The structures of Hausdorff metric in non-Archimedean spaces

For non-Archimedean spaces $X$ and $Y,$ let $\mathcal{M}_{\flat } (X), \mathfrak{M}(V \rightarrow W)$ and $\mathfrak{D}_{\flat }(X, Y)$ be the ballean of $X$ (the family of the balls in $X$), the space of mappings from $X$ to $Y,$ and the space of mappings from the ballen of $X$ to $Y,$ respectively. By studying explicitly the Hausdorff metric structures related to these spaces, we construct several families of new metric structures (e.g., $\widehat{\rho } _{u}, \widehat{\beta }_{X, Y}^{\lambda }, \widehat{\beta }_{X, Y}^{\ast \lambda }$) on the corresponding spaces, and study their convergence, structural relation, law of variation in the variable $\lambda,$ including some normed algebra structure. To some extent, the class $\widehat{\beta }_{X, Y}^{\lambda }$ is a counterpart of the usual Levy-Prohorov metric in the probability measure spaces, but it behaves very differently, and is interesting in itself. Moreover, when $X$ is compact and $Y = K$ is a complete non-Archimedean field, we construct and study a Dudly type metric of the space of $K-$valued measures on $X.$Comment: 43 pages; this is the final version. Thanks to the anonymous referee's helpful comments, the original Theorem 2.10 is removed, Proposition 2.10 is stated now in a stronger form, the abstact is rewritten, the Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more general for

Environmental impact of early palaeometallurgy: pollen and geochemical analysis

International audienceInterdisciplinary research was carried out in mid-level mountain areas in France with the aim of documenting historical mining and smelting activities by means of pollen and geochemical analyses. These investigations were made on cores collected in French peatlands in the Morvan (northern Massif Central), at Mont Lozère (southern Massif Central) and in the Basque Country (Pyrénées). Different periods of mining were recognised from Prehistory to modern times through the presence of anthropogenic lead in peat. Some of these were already known from archaeological dates or historical archives, especially for mediaeval and modern periods. However prehistoric ancient mining activities, as early as the Middle Bronze Age (ca. 1700 b.c.), were also discovered. They had all led to modifications in plant cover, probably related in part to forest clearance necessary to supply energy for mining and smelting

Phase transitions for PP-adic Potts model on the Cayley tree of order three

In the present paper, we study a phase transition problem for the $q$-state $p$-adic Potts model over the Cayley tree of order three. We consider a more general notion of $p$-adic Gibbs measure which depends on parameter \rho\in\bq_p. Such a measure is called {\it generalized $p$-adic quasi Gibbs measure}. When $\rho$ equals to $p$-adic exponent, then it coincides with the $p$-adic Gibbs measure. When $\rho=p$, then it coincides with $p$-adic quasi Gibbs measure. Therefore, we investigate two regimes with respect to the value of $|\rho|_p$. Namely, in the first regime, one takes $\rho=\exp_p(J)$ for some J\in\bq_p, in the second one $|\rho|_p<1$. In each regime, we first find conditions for the existence of generalized $p$-adic quasi Gibbs measures. Furthermore, in the first regime, we establish the existence of the phase transition under some conditions. In the second regime, when $|\r|_p,|q|_p\leq p^{-2}$ we prove the existence of a quasi phase transition. It turns out that if $|\r|_p<|q-1|_p^2<1$ and \sqrt{-3}\in\bq_p, then one finds the existence of the strong phase transition.Comment: 27 page

CLASH: z ~ 6 young galaxy candidate quintuply lensed by the frontier field cluster RXC J2248.7-4431

We present a quintuply lensed z ~ 6 candidate discovered in the field of the galaxy cluster RXC J2248.7-4431 (z ~ 0.348) targeted within the Cluster Lensing and Supernova survey with Hubble (CLASH) and selected in the deep HST Frontier Fields survey. Thanks to the CLASH 16-band HST imaging, we identify the quintuply lensed z ~ 6 candidate as an optical dropout in the inner region of the cluster, the brightest image having magAB=24.81+-0.02 in the f105w filter. We perform a detailed photometric analysis to verify its high-z and lensed nature. We get as photometric redshift z_phot ~ 5.9, and given the extended nature and NIR colours of the lensed images, we rule out low-z early type and galactic star contaminants. We perform a strong lensing analysis of the cluster, using 13 families of multiple lensed images identified in the HST images. Our final best model predicts the high-z quintuply lensed system with a position accuracy of 0.8''. The magnifications of the five images are between 2.2 and 8.3, which leads to a delensed UV luminosity of L_1600 ~ 0.5L*_1600 at z=6. We also estimate the UV slope from the observed NIR colours, finding a steep beta=-2.89+-0.38. We use singular and composite stellar population SEDs to fit the photometry of the hiz candidate, and we conclude that it is a young (age <300 Myr) galaxy with mass of M ~ 10^8Msol, subsolar metallicity (Z<0.2Zsol) and low dust content (AV ~ 0.2-0.4).Comment: 21 pages, 13 figures, 6 tables, submitted to MNRAS on 11 Aug 2013, accepted on 23 Nov 201

