Algorithmic problems for free-abelian times free groups

We study direct products of free-abelian and free groups with special emphasis on algorithmic problems. After giving natural extensions of standard notions into that family, we find an explicit expression for an arbitrary endomorphism of \ZZ^m \times F_n. These tools are used to solve several algorithmic and decision problems for \ZZ^m \times F_n : the membership problem, the isomorphism problem, the finite index problem, the subgroup and coset intersection problems, the fixed point problem, and the Whitehead problem.Comment: 38 page

A recursive presentation for Mihailova's subgroup

We give an explicit recursive presentation for Mihailova's subgroup $M(H)$ of $F_n \times F_n$ corresponding to a finite, concise and Peiffer aspherical presentation $H=$. This partially answers a question of R.I. Grigorchuk, [8, Problem 4.14]. As a corollary, we construct a finitely generated recursively presented orbit undecidable subgroup of $Aut(F_3)$.Comment: 9 page

Orbit decidability and the conjugacy problem for some extensions of groups

Given a short exact sequence of groups with certain conditions, $1\to F\to G\to H\to 1$, we prove that $G$ has solvable conjugacy problem if and only if the corresponding action subgroup $A\leqslant Aut(F)$ is orbit decidable. From this, we deduce that the conjugacy problem is solvable, among others, for all groups of the form $\mathbb{Z}^2\rtimes F_m$, $F_2\rtimes F_m$, $F_n \rtimes \mathbb{Z}$, and $\mathbb{Z}^n \rtimes_A F_m$ with virtually solvable action group $A\leqslant GL_n(\mathbb{Z})$. Also, we give an easy way of constructing groups of the form $\mathbb{Z}^4\rtimes F_n$ and $F_3\rtimes F_n$ with unsolvable conjugacy problem. On the way, we solve the twisted conjugacy problem for virtually surface and virtually polycyclic groups, and give an example of a group with solvable conjugacy problem but unsolvable twisted conjugacy problem. As an application, an alternative solution to the conjugacy problem in $Aut(F_2)$ is given

Concepts in cardiology : a historical perspective

Our current knowledge of the anatomy and physiology of the circulatory system has been reached by deduction and reasoning over several centuries. In this article, the history of these theories is briefly outlined.peer-reviewe

Slow and fast components in the X-ray light curves of Gamma-Ray Bursts

Gamma-ray burst light curves show quite different patterns: from very simple to extremely complex. We present a temporal and spectral study of the light curves in three energy bands (2-5, 5-10, 10-26 keV) of ten GRBs detected by the Wide Field Cameras on board BeppoSAX. For some events the time profiles are characterized by peaks superposed on a slowly evolving pedestal, which in some cases becomes less apparent at higher energies. We describe this behaviour with the presence of two components (slow and fast) having different variability time scales. We modelled the time evolution of slow components by means of an analytical function able to describe asymmetric rising and decaying profiles. The residual light curves, after the subtraction of the slow components, generally show structures more similar to the original curves in the highest energy band. Spectral study of these two components was performed evaluating their hardness ratios, used also to derive photon indices. Slow components are found generally softer than the fast ones suggesting that their origin is likely different. Being typical photon indices lower than those of the afterglows there is no evidence that the emission processes are similar. Another interesting possibility is that slow components can be related to the presence of a hot photosphere having a thermal spectrum with kT around a few keV superposed to a rapid variable non-thermal emission of the fast component.Comment: 16 pages, 20 figures (18 color, 2 B&W), accepted for publication in Astronomy and Astrophysic