Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations

In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solutions to the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.Comment: 29 page

Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations

preprintIn this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.Preprin

Functional systems derived from nucleobase self-assembly

Dynamic and reversible non‐covalent interactions endow synthetic systems and materials with smart adaptive functions that allow them to response to diverse stimuli, interact with external agents, or repair structural defects. Inspired by the outstanding performance and selectivity of DNA in living systems, scientists are increasingly employing Watson−Crick nucleobase pairing to control the structure and properties of self‐assembled materials. Two sets of complementary purine‐pyrimidine pairs (guanine:cytosine and adenine:thymine(uracil)) are available that provide selective and directional H‐bonding interactions, present multiple metal‐coordination sites, and exhibit rich redox chemistry. In this review, we highlight several recent examples that profit from these features and employ nucleobase interactions in functional systems and materials, covering the fields of energy/electron transfer, charge transport, adaptive nanoparticles, porous materials, macromolecule self‐assembly, or polymeric materials with adhesive or self‐healing ability

High-fidelity, broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noise modulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. Eye-diagram and signal-to-noise ratio (SNR) analysis show that this new broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR compared to a previous slow-modulation method

The tale as a tool for emotional development: a didactic proposal to promote emotional intelligence in Early Chidhood Education

[ES] Las emociones son innatas en los seres humanos, por lo que es de vital importancia que desde pequeños recibamos una buena educación emocional que nos permita aprender a reconocerlas, expresarlas y regularlas de una manera correcta y saludable para nosotros y para las personas que nos rodean. Del mismo modo, la literatura también está presente en nuestra vida desde el momento que nacemos. La literatura infantil tiene grandes beneficios para los más pequeños, ya que presenta ricos elementos emocionales y morales lo que la convierte en la herramienta perfecta para ayudarles a explorar y comprender las emociones. Por esta razón, el presente trabajo propone utilizar cuentos clásicos como elementos educativos para fomentar la educación emocional en la etapa de Educación Infantil. A través de tres cuentos de Hans Christian Andersen esta propuesta didáctica se centra en el desarrollo de la inteligencia emocional de niños de entre tres y cinco años.[EN] Emotions are innate in human beings, so it is vitally important that from a young age we receive a good emotional education that allows us to learn to recognize them, express them and regulate them in a correct and healthy way for us and for the people around us. Furthermore, literature is also present in our lives from the moment we are born. Children's literature has great benefits for children, as it has rich emotional and moral elements, making it the perfect tool to help them explore and understand emotions. For this reason, this paper proposes to use classic stories as educational elements to promote emotional education in the Early Childhood Education stage. Through three stories by Hans Christian Andersen, this didactic proposal focuses on the development of the emotional intelligence of children between the ages of three and fiv

Security Authentication using Phase-Encoded Nanoparticle Structures and Polarized Light

Phase encoded nano structures such as Quick Response (QR) codes made of metallic nanoparticles are suggested to be used in security and authentication applications. We present a polarimetric optical method able to authenticate random phase encoded QR codes. The system is illuminated using polarized light and the QR code is encoded using a phase-only random mask. Using classification algorithms it is possible to validate the QR code from the examination of the polarimetric signature of the speckle pattern. We used Kolmogorov-Smirnov statistical test and Support Vector Machine algorithms to authenticate the phase encoded QR codes using polarimetric signatures

Gamma-ray Burst UV/optical afterglow polarimetry as a probe of Quantum Gravity

A possible birefringence effect that arises in quantum gravity leads to a frequency-dependent rotation of the polarization angle of linearly polarized emission from distant sources. Here we use the UV/optical polarization data of the afterglows of GRB 020813 and GRB 021004 to constrain this effect. We find an upper limit on the Gambini & Pulin birefringence parameter $| \eta | <2\times 10^{-7}$. This limit is of 3 orders better than the previous limits from observations of AGNs and of the Crab pulsar. Much stronger limits may be obtained by the future observation of polarization of the prompt $\gamma$-rays.Comment: typos correcte

On the kinematics of the neutron star low mass X-ray binary Cen X-4

We present the first determination of the proper motion of the neutron star low mass X-ray binary {Cen X-4} measured from relative astrometry of the secondary star using optical images at different epochs. We determine the Galactic space velocity components of the system and find them to be significantly different from the mean values that characterize the kinematics of stars belonging to the halo, and the thin and the thick disc of the Galaxy. The high metallicity of the secondary star of the system rules out a halo origin and indicates that the system probably originated in the Galactic disc. A statistical analysis of the galactocentric motion revealed that this binary moves in a highly eccentric ($e\simeq 0.85\pm0.1$) orbit with an inclination of $\simeq 110^\circ$ to the Galactic plane. The large Galactic space velocity components strongly support that a high natal kick as a result of a supernova explosion could have propelled the system into such an orbit from a birth place in the Galactic disc. The high Li abundance in the secondary, comparable to that of stars in star forming regions and young stellar clusters like the Pleiades, may suggest a relatively recent formation of the system. Following the orbit backwards in time, we found that the system could have been in the inner regions of the Galactic disc $\sim$100--200 Myr ago. The neutron star might have formed at that moment. However, we cannot rule out the possibility that the system formed at a much earlier time if a Li production mechanism exists in this LMXB.Comment: 6 pages, 4 figures, accepted for publication in A&

Elemental abundance differences in the 16 Cygni binary system: a signature of gas giant planet formation?

The atmospheric parameters of the components of the 16Cygni binary system, in which the secondary has a gas giant planet detected, are measured accurately using high quality observational data. Abundances relative to solar are obtained for 25 elements with a mean error of 0.023 dex. The fact that 16CygA has about four times more lithium than 16CygB is normal considering the slightly different masses of the stars. The abundance patterns of 16CygA and B, relative to iron, are typical of that observed in most of the so-called solar twin stars, with the exception of the heavy elements (Z>30), which can, however, be explained by Galactic chemical evolution. Differential (A-B) abundances are measured with even higher precision (0.018 dex, on average). We find that 16CygA is more metal-rich than 16CygB by 0.041+/-0.007 dex. On an element-to-element basis, no correlation between the A-B abundance differences and dust condensation temperature (Tc) is detected. Based on these results, we conclude that if the process of planet formation around 16CygB is responsible for the observed abundance pattern, the formation of gas giants produces a constant downwards shift in the photospheric abundance of metals, without a Tc correlation. The latter would be produced by the formation of terrestrial planets instead, as suggested by other recent works on precise elemental abundances. Nevertheless, a scenario consistent with these observations requires the convective envelopes of 1 Msun stars to reach their present-day sizes about three times quicker than predicted by standard stellar evolution models.Comment: ApJ, in pres