Lattice calculations on the spectrum of Dirac and Dirac-K\"ahler operators

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.Comment: 11 page

The current status of dental education and the dental profession in Chile

Indexación: Scopus.Objective: To describe the current situation of the dental profession in Chile, including training and workforce issues. Material and Methods: Data were collected from different national institutions, which included information regarding number of current registered dentists, university of graduation, geographical distribution, professional position, additional specialty certifications obtained, the number and characteristics of dental surgeons who work in the public and private sectors, the traditional character of the university, the accreditation status of the undergraduate dental programs and the general population number. Results: Currently there are 32 schools of Dentistry in Chile, of which 21 have their quality certified. There are 19,100 Chilean dentists and 1,727 foreign dentists registered. The number of graduates from private universities has increased significantly. Currently, 2,164 dentists work for MINSAL. Less than a third hold a specialty certification. Forty-five percent of the dental specialists obtained their certification from universities. The current professional ratio is 104 dentists per 100,000 habitants. Conclusion: The number of dentists in Chile has increased progressively during the last years, mainly associated with the opening of new dental schools. Only 28% of the Chilean dental schools have certified their quality for the total duration of the undergraduate program. Regarding the workforce, there is a public/private and geographical inequities in dentists’ distribution.http://revista.uepb.edu.br/index.php/pboci/article/view/3875/pd