Recurrence relations in one-dimensional Ising models.

The exact finite-size partition function for the nonhomogeneous one-dimensional (1D) Ising model is found through an approach using algebra operators. Specifically, in this paper we show that the partition function can be computed through a trace from a linear second-order recurrence relation with nonconstant coefficients in matrix form. A relation between the finite-size partition function and the generalized Lucas polynomials is found for the simple homogeneous model, thus establishing a recursive formula for the partition function. This is an important property and it might indicate the possible existence of recurrence relations in higher-dimensional Ising models. Moreover, assuming quenched disorder for the interactions within the model, the quenched averaged magnetic susceptibility displays a nontrivial behavior due to changes in the ferromagnetic concentration probability.

Plasma mepivacaine concentrations in patients undergoing third molar surgery.

BACKGROUND: Local anaesthetic-related systemic toxicity mainly results from elevated plasma concentrations of these drugs. We hypothesized that intraoral injection of submaximal doses of mepivacaine does not lead to toxic levels of this drug in blood. This study evaluated the plasma levels of mepivacaine in third molars surgeries. METHODS: Twenty-one patients were randomly assigned into two groups: group I (two unilateral third molars; submaximal dose of mepivacaine 108 mg with epinephrine 54 µg) and group II (four third molars; submaximal dose of mepivacaine 216 mg with epinephrine 108 µg). Blood samples were collected before anaesthesia, and 5, 10, 15, 20, 30, 40, 60, 90 and 120 min after anaesthesia. RESULTS: Individual peak plasma concentrations ranged 0.77-8.31 µg/mL (group I) and from 2.36-7.72 µg/mL (group II). An increase in the average dose of mepivacaine from 1.88 ± 0.12 mg/kg (group I) to 3.35 ± 0.17 mg/kg (group II) increased the mean mepivacaine peak plasma levels from 2.33 ± 0.58 to 4.01 ± 0.69 µg/mL, respectively. Four patients obtained plasma levels of mepivacaine above the threshold for toxicity (5 µg/mL). CONCLUSIONS: Toxic levels of mepivacaine are possible, even when a submaximal dose is used. A twofold increase in the dose of mepivacaine caused the mean peak plasma concentration to increase proportionally, indicating that they may be predicted based on the relation of dose per bodyweight.

Structural and thermal investigations of an amorphous GaSe9 alloy using EXAFS, cumulant expansion, and reverse Monte Carlo simulations.

In this article, we investigated structural and thermal properties of an amorphous alloy of the Ga-Se system. The amorphous GaSe9 alloy was produced by mechanical alloying and it was studied using EXAFS spectroscopy and cumulant expansion method. We also made reverse Monte Carlo simulations using the total structure factor S(K) obtained from x-ray diffraction and the EXAFS χ(k) oscillations on Se and Ga K edges as input data. Several parameters, such as average coordination numbers and interatomic distances, structural and thermal disorders, asymmetry of the partial distribution functions gij(r), and Einstein and Debye temperatures, were determined. The gij (E)(r) functions were reconstructed from the cumulants C1, C2, and C3 obtained from the Einstein model, and they were compared to the gij (RMC)(r) functions obtained from the simulations. The simulations also furnished the partial bond angle distribution functions Θijℓ(cosθ), which describe the angular distribution of bonds between first neighbors, and give information about the kind of structural units present in the alloy.

Aggressive ameloblastic fibro-odontoma assessment with CBCT and treatment.

BACKGROUND: Ameloblastic fibro-odontomas (AFO) are rare lesions and defined by the World Health Organisation as a tumour composed of a proliferation of odontogenic epithelium immersed in ectomesenchyme reminiscent of the interdental papilla. It also presents inductive processes leading to formation of enamel and dentine, confusing, histopathologically, with odontoma. Despite numerous efforts, there is still considerable confusion over its controversial aetiopathogenesis and treatment. A brief review of the literature on the clinical, pathological and therapeutic features of this lesion is reported. CASE REPORT: A case of aggressive AFO in a 3-year-old boy was referred to the Oral Diagnostics Service of Hospital General de Fortaleza for evaluation following a 3-months painless swelling in the right mandibular and facial regions. During anamnesis, the patient's carers reported no systemic problem and his medical history was non-contributory. Intra-orally there was a swelling of the right lateral portion of the mandible, adjacent teeth were not mobile and the oral mucosa appeared normal and showed no signs of ulceration. Radiographic examination, with panoramic radiography and cone beam computed tomography with three-dimensional (3D) reconstruction, was better able to identify the extent of bone involvement and showed an expansive hypodense image in the right mandibular region. 3D reconstruction showed expansion of buccal and lingual cortical bone and the preservation of basal bone. TREATMENT: Enucleation and curettage of the lesion were carried out and care was taken not to fracture the basal bone during the surgical procedure. Tissue specimens were sent for histopathologic analysis. Aspiration performed during surgery was negative for blood and other exudates. FOLLOW-UP: No recurrence has occurred during a follow-up period of 11 months. CONCLUSION: A comprehensive diagnosis including all clinical, radiographic and histopathologic features is necessary for the success of therapy, which varies from case to case, thus, improving the quality of life of patients with AFO.