Torsion of elliptic curves over quadratic cyclotomic fields

In this paper we study the possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt {-3})$.Comment: 9 pages, to appear in Math. J. Okayama Univ

Smooth values of some quadratic polynomials

In this paper, using a method of Luca and the author, we find all values $x$ such that the quadratic polynomials $x^2+1,$ $x^2+4,$ $x^2+2$ and $x^2-2$ are 200-smooth and all values $x$ such that the quadratic polynomial $x^2-4$ is 100-smooth.Comment: 12 pages, to appear in Glas. Mat. Ser. II

Complete classification of torsion of elliptic curves over quadratic cyclotomic fields

In a previous paper, the author examined the possible torsions of an elliptic curve over the quadratic fields $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$. Although all the possible torsions were found if the elliptic curve has rational coefficients, we were unable to eliminate some possibilities for the torsion if the elliptic curve has coefficients that are not rational. In this note, by finding all the points of two hyperelliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$, we solve this problem completely and thus obtain a classification of all possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt{-3})$.Comment: 6 pages, to appear in J. Number Theor

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

Labor Hoarding in Russia: Where Does it Come From?

The paper focuses on the labor "hoarding" problem in Russian. We studied two forms of "hoarding": unpaid leaves and short-time work. Our research is based on the Russian Longitudinal Monitoring Survey (RLMS) database. The paper exploits individual panel data between 1994 and 1996. We show that unpaid leaves and short-time work do not represent a form of hidden unemployment. Both types of labor "hoarding" reflect the nature of employees' professional competencies. First, unpaid leaves concern primarily the employees with firm-specific knowledge, while short-time work affects strongly unskilled workers. Second, external mobility is mostly related to young people and unskilled blue-collar workers while employees with specific competencies do not change jobs so much. The paper insists on significant internal adjustments which are taking place through unpaid leaves and short-time work. This explains why there has been no massive unemployment in Russia until now. In conclusion, Russian labor market is characterized rather by internal flexibility than by labor "hoarding".http://deepblue.lib.umich.edu/bitstream/2027.42/39778/3/wp394.pd