Characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups.

We work with Besov spaces Bp,q0,b defined by means of differences, with zero classical smoothness and logarithmic smoothness with exponent b. We characterize Bp,q0,b by means of Fourier-analytical decompositions, wavelets and semi-groups. We also compare those results with the well-known characterizations for classical Besov spaces Bp,qs.

Assessment of groups in a network organization based on the Shapley group value.

The focus of this paper is the assessment of groups of agents or units in a network organization. Given a social network, the relations between agents are modeled by means of a graph, and its functionality will be codified by means of a cooperative game. Building on previous work of Gomez et al. (2003) for the individual case, we propose a Myerson group value to evaluate the ability of each group of agents inside the social network to achieve the organization's goals. We analyze this centrality measure, and in particular we offer several decompositions that facilitate obtaining a precise interpretation of it.

FR Cnc revisited: photometry, polarimetry and spectroscopy

This paper is part of a multiwavelength study aimed at using complementary photometric, polarimetric and spectroscopic data to achieve an understanding of the activity process in late-type stars. Here, we present the study of FR Cnc, a young, active and spotted star. We performed analysis of All Sky Automated Survey 3 (ASAS-3) data for the years 2002–08 and amended the value of the rotational period to be 0.826518 d. The amplitude of photometric variations decreased abruptly in the year 2005, while the mean brightness remained the same, which was interpreted as a quick redistribution of spots. BVR_C and I_C broad-band photometric calibration was performed for 166 stars in FR Cnc vicinity. The photometry at Terskol Observatory shows two brightening episodes, one of which occurred at the same phase as the flare of 2006 November 23. Polarimetric BVR observations indicate the probable presence of a supplementary source of polarization. We monitored FR Cnc spectroscopically during the years 2004–08. We concluded that the radial velocity changes cannot be explained by the binary nature of FR Cnc. We determined the spectral type of FR Cnc as K7V. Calculated galactic space-velocity components (U, V, W) indicate that FR Cnc belongs to the young disc population and might also belong to the IC 2391 moving group. Based on Li Iλ6707.8 measurement, we estimated the age of FR Cnc to be between 10 and 120 Myr. Doppler tomography was applied to create a starspot image of FR Cnc. We optimized the goodness of fit to the deconvolved profiles for axial inclination, equivalent width and v sin i, finding v sin  i=46.2 km s^−1 and i= 55°. We also generated a syntheticV-band light curve based on Doppler imaging that makes simultaneous use of spectroscopic and photometric data. This synthetic light curve displays the same morphology and amplitude as the observed one. The starspot distribution of FR Cnc is also of interest since it is one of the latest spectral types to have been imaged. No polar spot was detected on FR Cnc.