DESTILASI AIR LAUT DENGAN MEMANFAATKAN PANAS MATAHARI MENGGUNAKAN REFLEKTOR CERMIN CEKUNG UNTUK MEMENUHI KEBUTUHAN AIR DI DESA RANGAI TRITUNGGAL LAMPUNG SELATAN

Provinsi Lampung memiliki garis pantai yang cukup panjang yaitu sekitar 81.000 km. Namun,pasokan air bersih di wilayah pesisir pantai sangatlah terbatas terutama pada daerah-daerah yang padat penduduk.Pengabdian kepada masyarakat ini bertujuan untuk mengatasi permasalahan air bersih di daerah pesisir masyarakat Desa Rangai Tri Tunggal, Lampung Selatan.Metode penentuan perumusan masalah dilakukan dengan metode observasi dan wawancara warga di Desa Rangai Tri Tunggal, Lampung Selatan.Pada pengabdian kepada masyarakat ini, kami membuat alat destilasi air laut untuk memperoleh air tawar berupa alat reflektor cermin cekungyang memanfaatkanpanas energi matahari.Reflektor cermin cekung memiliki diameter 1,8 meter, tinggi cermin 0,4m dan titik fokusnya 0,45m. Reflektor cermin cekung diletakkan di atas tanah dan disinari langsung matahari. Kolektor yang berisi sampel air laut diletakkan diatas reflektor tepat pada posisi titik fokus untuk melakukan proses destilasi. Waktu pengamatan penggunaan reflektor cermin dilakukan selama 7 hari pada cuaca cerah dan dimulai pukul 8 pagi hingga 4 sore. Dari pengamatan yang dilakukan dihasilkan temperatur maksimum suhu destilasi air laut yang didapat menggunakan reflektor cermin cekung adalah 79,4˚C dengan hasil destilasi air tawar diperoleh rata - rata sebesar 508 ml dari volume awal air laut sebesar 2 liter.Provinsi Lampung memiliki garis pantai yang cukup panjang yaitu sekitar 81.000 km. Namun,pasokan air bersih di wilayah pesisir pantai sangatlah terbatas terutama pada daerah-daerah yang padat penduduk.Pengabdian kepada masyarakat ini bertujuan untuk mengatasi permasalahan air bersih di daerah pesisir masyarakat Desa Rangai Tri Tunggal, Lampung Selatan.Metode penentuan perumusan masalah dilakukan dengan metode observasi dan wawancara warga di Desa Rangai Tri Tunggal, Lampung Selatan.Pada pengabdian kepada masyarakat ini, kami membuat alat destilasi air laut untuk memperoleh air tawar berupa alat reflektor cermin cekungyang memanfaatkanpanas energi matahari.Reflektor cermin cekung memiliki diameter 1,8 meter, tinggi cermin 0,4m dan titik fokusnya 0,45m. Reflektor cermin cekung diletakkan di atas tanah dan disinari langsung matahari. Kolektor yang berisi sampel air laut diletakkan diatas reflektor tepat pada posisi titik fokus untuk melakukan proses destilasi. Waktu pengamatan penggunaan reflektor cermin dilakukan selama 7 hari pada cuaca cerah dan dimulai pukul 8 pagi hingga 4 sore. Dari pengamatan yang dilakukan dihasilkan temperatur maksimum suhu destilasi air laut yang didapat menggunakan reflektor cermin cekung adalah 79,4˚C dengan hasil destilasi air tawar diperoleh rata - rata sebesar 508 ml dari volume awal air laut sebesar 2 liter

CLASH-VLT: A Highly Precise Strong Lensing Model of the Galaxy Cluster RXC J2248.7-4431 (Abell S1063) and Prospects for Cosmography

