From circular paths to elliptic orbits: A geometric approach to Kepler's motion

The hodograph, i.e. the path traced by a body in velocity space, was introduced by Hamilton in 1846 as an alternative for studying certain dynamical problems. The hodograph of the Kepler problem was then investigated and shown to be a circle, it was next used to investigate some other properties of the motion. We here propose a new method for tracing the hodograph and the corresponding configuration space orbit in Kepler's problem starting from the initial conditions given and trying to use no more than the methods of synthetic geometry in a sort of Newtonian approach. All of our geometric constructions require straight edge and compass only.Comment: 9 pages, 4 figure

Null geodesics in five-dimensional Reissner-Nordstr\"om anti-de Sitter black hole

The study of the motion of photons around massive bodies is one of the most useful tools to know the geodesic structure associated with said gravitational source. In the present work, different possible paths projected in an invariant hyperplane are investigated, considering five-dimensional Reissner-Nordstr\"om anti-de Sitter black hole. Also, we study some observational test such as the bending of light and the Shapiro time delay effect. Mainly, we found that the motion of photons follows the hippopede of Proclus geodesic, which is a new type of trajectory of second kind, being the Lima\c{c}on of Pascal their analogue geodesic in four-dimensional Reissner-Nordstr\"om anti-de Sitter black hole.Comment: Version accepted for publication by EPJ

Weak Hopf algebras with projection and weak smash bialgebra structures

AbstractIn this paper we study weak Hopf algebras with projection. If f:H→B, g:B→H are morphisms of weak Hopf algebras such that g∘f=idH, we prove that it is possible to find an object BH, in the new category of weak Yetter–Drinfeld modules, that verifies similar conditions to the ones include in the definition of weak Hopf algebra. Finally, we define weak smash bialgebra structures and prove that, under central and cocentral conditions, BH and H determine an example of them

Los espectadores ante la violencia televisiva: funciones, efectos e interpretaciones situadas

La investigación sobre violencia en televisión se ha orientado a una labor cuantificadora de lo emitido o a la práctica experimental para determinar sus posibles efectos. El presente trabajo se centra en cómo interpretan los espectadores las imágenes de violencia. Basado en el análisis de 16 grupos de discusión, muestra las dimensiones que mediatizan los posibles efectos de la violencia televisiva; en concreto, las condiciones en que se reconocen y clasifican escenas de violencia, las funciones de la imagen violenta, las emociones y sentimientos despertados por ella y los procesos de identificación que se pueden producir con los personajes de las escenas

Giant cell granuloma of the maxilla: global management, review of literature and case report

Giant cell granuloma is a relatively rare benign entity but can be locally aggressive. Histologically characterized by intense proliferation of multinucleated giant cells and fibroblasts. Affects bone supported tissues. Definitive diagnosis is given by biopsy. Clinically manifest as a mass or nodule of reddish color and fleshy, occasionally ulcerated surface. They can range from asymptomatic to destructive lesions that grow quickly. It is a lesion to be considered in the differential diagnosis of osteolytic lesions affecting the maxilla or jaw. Its management passed from conservative treatment with intralesional infiltration of corticosteroids, calcitonin or interferon, to the surgical resection and reconstruction, for example with microvascular free flaps. Keywords: giant cell granuloma, intralesional injection, microvascular free flap, fibula

Comparison of implant primary stability between maxillary edentulous ridges receiving intramembranous origin block grafts

Purpose: The purposes of the present study were: to compare the resonance frequency analysis (RFA) values of implant placed in either ramus or calvaria block grafts; and to determine if implant diameter influences RFA implant stability quotient (ISQ) value. Material and Methods: This was a retrospective study that included 16 consecutives healthy patients treated with autogenous onlay block grafts for horizontal bone reconstruction in maxilla. Ten ramus and ten calvaria block graft treated patients were selected and compared. Results: Totally, 59 implants were placed, 35 (59.3%) were placed on the calvaria bone grafts and the remaining 24 (40.7%) were on the ramus bone graft. Of all the implants studied, 13 (22%), 35 (59.3%), and 11 (18.6%) were 10 mm, 11.5 mm and 13 mm in length respectively. Regarding the diameter, 4 (7%) were 3.3 mm, 3 (5%) were 3.5 mm, 20 (34%) were 3.7 mm and 32 (54%) were 4 mm. Mean ISQ value obtained by RFA was 73.06 ± 6.08, being 72.19 ± 6 and 74.47 ± 6.06 for the calvaria and ramus treated group respectively. No significant differences were noted between the two groups (p= 0.154). Implants were pooled and divided by their diameter. Mean ISQ value obtained for 3.3 mm was 80 ± 5.09, while for 4.0 mm was 72.5 ± 7.19. Again, no significant differences were found among the groups (p= 0.138). Conclusion: For RFA ISQ value, the bone graft origins (calvaria or ramus) or implant diameters did not influence the outcome