Geometric triangulations and flips

We prove that for a given flat surface with conical singularities, any pair of geometric triangulations can be connected by a chain of flips.Comment: 5 page

Housing supply in Algeria: affordability matters rather than availability

This paper analyses the performance of the housing supply sector in Algeria. The country is witnessing a high rate of urbanization, and a fast growing labor force. The effects of housing policy on labor market, and ultimately economic growth are important. Similarly, policies that cause housing costs to rise significantly can have a much greater effect on the poor than does, for instance, a relatively small housing subsidy program. Accordingly, the scope of the research expanded to consider these broader issues, even if the focus continued to remain on how policies could be designed to improve the situation of the poor. After the introduction, the structure of the paper discusses briefly the methodology used. Then it presents the housing situation, policies and practices, followed by the dynamics of the housing sector. The main findings of the study, low levels of affordability and related problems are presented. Finally the study presents recommendations to help to improve the situation.housing supply, affordability, availability, housing policies, housing market

3D magnetic configuration of the Halpha filament and X-ray sigmoid in NOAA AR 8151

We investigate the structure and relationship of an H $\alpha$ filament and an X-ray sigmoid observed in active region NOAA 8151. We first examine the presence of such structures in the reconstructed 3D coronal magnetic field obtained from the non-constant- $\alpha$ force-free field hypothesis using a photospheric vector magnetogram (IVM, Mees Solar Observatory). This method allows us to identify several flux systems: a filament (height 30 Mm, aligned with the polarity inversion line (PIL), magnetic field strength at the apex 49 G, number of turns 0.5-0.6), a sigmoid (height 45 Mm, aligned with the PIL, magnetic field strength at the apex 56 G, number of turns 0.5-0.6) and a highly twisted flux tube (height 60 Mm, magnetic field strength at the apex 36 G, number of turns 1.1-1.2). By searching for magnetic dips in the configuration, we identify a filament structure which is in good agreement with the H $\alpha$ observations. We find that both filament and sigmoidal structures can be described by a long twisted flux tube with a number of turns less than 1 which means that these structures are stable against kinking. The filament and the sigmoid have similar absolute values of $\alpha$ and Jz in the photosphere. However, the electric current density is positive in the filament and negative in the sigmoid: the filament is right-handed whereas the sigmoid is left-handed. This fact can explain the discrepancies between the handedness of magnetic clouds (twisted flux tubes ejected from the Sun) and the handedness of their solar progenitors (twisted flux bundles in the low corona). The mechanism of eruption in AR 8151 is more likely not related to the development of instability in the filament and/or the sigmoid but is associated with the existence of the highly twisted flux tube (~1.1-1.2 turns)

Computing Beltrami Fields

International audienceFor solving the nonlinear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is solved by means of a mixed method. The last problem is a transport equation which is approximated using a streamline diffusion technique. Numerical three-dimensional experiments and results are given to illustrate the efficiency of the method