Notes on Lie symmetry group methods for differential equations

Fundamentals on Lie group methods and applications to differential equations are surveyed. Many examples are included to elucidate their extensive applicability for analytically solving both ordinary and partial differential equations.Comment: 85 Pages. expanded and misprints correcte

Dependency insurance in Belgium

In this paper we analyze the system of long-term care insurance currently in place in Belgium or rather in Flanders (the Dutch-speaking part of the country), since the French and German-speaking parts have not yet such insurance. More precisely, we review the scope, benefits, financing and functioning of the Flemish dependency insurance (called the Vlaamse Zorgverzekering) and present some statistics regarding the number of persons affiliated to the Vlaamse Zorgverzekering, the number and percentage of approved applications, the grants awarded by the Government of Flanders and the revenue and expenditure/costs relating to the Flemish dependency insurance system in order to comprehend the key factors explaining some evolution related to the dependency in Belgium. Analyses show that the adjustments and successive changes that the dependency insurance has undergone are explained by its success in terms of claims for benefits. We also find that the problem of equity and adverse selection favorable to the inhabitants of Brussels at the expense of the Flemish people is reduced owing to the different treatments for the two regions.Long-term care; Old age assistance; Subsidies; Revenue and Expenditures for health

An evaluation of mesiodentes: A retrospective study with cone-beam computed tomography

Background: The mesiodens, located in the palatal midline between the two maxillary central incisors, is the most common type of supernumerary tooth. The aim of this study was to evaluate the distribution of mesiodentes according to shape, position, and complications using cone-beam computed tomography (CBCT) images. Methods: This study was carried out retrospectively on the CBCT images of cases. The following data were recorded: age, gender, number, shape (conical, incisor, tuberculate, round), size (less than 8 mm, 8-16 mm, and over 16 mm), direction (vertical, semi-vertical, horizontal, inverted), position (impacted or erupted) of the mesiodens, any pathologies or complications (delayed eruption of adjacent tooth, root resorption, cystic formation, diastema, displacement of adjacent tooth) and relation with neighboring anatomical structures (nasal cavity, nasopalatine canal). Results: The age distribution of the patients ranged from 7 to 61 years; mean 16.8±14.2 years. In total, 65 mesiodens were seen in 50 patients. The results showed that; mesiodentes were observed in the form of an incisor tooth (38.5%) mostly, followed conical shape (33.8%). A majority of the mesiodentes were in vertical direction (38.5%) and impacted (92.3%) in the CBCT images. Thirty-six patients (72%) had one mesiodens, 13 patients (26%) had two, and one patient (2%) had three mesiodentes. The most common complication was delayed eruption (29.2%). No complications were found in 49.2% of the cases. Sixteen cases (24.1%) were associated with the nasal cavity, while 43 cases (66.1%) were associated with the nasopalatine canal. Conclusion: Radiographic examination, especially with CBCT images, is important for an exact diagnosis, evaluation, and management of mesiodens

Brain Drain from Turkey: Return Intentions of Skilled Migrants

The study estimates an empirical model of return intentions using a dataset compiled from an internet survey of Turkish professionals residing abroad. In the migration literature, wage differentials are often cited as an important factor explaining skilled migration. The findings of our study suggest, however, that non-pecuniary factors, such as the importance of family and social considerations, are also influential in the return or non-return decision of the highly educated. In addition, economic instability in Turkey, prior intentions to stay abroad and work experience in Turkey also increase non-return. Female respondents also appear less likely to return indicating a more selective migration process for females.Skilled migration, Brain drain, Return intentions, Turkey

Classification and Spectral Evolution of Outbursts of Aql X-1

We present a broad classification of all outbursts detected with the All-Sky Monitor (ASM) on the Rossi X-Ray Timing Explorer (RXTE) and the Monitor of All Sky X-Ray Image (MAXI) of Aql X-1. We identify three types of outbursts; long-high, medium-low, and short-low, based on the duration and maximum flux. We analyse the trends in the "phase-space" of flux-derivative versus flux to demonstrate the differences in the three identified outburst types. We present a spectral analysis of the observations of Aql X-1 performed by the Proportional Counter Array (PCA) onboard RXTE during the 2000 and 2011 outbursts of the long-high class and the 2010 outburst of the medium-low class. We model the source spectrum with a hybrid thermal/non-thermal hot plasma emission model (EQPAIR in XSPEC, Coppi 2000) together with a Gaussian component to model the Fe K_alpha emission line. We construct time histories of the source flux, the optical depth of the corona (tau), the seed photon temperature (kT_bb) and the hard state compactness (l_h) for these three outbursts. We show that the physical parameters of either classes reach the same values throughout the outbursts, the only difference being the maximum flux. We discuss our results in the terms of modes of interaction of the star with the disc and size of the disc kept hot by irradiation. We conclude that irradiation is the dominant physical process leading to the different classes of outbursts.Comment: MNRAS accepted. 12 pages, 9 figures, 3 table