We perform a comprehensive study of the total mass distribution of the galaxy cluster RXCJ2248 ($z=0.348$) with a set of high-precision strong lensing models, which take advantage of extensive spectroscopic information on many multiply lensed systems. In the effort to understand and quantify inherent systematics in parametric strong lensing modelling, we explore a collection of 22 models where we use different samples of multiple image families, parametrizations of the mass distribution and cosmological parameters. As input information for the strong lensing models, we use the CLASH HST imaging data and spectroscopic follow-up observations, carried out with the VIMOS and MUSE spectrographs, to identify bona-fide multiple images. A total of 16 background sources, over the redshift range $1.0-6.1$, are multiply lensed into 47 images, 24 of which are spectroscopically confirmed and belong to 10 individual sources. The cluster total mass distribution and underlying cosmology in the models are optimized by matching the observed positions of the multiple images on the lens plane. We show that with a careful selection of a sample of spectroscopically confirmed multiple images, the best-fit model reproduces their observed positions with a rms of $0.3$ in a fixed flat $\Lambda$CDM cosmology, whereas the lack of spectroscopic information lead to biases in the values of the model parameters. Allowing cosmological parameters to vary together with the cluster parameters, we find (at $68\%$ confidence level) $\Omega_m=0.25^{+0.13}_{-0.16}$ and $w=-1.07^{+0.16}_{-0.42}$ for a flat $\Lambda$CDM model, and $\Omega_m=0.31^{+0.12}_{-0.13}$ and $\Omega_\Lambda=0.38^{+0.38}_{-0.27}$ for a universe with $w=-1$ and free curvature. Using toy models mimicking the overall configuration of RXCJ2248, we estimate the impact of the line of sight mass structure on the positional rms to be $0.3\pm 0.1$.(ABRIDGED)Comment: 23 pages, 13 figures, accepted for publication in A&

CLASH: A Census of Magnified Star-Forming Galaxies at z ~ 6-8

We utilize 16 band Hubble Space Telescope (HST) observations of 18 lensing clusters obtained as part of the Cluster Lensing And Supernova survey with Hubble (CLASH) Multi-Cycle Treasury program to search for $z\sim6-8$ galaxies. We report the discovery of 204, 45, and 13 Lyman-break galaxy candidates at $z\sim6$, $z\sim7$, and $z\sim8$, respectively, identified from purely photometric redshift selections. This large sample, representing nearly an order of magnitude increase in the number of magnified star-forming galaxies at $z\sim 6-8$ presented to date, is unique in that we have observations in four WFC3/UVIS UV, seven ACS/WFC optical, and all five WFC3/IR broadband filters, which enable very accurate photometric redshift selections. We construct detailed lensing models for 17 of the 18 clusters to estimate object magnifications and to identify two new multiply lensed $z \gtrsim 6$ candidates. The median magnifications over the 17 clusters are 4, 4, and 5 for the $z\sim6$, $z\sim7$, and $z\sim8$ samples, respectively, over an average area of 4.5 arcmin$^2$ per cluster. We compare our observed number counts with expectations based on convolving "blank" field UV luminosity functions through our cluster lens models and find rough agreement down to $\sim27$ mag, where we begin to suffer significant incompleteness. In all three redshift bins, we find a higher number density at brighter observed magnitudes than the field predictions, empirically demonstrating for the first time the enhanced efficiency of lensing clusters over field surveys. Our number counts also are in general agreement with the lensed expectations from the cluster models, especially at $z\sim6$, where we have the best statistics.Comment: Accepted for publication in the Astrophysical Journal, 25 pages, 13 figures, 7 table

CLASH: Extending galaxy strong lensing to small physical scales with distant sources highly-magnified by galaxy cluster members

