On sets of numbers rationally represented in a rational base number system

In this work, it is proved that a set of numbers closed under addition and whose representations in a rational base numeration system is a rational language is not a finitely generated additive monoid. A key to the proof is the definition of a strong combinatorial property on languages : the bounded left iteration property. It is both an unnatural property in usual formal language theory (as it contradicts any kind of pumping lemma) and an ideal fit to the languages defined through rational base number systems

Different Power-law Indices in the Frequency Distributions of Flares with and without Coronal Mass Ejections

We investigated the frequency distributions of flares with and without coronal mass ejections (CMEs) as a function of flare parameters (peak flux, fluence, and duration of soft X-ray flares). We used CMEs observed by the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO) mission and soft X-ray flares (C3.2 and above) observed by the GOES satellites during 1996 to 2005. We found that the distributions obey a power-law of the form: dN/dX~X^-alpha, where X is a flare parameter and dN is the number of events recorded within the interval [X, X+dX]. For the flares with (without) CMEs, we obtained the power-law index alpha=1.98+-0.05 (alpha=2.52+-0.03) for the peak flux, alpha=1.79+-0.05 (alpha=2.47+-0.11) for the fluence, and alpha=2.49+-0.11 (alpha=3.22+-0.15) for the duration. The power-law indices for flares without CMEs are steeper than those for flares with CMEs. The larger power-law index for flares without CMEs supports the possibility that nanoflares contribute to coronal heating.Comment: 4 pages, 2 figures embedded, accepted for publication in ApJ

A Hierarchical Relationship between the Fluence Spectra and CME Kinematics in Large Solar Energetic Particle Events: A Radio Perspective

We report on further evidence that solar energetic particles are organized by the kinematic properties of coronal mass ejections (CMEs)[1]. In particular, we focus on the starting frequency of type II bursts, which is related to the distance from the Sun where the radio emission starts. We find that the three groups of solar energetic particle (SEP) events known to have distinct values of CME initial acceleration, also have distinct average starting frequencies of the associated type II bursts. SEP events with ground level enhancement (GLE) have the highest starting frequency (107 MHz), while those associated with filament eruption (FE) in quiescent regions have the lowest starting frequency (22 MHz); regular SEP events have intermediate starting frequency (81 MHz). Taking the onset time of type II bursts as the time of shock formation, we determine the shock formation heights measured from the Sun center. We find that the shocks form on average closest to the Sun (1.51 Rs) in GLE events, farthest from the Sun in FE SEP events (5.38 Rs), and at intermediate distances in regular SEP events (1.72 Rs). Finally, we present the results of a case study of a CME with high initial acceleration (~3 km s^-2) and a type II radio burst with high starting frequency (~200 MHz) but associated with a minor SEP event. We find that the relation between the fluence spectral index and CME initial acceleration continues to hold even for this minor SEP event.Comment: 11 pages, 7 figures, 1 table, to appear in Journal of Physics: Conference Series (JPCS), Proceedings of the 16th Annual International Astrophysics Conference held in Santa Fe, NM, 201

The Peculiar Behavior of Halo Coronal Mass Ejections in Solar Cycle 24

We report on a remarkable finding that the halo coronal mass ejections (CMEs) in cycle 24 are more abundant than in cycle 23, although the sunspot number in cycle 24 has dropped by about 40%. We also find that the distribution of halo-CME source locations is different in cycle 24: the longitude distribution of halos is much flatter with the number of halos originating at central meridian distance >/=60 degrees twice as large as that in cycle 23. On the other hand, the average speed and the associated soft X-ray flare size are the same in the two cycles, suggesting that the ambient medium into which the CMEs are ejected is significantly different. We suggest that both the higher abundance and larger central meridian longitudes of halo CMEs can be explained as a consequence of the diminished total pressure in the heliosphere in cycle 24 (Gopalswamy et al. 2014). The reduced total pressure allows CMEs expand more than usual making them appear as halos.Comment: 12 pages, 5 figures, accepted for publication in the Astrophysical Journal Letters, April 7, 201

Breadth-first serialisation of trees and rational languages

We present here the notion of breadth-first signature and its relationship with numeration system theory. It is the serialisation into an infinite word of an ordered infinite tree of finite degree. We study which class of languages corresponds to which class of words and,more specifically, using a known construction from numeration system theory, we prove that the signature of rational languages are substitutive sequences.Comment: 15 page