How semiregular are irregular variables?

We investigate the question whether there is a real difference in the light change between stars classified as semiregular (SRV) or irregular (Lb) variables by analysing photometric light curves of 12 representatives of each class. Using Fourier analysis we try to find a periodic signal in each light curve and determine the S/N of this signal. For all stars, independent of their variability class we detect a period above the significance threshold. No difference in the measured S/N between the two classes could be found. We propose that the Lb stars can be seen as an extension of the SRVs towards shorter periods and smaller amplitudes. This is in agreement with findings from other quantities which also showed no marked difference between the two classes.Comment: 7 pages, accepted for publication by A

About [q]-regularity properties of collections of sets

We examine three primal space local Hoelder type regularity properties of finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and uniform [q]-regularity as well as their quantitative characterizations. Equivalent metric characterizations of the three mentioned regularity properties as well as a sufficient condition of [q]-subregularity in terms of Frechet normals are established. The relationships between [q]-regularity properties of collections of sets and the corresponding regularity properties of set-valued mappings are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1309.700

Ultracoproduct Continua and their Regular Subcontinua

We continue our study of ultracoproduct continua, focusing on the role played by the regular subcontinua—those subcontinua which are themselves ultracoproducts. Regular subcontinua help us in the analysis of intervals, composants, and noncut points of ultracoproduct continua. Also, by identifying two points when they are contained in the same regular subcontinua, we naturally generalize the partition of a standard subcontinuum of H⁎ role= presentation style= box-sizing: border-box; margin: 0px; padding: 0px; display: inline-block; font-style: normal; font-weight: normal; line-height: normal; font-size: 14.4px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative; \u3e⁎H⁎ into its layers

The Mittag-Leffler Theorem for regular functions of a quaternionic variable

We prove a version of the classical Mittag-Leffler Theorem for regular functions over quaternions. Our result relies upon an appropriate notion of principal part, that is inspired by the recent definition of spherical analyticity.Comment: 10 page

Singularities of slice regular functions

Beginning in 2006, G. Gentili and D.C. Struppa developed a theory of regular quaternionic functions with properties that recall classical results in complex analysis. For instance, in each Euclidean ball centered at 0 the set of regular functions coincides with that of quaternionic power series converging in the same ball. In 2009 the author proposed a classification of singularities of regular functions as removable, essential or as poles and studied poles by constructing the ring of quotients. In that article, not only the statements, but also the proving techniques were confined to the special case of balls centered at 0. In a subsequent paper, F. Colombo, G. Gentili, I. Sabadini and D.C. Struppa (2009) identified a larger class of domains, on which the theory of regular functions is natural and not limited to quaternionic power series. The present article studies singularities in this new context, beginning with the construction of the ring of quotients and of Laurent-type expansions at points other than the origin. These expansions, which differ significantly from their complex analogs, allow a classification of singularities that is consistent with the one given in 2009. Poles are studied, as well as essential singularities, for which a version of the Casorati-Weierstrass Theorem is proven.Comment: 25 pages, 1 figur