We present a strong lensing system in which a double source is imaged 5 times by 2 early-type galaxies. We take advantage in this target of the multi-band photometry obtained as part of the CLASH program, complemented by the spectroscopic data of the VLT/VIMOS and FORS2 follow-up campaign. We use a photometric redshift of 3.7 for the source and confirm spectroscopically the membership of the 2 lenses to the galaxy cluster MACS J1206.2-0847 at redshift 0.44. We exploit the excellent angular resolution of the HST/ACS images to model the 2 lenses in terms of singular isothermal sphere profiles and derive robust effective velocity dispersions of (97 +/- 3) and (240 +/- 6) km/s. The total mass distribution of the cluster is also well characterized by using only the local information contained in this lensing system, that is located at a projected distance of more than 300 kpc from the cluster luminosity center. According to our best-fitting lensing and composite stellar population models, the source is magnified by a total factor of 50 and has a luminous mass of about (1.0 +/- 0.5) x 10^{9} M_{Sun}. By combining the total and luminous mass estimates of the 2 lenses, we measure luminous over total mass fractions projected within the effective radii of 0.51 +/- 0.21 and 0.80 +/- 0.32. With these lenses we can extend the analysis of the mass properties of lens early-type galaxies by factors that are about 2 and 3 times smaller than previously done with regard to, respectively, velocity dispersion and luminous mass. The comparison of the total and luminous quantities of our lenses with those of astrophysical objects with different physical scales reveals the potential of studies of this kind for investigating the internal structure of galaxies. These studies, made possible thanks to the CLASH survey, will allow us to go beyond the current limits posed by the available lens samples in the field.Comment: 20 pages, 10 figures, accepted for publication in the Astrophysical Journa

The MUSIC of CLASH: predictions on the concentration-mass relation

We present the results of a numerical study based on the analysis of the MUSIC-2 simulations, aimed at estimating the expected concentration-mass relation for the CLASH cluster sample. We study nearly 1400 halos simulated at high spatial and mass resolution, which were projected along many lines-of-sight each. We study the shape of both their density and surface-density profiles and fit them with a variety of radial functions, including the Navarro-Frenk-White, the generalised Navarro-Frenk-White, and the Einasto density profiles. We derive concentrations and masses from these fits and investigate their distributions as a function of redshift and halo relaxation. We use the X-ray image simulator X-MAS to produce simulated Chandra observations of the halos and we use them to identify objects resembling the X-ray morphologies and masses of the clusters in the CLASH X-ray selected sample. We also derive a concentration-mass relation for strong-lensing clusters. We find that the sample of simulated halos which resemble the X-ray morphology of the CLASH clusters is composed mainly by relaxed halos, but it also contains a significant fraction of un-relaxed systems. For such a sample we measure an average 2D concentration which is ~11% higher than found for the full sample of simulated halos. After accounting for projection and selection effects, the average NFW concentrations of CLASH clusters are expected to be intermediate between those predicted in 3D for relaxed and super-relaxed halos. Matching the simulations to the individual CLASH clusters on the basis of the X-ray morphology, we expect that the NFW concentrations recovered from the lensing analysis of the CLASH clusters are in the range [3-6], with an average value of 3.87 and a standard deviation of 0.61. Simulated halos with X-ray morphologies similar to those of the CLASH clusters are affected by a modest orientation bias.Comment: 21 pages, 16 figures, 3 tables, submitted to Ap

CLASH-VLT: spectroscopic confirmation of a z=6.11 quintuply lensed galaxy in the Frontier Fields Cluster RXC J2248.7-4431

We present VIsible Multi-Object Spectrograph (VIMOS) observations of a z 6 galaxy quintuply imaged by the Frontier Fields galaxy cluster RXC J2248.7-4431 (z=0.348). This sub-L^*, high-z galaxy has been recently discovered by Monna et al. (2013) using dropout techniques with the 16-band HST photometry acquired as part of the Cluster Lensing And Supernova survey with Hubble (CLASH). Obtained as part of the CLASH-VLT survey, the VIMOS medium-resolution spectra of this source show a very faint continuum between ~8700A and ~9300A and a prominent emission line at 8643A, which can be readily identified with Lyman-alpha at z=6.110. The emission line exhibits an asymmetric profile, with a more pronounced red wing. The rest-frame equivalent width of the line is EW=79+-10A. After correcting for magnification, the star-formation rate (SFR) estimated from the Lya line is SFR(Lya)=11 M_{sol}/yr and that estimated from the UV data is SFR(UV)=3 M_{sol}/yr. We estimate that the effective radius of the source is R_e6 M_{sol}/yr/kpc^2 and, using the Kennicutt-Schmidt relation, a gas surface mass density Sigma_{gas}>10^3 M_{sol}/pc^2. Our results support the idea that this magnified, distant galaxy is a young and compact object with 0.4 L^* at z=6, with comparable amount of mass in gas and stars. Future follow-up observations with ALMA will provide valuable insight into the SFR and molecular gas content of this source. In the spirit of the Frontier Fields initiative, we also publish the redshifts of several multiply imaged sources and other background objects which will help improving the strong lensing model of this galaxy cluster.Comment: 4 pages, 3 figures, 1 table, Accepted for publication in A&A (minor changes, published version