Perturbed Fourier uniqueness and interpolation results in higher dimensions

We obtain new Fourier interpolation and -uniqueness results in all dimensions, extending methods and results by the first author and M. Sousa, and by the second author. We show that the only Schwartz function which, together with its Fourier transform, vanishes on surfaces close to the origin-centered spheres whose radius are square roots of integers, is the zero function. In the radial case, these surfaces are spheres with perturbed radii, while in the non-radial case, they can be graphs of continuous functions over the sphere. As an application, we translate our perturbed Fourier uniqueness results to perturbed Heisenberg uniqueness for the hyperbola, using the interrelation between these fields introduced and studied by Bakan, Hedenmalm, Montes-Rodriguez, Radchenko and Viazovska.Comment: 22 page

Smartphones in the teaching of Physics Laws: Projectile motion

New technologies are called upon to play an important role as beneficial tools for meaningful learning in the classroom. In particular, smartphones can be regarded as pocket computers that, in addition to a remarkable memory and computing capacity, incorporate sensors such as accelerometers, gyroscopes, magnetometers, light sensors, etc., which turn them into easily available measurement instruments for practical classes in an educational environment. In this study, the suitability of these devices for demonstrating Classical Mechanics, minimizing the use of resources and class time, has been assessed in two real classrooms (with 16 to 19 year-old students) by conducting experiments related to projectile motion (vertical free fall and parabolic motion). A simple methodology that only involves a mobile phone, a free burst camera application and open-source tools (GIMP and OpenOffice Calc) for data processing is presented. The results obtained in non-perfected conditions led to an estimate of the acceleration of gravity with an error lower than 2%. Further analyses and alternative procedures are also suggested in the discussion section. No major difficulties were encountered with the high school students or with the first year university ones, and a high degree of satisfaction was found

Optical and Infrared Imaging and Spectroscopy of the Multiple-Shell Planetary Nebula NGC 6369

NGC 6369 is a double-shell planetary nebula (PN) consisting of a bright annular inner shell with faint bipolar extensions and a filamentary envelope. We have used ground- and space-based narrow-band optical and near-IR images, broad-band mid-IR images, optical long-slit echelle spectra, and mid-IR spectra to investigate its physical structure. These observations indicate that the inner shell of NGC 6369 can be described as a barrel-like structure shape with polar bubble-like protrusions, and reveal evidence for H2 and strong polycyclic aromatic hydrocarbons (PAHs) emission from a photo-dissociative region (PDR) with molecular inclusions located outside the bright inner shell. High-resolution HST narrow-band images reveal an intricate excitation structure of the inner shell and a system of "cometary" knots. The knotty appearance of the envelope, the lack of kinematical evidence for shell expansion and the apparent presence of emission from ionized material outside the PDR makes us suggest that the envelope of NGC 6369 is not a real shell, but a flattened structure at its equatorial regions. We report the discovery of irregular knots and blobs of diffuse emission in low-excitation and molecular line emission that are located up to 80" from the central star, well outside the main nebular shells. We also show that the filaments associated to the polar protrusions have spatial extents consistent with post-shock cooling regimes, and likely represent regions of interaction of these structures with surrounding material.Comment: 14 pages, 13 figures. Accepted for publication in MNRA

Study on the vibration characteristics of the telescope T80 in the Javalambre astrophysical observatory (JAO) aimed at detecting invalid images

The location of large telescopes, generally far from the data processing centers, represents a logistical problem for the supervision of the capture of images. In this work, we carried out a preliminary study of the vibration signature of the T80 telescope at the Javalambre Astrophysical Observatory (JAO). The study analyzed the process of calculating the displacement that occurs because of the vibration in each of the frequencies in the range of interest. We analyzed the problems associated with very low frequencies by means of simulation, finding the most critical vibrations below 20 Hz, since they are the ones that generate greater displacements. The work also relates previous studies based on simulation with the real measurements of the vibration of the telescope taken remotely when it is subjected to different positioning movements (right ascension and/or declination) or when it performs movement actions such as those related to filter trays or mirror cover. The obtained results allow us to design a remote alarm system to detect invalid images (taken with excess vibration)

Modified filtered-x hierarchical lms algorithm with sequential partial updates for active noise control

