The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n ? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.

Lepromatous leprosy: a review and case report

Leprosy is a contagious and chronic systemic granulomatous disease caused by Mycobacterium leprae (Hansen"s bacillus). It is transmitted from person to person and has a long incubation period (between two and six years). The disease presents polar clinical forms (the"multibacillary" lepromatous leprosy and the"paucibacillary" tuberculoid leprosy), as well as other intermediate forms with hybrid characteristics. Oral manifestations usually appear in lepromatous leprosy and occur in 20-60% of cases. They may take the form of multiple nodules (lepromas) that progress to necrosis and ulceration. The ulcers are slow to heal, and produce atrophic scarring or even tissue destruction. The lesions are usually located on the hard and soft palate, in the uvula, on the underside of the tongue, and on the lips and gums. There may also be destruction of the anterior maxilla and loss of teeth. The diagnosis, based on clinical suspicion, is confirmed through bacteriological and histopathological analyses, as well as by means of the lepromin test (intradermal reaction that is usually negative in lepromatous leprosy form and positive in the tuberculoid form). The differential diagnosis includes systemic lupus erythematosus, sarcoidosis, cutaneous leishmaniasis and other skin diseases, tertiary syphilis, lymphomas, systemic mycosis, traumatic lesions and malignant neoplasias, among other disorders. Treatment is difficult as it must be continued for long periods, requires several drugs with adverse effects and proves very expensive, particularly for less developed countries. The most commonly used drugs are dapsone, rifampicin and clofazimine. Quinolones, such as ofloxacin and pefloxacin, as well as some macrolides, such as clarithromycin and minocyclin, are also effective. The present case report describes a patient with lepromatous leprosy acquired within a contagious family setting during childhood and adolescence

Angular distributions of leptons from J/ ψ's produced in 920 GeV fixed-target proton-nucleus collisions

A study of the angular distributions of leptons from decays of J/ψ"s produced in p-C and p-W collisions at s√=41.6~GeV has been performed in the J/ψ Feynman-x region −0.34-B experiment at the HERA proton ring of the DESY laboratory. The results, based on a clean selection of 2.3×105 J/ψ"s reconstructed in both the e + e − and μ + μ − decay channels, indicate that J/ψ"s are produced polarized. The magnitude of the effect is maximal at low p T . For p T >1 GeV/c a significant dependence on the reference frame is found: the polar anisotropy is more pronounced in the Collins-Soper frame and almost vanishes in the helicity frame, where, instead, a significant azimuthal anisotropy arises.

Endosseous dental implant fractures an analysis of 21 cases

Implant fracture is an infrequent cause of implant failure. The present study evaluates 21 fractured implants, with an analysis of patient age and sex, the type, length and diameter of the implant, positioning in the dental arch, the type of prosthetic rehabilitation involved, the number of abutments and pontics, the presence or absence of distal extensions or cantilevers, and loading time to fracture. Implant fracture was more common in males than in females (15:4), and the mean patient age was 56.9 years. Most cases (n = 19) corresponded to implant-supported fixed prostheses - 16 with cantilevers of different lengths- while only two fractured implants were supporting overdentures instead of fixed prostheses. The great majority of fractured implants (80.9%) were located in the molar and premolar regions, and most fractured within 3-4 years after loading. It is important to know and apply the measures required to prevent implant fracture, and to seek the best individualized solution for each case - though complete implant removal is usually the treatment of choice

Klammt's elastic open activator: Ricketts' cephalometrics results

The purpose of this study is to investigate the orthodontic and orthopaedic real effects of the Klammt's Elastic Open Activator (EOA) in 25 Class II Division 1 patients in growing period. We wanted to determine statistically the cephalometrics changes produced in the patients, comparing the lateral cranium teleradiographies we took for the diagnosis with the ones we took at the end of treatment. At the end of this study we confirm that by using the EOA we obtained the desired effects, especially reducing the molar relation 2.53 mm and the overjet 2.56 mm. The EOA corrected the inclination and protrusion of incisors, although we cannot avoid the use of fixed appliances to round off. The reduction of 2.48 mm of facial convexity stands out as the most important skeletal effect; the facial depth angle increases 0.8 degree, and the maxillary depth decreases 1.16 degrees. The length of the mandibular corpus also increases 6.7 mm, although this change is mainly due to the growth of the patient. The changes in the aesthetic profile do not stand out

Lepromatous leprosy: a review and case report

Leprosy is a contagious and chronic systemic granulomatous disease caused by Mycobacterium leprae (Hansen"s bacillus). It is transmitted from person to person and has a long incubation period (between two and six years). The disease presents polar clinical forms (the"multibacillary" lepromatous leprosy and the"paucibacillary" tuberculoid leprosy), as well as other intermediate forms with hybrid characteristics. Oral manifestations usually appear in lepromatous leprosy and occur in 20-60% of cases. They may take the form of multiple nodules (lepromas) that progress to necrosis and ulceration. The ulcers are slow to heal, and produce atrophic scarring or even tissue destruction. The lesions are usually located on the hard and soft palate, in the uvula, on the underside of the tongue, and on the lips and gums. There may also be destruction of the anterior maxilla and loss of teeth. The diagnosis, based on clinical suspicion, is confirmed through bacteriological and histopathological analyses, as well as by means of the lepromin test (intradermal reaction that is usually negative in lepromatous leprosy form and positive in the tuberculoid form). The differential diagnosis includes systemic lupus erythematosus, sarcoidosis, cutaneous leishmaniasis and other skin diseases, tertiary syphilis, lymphomas, systemic mycosis, traumatic lesions and malignant neoplasias, among other disorders. Treatment is difficult as it must be continued for long periods, requires several drugs with adverse effects and proves very expensive, particularly for less developed countries. The most commonly used drugs are dapsone, rifampicin and clofazimine. Quinolones, such as ofloxacin and pefloxacin, as well as some macrolides, such as clarithromycin and minocyclin, are also effective. The present case report describes a patient with lepromatous leprosy acquired within a contagious family setting during childhood and adolescence

Regulating Concessions of Toll Motorways, An Empirical Study on Fixed vs. Variable Term Contracts

Recent theoretical developments on concession contracts for long term infrastructure projects under uncertain demand show the benefits of allowing for flexible term contracts rather than fixing a rigid term. This study presents a simulation to compare both alternatives by using real data from the oldest Spanish toll motorway. For this purpose, we analyze how well the flexible term would have performed instead of the fixed length actually established. Our results show a huge reduction of the term of concession that would have dramatically decreased the firm’s benefits and the user’s overpayment due to the internalization of an unexpected traffic increase.