As recently found, the distribution of sunspots is non-axisymmetric and spot group formation implies the existence of two persistent active longitudes separated by 180◦. Here we quantitatively study the non-axisymmetry of sunspot occurrence. In a dynamic reference frame inferred from the differential rotation law, the raw sunspot data show a clear clustering around the persistent active longitu...

We study the subtree isomorphism problem: Given trees H and G, find a subtree of G which is isomorphic to H or decide that there is no such subtree. We give an O( k1:5 logkn)time algorithm for this problem, where k and n are the number of vertices in H and G respectively. This improves over the O(k1:5n) algorithms of Chung and Matula. We also give a randomized (Las Vegas) O(min(k1:45n; kn1:43))...

In this paper we explicitly work out the effects that a spherically symmetric distribution of dark matter with constant density would induce on the Keplerian orbital elements of the Solar System planets and compare them with the latest results in planetary orbit determination from the EPM2004 ephemerides. It turns out that the longitudes of perihelia ̟ and the mean longitudes λ are affected by s...

We determine the shape of all sum-free sets in {1,2,…,n}2 size close to maximum 35n2, solving a problem Elsholtz and Rackham. show that such asymptotic lie completely stripe 45n−o(n)≤x+y≤85n+o(n). also for any positive integer p subset A⊆{1,2,…,n}2 which forbids triple (x,y,z) satisfying px+py=z.

We discuss the problem of solar active longitudes from the viewpoint of dynamo theory. We start from a recent observational analysis of the problem undertaken by Berdyugina & Usoskin (2003, A&A, 405, 1121) and Usoskin et al. (2005, A&A, 441, 347) who demonstrated from a study of sunspot data that solar active longitudes rotate differentially, with a small but significant asynchrony between nort...

The observed persistence of specific periodicities detected in time series associated with solar surface magnetic activity over several solar cycles has led to numerous papers supporting the existence of preferred longitudes. Recent analysis of the past 120 years of sunspot number data showed that no observed periodicity remained coherent for durations greater than two 11-year solar cycles. Her...