On the propagation of the highest energy cosmic ray nuclei

We study the propagation of ultra-high energy cosmic ray nuclei through the background of cosmic microwave and intergalactic infrared photons, using recent re-estimates for the density of the last ones. We perform a detailed Monte Carlo simulation to follow the disintegration histories of nuclei starting as Fe and reaching the Earth from extragalactic sources. We obtain the maximum energies of the arriving nuclear fragments as well as the mass composition as a function of the distance traveled. Cosmic rays with energies in excess of $2\times 10^{20}$ eV cannot originate from Fe nuclei produced in sources beyond 10 Mpc.Comment: 8 page

Comparing the performance of the SF-6D and the EQ-5D in different patient groups

Introduction: This research aims to explore the performance of the SF-6D and the EQ-5D in patients suffering from asthma, chronic obstructive pulmonary disease, cataracts, and rheumatoid arthritis. In particular, the aim of this research is twofold: 1) to study the level of agreement between the indexes and the descriptive systems of the dimensions of the SF-6D and the EQ-5D, and 2) to analyze the discriminative ability of the instruments. Material and Methods: A sample of 643 patients completed both the SF-36v2 and the EQ-5D. The discriminative ability of the instruments was analyzed. Furthermore, the level of agreement between the indexes and the descriptive systems of the dimensions of the SF-6D and the EQ-5D were studied. The level of agreement between instruments was investigated using correlation coefficients and the Bland-Altman plots, while the influence of medical condition and other socio-demographic variables was analyzed using non-parametric tests. Paired-samples tests were used to identify differences between the scores. Results and Discussion: The results show a strong correlation and agreement between both indexes. Overall, questionnaire indexes differ by medical condition and socio-demographic groups and both instruments are able to discriminate between socio-demographic groups. Conclusion: This study confirmed the hypothesis that the SF-6D generates higher utility values in less healthy individuals. The SF-6D and the EQ-5D seem to perform differently in each of the diseases studied since the descriptive statistics differ between instruments and the level of correlation is not uniform. Results show that the instruments generate different utility values, but there is a strong agreement between both indexes. Thus, the two instruments are not interchangeable and their results cannot be directly comparable.Portuguese Foundation for Science and Technology (Fundacao para a Ciencia e a Tecnologia)info:eu-repo/semantics/publishedVersio

Gravitational lens system SDSS J1339+1310: microlensing factory and time delay

We spectroscopically re-observed the gravitational lens system SDSS J1339+1310 using OSIRIS on the GTC. We also monitored the $r$-band variability of the two quasar images (A and B) with the LT over 143 epochs in the period 2009$-$2016. These new data in both the wavelength and time domains have confirmed that the system is an unusual microlensing factory. The C$\scriptsize{\rm{IV}}$ emission line is remarkably microlensed, since the microlensing magnification of B relative to that for A, $\mu_{\rm{BA}}$, reaches a value of 1.4 ($\sim$ 0.4 mag) for its core. Moreover, the B image shows a red wing enhancement of C$\scriptsize{\rm{IV}}$ flux (relative to A), and $\mu_{\rm{BA}}$ = 2 (0.75 mag) for the C$\scriptsize{\rm{IV}}$ broad-line emission. Regarding the nuclear continuum, we find a chromatic behaviour of $\mu_{\rm{BA}}$, which roughly varies from $\sim$ 5 (1.75 mag) at 7000 \AA\ to $\sim$ 6 (1.95 mag) at 4000 \AA. We also detect significant microlensing variability in the $r$ band, and this includes a number of microlensing events on timescales of 50$-$100 d. Fortunately, the presence of an intrinsic 0.7 mag dip in the light curves of A and B, permitted us to measure the time delay between both quasar images. This delay is $\Delta t_{\rm{AB}}$ = 47$^{+5}_{-6}$ d (1$\sigma$ confidence interval; A is leading), in good agreement with predictions of lens models.Comment: Accepted to A&A; 19 pages, 2 appendices, 3 long tables (Tables 1-3). Tables 1-2 and an updated version of Table 3 are available at http://grupos.unican.es/glendama/q1339.ht

Linear recurrences and asymptotic behavior of exponential sums of symmetric boolean functions

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic behavior of symmetric Boolean functions and provide a formula that allows us to determine if a symmetric boolean function is asymptotically not balanced. In particular, when the degree of the symmetric function is a power of two, then the exponential sum is much smaller than $2^n$.Comment: 18 pages, 3 figure

The Keynesian multiplier and the Pigou effect under substitution between private and public consumption

In this paper we present a fixprice model in which private and public consumption show some degree of substitution. We offer formulae for the Keynesian multiplier which depend on this degree of substitution. We also show that there is a Pigou effect and that, sometimes, this effect is larger than the Keynesian multiplier.Keynes, Multiplier, Unemployment, Pigou

The Long-Run Keynesian Multiplier

We study the impact of investment on employment. In the short-run an increase in investment stimulates employment (this is the standard Keynesian multiplier). However increases of investment translate into increases in the capital stock. If labor and capital are substitutes (resp. complements), an increase in investment today decreases (resp. increases) employment tomorrow. We provide a formula to measure the overall effect of an increase in investment on emplyment, assuming that certain regularities hold.Disequilibrium

On the disintegration of cosmic ray nuclei by solar photons

We discuss in detail the possibility of observing pairs of simultaneous parallel air showers produced by the fragments of cosmic ray nuclei which disintegrated in collisions with solar photons. We consider scenarios with different cosmic ray compositions, exploring the predicted rates for existing and planned detectors and looking for methods to extract information on the initial composition from the characteristics of the signal. In particular, we find that fluorescence detectors, such as HiRes or the Telescope Array, due to their low threshold ($\sim 10^{17}$ eV) and large area ($\sim 10^4 km^2$) may observe several events per year if cosmic rays at those energies are indeed heavy nuclei. The possibility of exploiting the angular orientation of the plane containing the two showers to further constrain the cosmic ray composition is also discussed.Comment: 15 page