On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems

Distributional versions of Littlewood's Tauberian theorem

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We apply these Tauberian results to deduce a number of Tauberian theorems for power series where Ces\`{a}ro summability follows from Abel summability. We also use our general results to give a new simple proof of the classical Littlewood one-sided Tauberian theorem for power series.Comment: 15 page

Characterization of distributions having a value at a point in the sense of Robinson

We characterize Schwartz distributions having a value at a single point in the sense introduced by means of nonstandard analysis by A. Robinson. They appear to be distributions continuous in a neighborhood of the point.Comment: 5 page

Regularity properties of distributions through sequences of functions

We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations $(T\ast\phi_{n})$.Comment: 10 page

White light supercontinuum generation in a Y-shaped microstructured tapered fiber pumped at 1064 nm

We report the generation of supercontinuum in a Ge-doped Y-shape tapered fiber pumped at 1064 nm in the ns pump regime. The taper was designed to have long taper transitions and a taper waist with a core diameter of 0.9 μm. The large air-filling fraction and diameter of the air-hole microstructure reduces the confinement loss at long wavelengths so, enabling the extension of the spectrum to longer wavelengths. Along the taper transition the zero-dispersion wavelength decreases as the diameter of the taper becomes smaller. The spectral components generated along the taper transition pump the taper waist, enhancing the generation of short wavelengths. A flat spectrum spanning from 420 nm to 1850 nm is reported

Classes of generalized functions with finite type regularities

We introduce and analyze spaces and algebras of generalized functions which correspond to Hölder, Zygmund, and Sobolev spaces of functions. The main scope of the paper is the characterization of the regularity of distributions that are embedded into the corresponding space or algebra of generalized functions with finite type regularities

Cognitive appraisal of environmental stimuli induces emotion-like states in fish

The occurrence of emotions in non-human animals has been the focus of debate over the years. Recently, an interest in expanding this debate to non-tetrapod vertebrates and to invertebrates has emerged. Within vertebrates, the study of emotion in teleosts is particularly interesting since they represent a divergent evolutionary radiation from that of tetrapods, and thus they provide an insight into the evolution of the biological mechanisms of emotion. We report that Sea Bream exposed to stimuli that vary according to valence (positive, negative) and salience (predictable, unpredictable) exhibit different behavioural, physiological and neuromolecular states. Since according to the dimensional theory of emotion valence and salience define a two-dimensional affective space, our data can be interpreted as evidence for the occurrence of distinctive affective states in fish corresponding to each the four quadrants of the core affective space. Moreover, the fact that the same stimuli presented in a predictable vs. unpredictable way elicited different behavioural, physiological and neuromolecular states, suggests that stimulus appraisal by the individual, rather than an intrinsic characteristic of the stimulus, has triggered the observed responses. Therefore, our data supports the occurrence of emotion-like states in fish that are regulated by the individual's perception of environmental stimuli.European Commission [265957 Copewell]; Fundacao para a Ciencia e Tecnologia [SFRH/BD/80029/2011, SFRH/BPD/72952/2010]info:eu-repo/semantics/publishedVersio

Systematic radon survey over active volcanoes

In-soil radon-222 monitoring has been conducted on active volcanoes, in particular on the Arenal, Irazu and Poas volcanoes in Costa Rica and on the Piton de la Fournaise volcano, La Réunion island. Automatic electronic probes buried in soil at one meter depth were used to study the short- and long-term fluctuations of radon related to the external parameters and/or related with the volcanic activity. Three radon stations are in operation on each Costa Rican volcano and a network of 24 stations (with 3 teletransmitted) is operated on the Piton de la Fournaise. Data obtained since 1993 on Costa Rica volcanoes are presented and radon anomalies recorded before the December 8, 1994 eruption of the Irazu volcano are discussed. The Piton de la Fournaise volcano is inactive since mid 1992. We could intensively study the influence of the external parameters on the radon behavior and individuate the type of perturbations induced on short-term measurements. One seismic crisis occurred on November 27, 1996. Radon anomalies appear on most of 50% of the stations 36 hours before the occurrence of the crisis

Influence of experimental set-up and methodology for measurements of metabolic rates and critical swimming speed in Atlantic salmon Salmo salar

In this study, swim‐tunnel respirometry was performed on Atlantic salmon Salmo salar post‐smolts in a 90 l respirometer on individuals and compared with groups or individuals of similar sizes tested in a 1905 l respirometer, to determine if differences between set‐ups and protocols exist. Standard metabolic rate (SMR) derived from the lowest oxygen uptake rate cycles over a 20 h period was statistically similar to SMR derived from back extrapolating to zero swim speed. However, maximum metabolic rate (MMR) estimates varied significantly between swimming at maximum speed, following an exhaustive chase protocol and during confinement stress. Most notably, the mean (±SE) MMR was 511 ± 15 mg O2 kg−1 h−1 in the swim test which was 52% higher compared with 337 ± 9 mg O2 kg−1 in the chase protocol, showing that the latter approach causes a substantial underestimation. Performing group respirometry in the larger swim tunnel provided statistically similar estimates of SMR and MMR as for individual fish tested in the smaller tunnel. While we hypothesised a larger swim section and swimming in groups would improve swimming performance, Ucrit was statistically similar between both set‐ups and statistically similar between swimming alone v. swimming in groups in the larger set‐up, suggesting that this species does not benefit hydrodynamically from swimming in a school in these conditions. Different methods and set‐ups have their own respective limitations and advantages depending on the questions being addressed, the time available, the number of replicates required and if supplementary samplings such as blood or gill tissues are needed. Hence, method choice should be carefully considered when planning experiments and when comparing previous studies.publishedVersio