B-C33. The research of A. Díaz-González was supported by the Research Fellowship Program, Ministry of Economy and Competitiveness of Spain, under grant BES-2016-076613

The phenomenon of sexting among Mexican and Spanish university students: A multigroup model

This paper has been funded by the Vice-rectorate for Research and Transfer of the University of Granada (Spain), programme of pre-competitive research Projects for young researchers (Reference: PPJIB2019-06).The practice of sexting is a phenomenon that has been growing in recent times due to the use of technology and the advance of mobile devices. This practice can have negative consequences for young people who practice it without knowing the risk involved. The main objectives of this paper were to analyze sexting behavior in Mexican and Spanish university students, and to determine the possible sociode- mographic factors that influence sexting practice in order to generate explanatory models. A cross-sectional study design was adopted by applying an online survey to a sample of 781 university students. The students belonged to two different institu- tions, 394 from a Mexican university and 387 from a Spanish university. The results indicated that the practice of sexting was higher in Spanish university students and there were significant differences between the two populations. Furthermore, the model generated on sexting indicated that the country, gender, sexual orientation and use of dating applications were possible predictors of this phenomenon. At the same time, the practice of sexting had a possible influence on students’ levels of depression and stress. Finally, the data and findings obtained showed relevant data on the practice of sexting in Mexican and Spanish students and on the sociodemo- graphic factors that can be influential.University of Granada (Spain) PPJIB2019-0

Interactive visualization for NILM in large buildings using non-negative matrix factorization

Artículo publicado en abierto mediante APC Elsevier Open AccessNon-intrusive load monitoring (NILM) techniques have recently attracted much interest, since they allow to obtain latent patterns from power demand data in buildings, revealing useful information to the expert user. Unsupervised methods are specially attractive, since they do not require labeled datasets. Particularly, non-negative matrix factorization (NMF) methods decompose a single power demand measurement over a certain time period into a set of components or “parts” that are sparse, non-negative and sum up the original measured quantity. Such components reveal hidden temporal patterns which may be difficult to interpret in complex systems such as large buildings. We suggest to integrate the knowledge of the user into the analysis in order to recognize the real events inside the electric network behind the learnt patterns. In this paper, we integrate the available domain knowledge of the user by means of a visual analytics web application in which an expert user can interact in a fluid way with the NMF outcome through visual approaches such as barcharts, heatmaps or calendars. Our approach is tested with real electric power demand data from a hospital complex, showing how the interpretation of the decomposition is improved by means of interactive data cube visualizations, in which the user can insightfully relate the NMF components to characteristic demand patterns of the hospital such as those derived from human activity, as well as to inefficient behaviors of the largest systems in the hospita

Observations of Sagittarius A* during the pericenter passage of the G2 object with MAGIC

Context. We present the results of a multi-year monitoring campaign of the Galactic center (GC) with the MAGIC telescopes. These observations were primarily motivated by reports that a putative gas cloud (G2) would be passing in close proximity to the super-massive black hole (SMBH), associated with Sagittarius A*, located at the center of our galaxy. This event was expected to give astronomers a unique chance to study the effect of in-falling matter on the broad-band emission of a SMBH. Aims. We search for potential flaring emission of very-high-energy (VHE; >= 100 GeV) gamma rays from the direction of the SMBH at the GC due to the passage of the G2 object. Using these data we also study the morphology of this complex region. Methods. We observed the GC region with the MAGIC Imaging Atmospheric Cherenkov Telescopes during the period 2012-2015, collecting 67 h of good-quality data. In addition to a search for variability in the flux and spectral shape of the GC gamma-ray source, we use a point-source subtraction technique to remove the known gamma-ray emitters located around the GC in order to reveal the TeV morphology of the extended emission inside that region. Results. No effect of the G2 object on the VHE gamma-ray emission from the GC was detected during the 4 yr observation campaign. We confirm previous measurements of the VHE spectrum of Sagittarius A*, and do not detect any significant variability of the emission from the source. Furthermore, the known VHE gamma-ray emitter at the location of the supernova remnant G0.9+0.1 was detected, as well as the recently discovered VHE source close to the GG radio arc

Interactive visualization for NILM in large buildings using non-negative matrix factorization

[EN] Non-intrusive load monitoring (NILM) techniques have recently attracted much interest, since they allow to obtain latent patterns from power demand data in buildings, revealing useful information to the expert user. Unsupervised methods are specially attractive, since they do not require labeled datasets. Particularly, non-negative matrix factorization (NMF) methods decompose a single power demand measurement over a certain time period into a set of components or “parts” that are sparse, non-negative and sum up the original measured quantity. Such components reveal hidden temporal patterns which may be difficult to interpret in complex systems such as large buildings. We suggest to integrate the knowledge of the user into the analysis in order to recognize the real events inside the electric network behind the learnt patterns. In this paper, we integrate the available domain knowledge of the user by means of a visual analytics web application in which an expert user can interact in a fluid way with the NMF outcome through visual approaches such as barcharts, heatmaps or calendars. Our approach is tested with real electric power demand data from a hospital complex, showing how the interpretation of the decomposition is improved by means of interactive data cube visualizations, in which the user can insightfully relate the NMF components to characteristic demand patterns of the hospital such as those derived from human activity, as well as to inefficient behaviors of the largest systems in the hospital.SIMinisterio de Economía y fondos europeos FEDE