De Branges spaces and Krein's theory of entire operators

This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors were corrected. The bibliography style was change

Binary open clusters in the Milky Way: photometric and spectroscopic analysis of NGC 5617 and Trumpler 22

Using photometry and high resolution spectroscopy we investigate for the first time the physical connection between the open clusters NGC 5617 and Trumpler 22. Based on new CCD photometry we report their spatial proximity and common age of ~70 Myr. Based on high resolution spectra collected using the HERMES and UCLES spectrographs on the Anglo-Australian telescope, we present radial velocities and abundances for Fe, Na, Mg, Al, Si, Ca and Ni. The measured radial velocities are -38.63 +/-2.25 km/s for NGC 5617 and -38.46 +/-2.08 km/s for Trumpler 22. The mean metallicity of NGC 5617 was found to be [Fe/H] =-0.18 +/-0.02 and for Trumpler 22 was found to be [Fe/H] = -0.17 +/-0.04. The two clusters share similar abundances across the other elements, indicative of a common chemical enrichment history of these clusters. Together with common motions and ages we confirm that NGC 5617 and Trumpler 22 are a primordial binary cluster pair in the Milky Way.Comment: 7 pages, 3 figure, accepted by MNRA

Diagnóstico da agricultura familiar no município de Moju, Pará.

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