In the field of active noise control (ANC), a popular method is the modified filtered-x LMS algorithm. However, it has two drawbacks: Its computational complexity higher than that of the conventional FxLMS, and its convergence rate that could still be improved. Therefore, we propose an adaptive strategy which aims at speeding up the convergence rate of an ANC system dealing with periodic disturbances. This algorithm consists in combining the organization of the filter weights in a hierarchy of subfilters of shorter length and their sequential partial updates (PU). Our contribution is threefold: (1) we provide the theoretical basis of the existence of a frequency-depend-ent parameter, called gain in step-size. (2) The theoretical upper bound of the step-size is compared with the limit obtained from simulations. (3) Additional experiments show that this strategy results in a fast algorithm with a computational complexity close to that of the conventional FxLMS

Diodos emisores de luz para irradiación de plantas

Los recientes desarrollos conseguidos en el área de la iluminación con diodos emisores de luz (LEDs, cuando son inorgánicos, y OLEDs, cuando son orgánicos) resultan de gran interés en horticultura, al permitir manipular el espectro radiante que va a incidir sobre las plantas, con el objetivo de aumentar su producción o de generar determinados efectos fisiológicos, sobre todo en invernaderos. Puesto que los vegetales crecen mejor cuando son iluminados (irradiados) en las regiones roja y azul del espectro, resulta aconsejable sustituir los sistemas de iluminación fotosintética actuales, fundamentalmente mediante lámparas de descarga en gases (vapor de sodio a alta presión y, en menor medida, halogenuros metálicos), por LEDs comerciales que emiten separadamente en esas regiones o por OLEDs susceptibles de emisión conjunta. Además, estos dispositivos son más eficientes que las lámparas incandescentes (consumen mucha menor energía eléctrica y poseen una vida media de uso mucho más larga), no generan exceso de calor (y por tanto no dañan a plantas térmicamente sensibles), e incluso, en el caso de los LEDs rojos, repelen insectos, por lo que contribuyen a la disminución en el uso de agrotóxicos. En el presente artículo, se revisan las últimas contribuciones en Fitofotónica relacionadas con los diodos emisores de luz, se aporta la experiencia existente sobre la aplicación de LEDs a invernaderos y se divulga el estado de las investigaciones que algunos grupos de investigación estamos realizando sobre OLEDs emisores bien en el rojo o bien en las regiones del rojo y el azul

KH domains with impaired nucleic acid binding as a tool for functional analysis

In eukaryotes, RNA-binding proteins that contain multiple K homology (KH) domains play a key role in coordinating the different steps of RNA synthesis, metabolism and localization. Understanding how the different KH modules participate in the recognition of the RNA targets is necessary to dissect the way these proteins operate. We have designed a KH mutant with impaired RNA-binding capability for general use in exploring the role of individual KH domains in the combinatorial functional recognition of RNA targets. A double mutation in the hallmark GxxG loop (GxxG-to-GDDG) impairs nucleic acid binding without compromising the stability of the domain. We analysed the impact of the GDDG mutations in individual KH domains on the functional properties of KSRP as a prototype of multiple KH domain-containing proteins. We show how the GDDG mutant can be used to directly link biophysical information on the sequence specificity of the different KH domains of KSRP and their role in mRNA recognition and decay. This work defines a general molecular biology tool for the investigation of the function of individual KH domains in nucleic acid binding proteins

Mid-infrared imaging- and spectro-polarimetric subarcsecond observations of NGC 1068

We present sub-arcsecond 7.5$-$13 $\mu$m imaging- and spectro-polarimetric observations of NGC 1068 using CanariCam on the 10.4-m Gran Telescopio CANARIAS. At all wavelengths, we find: (1) A 90 $\times$ 60 pc extended polarized feature in the northern ionization cone, with a uniform $\sim$44$^{\circ}$ polarization angle. Its polarization arises from dust and gas emission in the ionization cone, heated by the active nucleus and jet, and further extinguished by aligned dust grains in the host galaxy. The polarization spectrum of the jet-molecular cloud interaction at $\sim$24 pc from the core is highly polarized, and does not show a silicate feature, suggesting that the dust grains are different from those in the interstellar medium. (2) A southern polarized feature at $\sim$9.6 pc from the core. Its polarization arises from a dust emission component extinguished by a large concentration of dust in the galaxy disc. We cannot distinguish between dust emission from magnetically aligned dust grains directly heated by the jet close to the core, and aligned dust grains in the dusty obscuring material surrounding the central engine. Silicate-like grains reproduce the polarized dust emission in this feature, suggesting different dust compositions in both ionization cones. (3) An upper limit of polarization degree of 0.3 per cent in the core. Based on our polarization model, the expected polarization of the obscuring dusty material is $\lesssim$0.1 per cent in the 8$-$13 $\mu$m wavelength range. This low polarization may be arising from the passage of radiation through aligned dust grains in the shielded edges of the clumps.Comment: 17 pages, 10 figures, accepted for publication at MNRA