Solvability near the characteristic set for a special class of complex vector fields

This work deals with the solvability near the characteristic set Sigma = {0} x S-1 of operators of the form L = partial derivative/partial derivative t+(x(n) a(x)+ ix(m) b(x))partial derivative/partial derivative x, b not equivalent to 0 and a(0) not equal 0, defined on Omega(epsilon) = (-epsilon, epsilon) x S-1, epsilon > 0, where a and b are real-valued smooth functions in (-epsilon, epsilon) and m >= 2n. It is shown that given f belonging to a subspace of finite codimension of C-infinity (Omega(epsilon)) there is a solution u is an element of L-infinity of the equation Lu = f in a neighborhood of Sigma; moreover, the L-infinity regularity is sharp.

The Map of the Courts and the Brazilian Borders

The formation of our borders are analyzed, at first presenting the question of the demarcation line of Tordesillas and the problems that led to the abandonment of this trace to adopt a configuration thatwould deal with both the actual possession of the territory (uti possidetis) as the natural borders formed by rivers and water borders. Next, the Map of the Courts is examined, having served as the basis for the Treaty of Madrid, and it determines, actually, the current configuration of our country. An analysis is made of this cartographic document, with the aid of digital cartography, which yieldeds in the quantity of existing distortions, to modeled its trait and found out how it was built.

Auditory brainstem implant outcomes and MAP parameters: Report of experiences in adults and children

The auditory brainstem implant (ABI) was first developed to help neurofibromatosis type 2 patients. Recently, its use has been recently extended to adults with non-tumor etiologies and children with profound hearing loss who were not candidates for a cochlear implant (Cl). Although the results has been extensively reported, the stimulation parameters involved behind the outcomes have received less attention. Objective: The aim of this study is to describe the audiologic outcomes and the MAP parameters in ABI adults and children at our center. Methods: Retrospective chart review. Five adults and four children were implanted with the ABI24M from September 2005 to June 2009. In the adult patients, four had Neurofibromatosis type 2, and one had postmeningitic deafness with complete ossification of both cochleae. Three of the children had cochlear malformation or dysplasia, and one had complete ossified cochlea due to meningitis. Map parameters as well as the intraoperative electrical auditory brainstem responses were collected. Evaluation was performed with at least six months of device use and included free-field hearing thresholds, speech perception tests in the adult patients and for the children, the Infant-Toddler Meaningful Auditory Integration Scale (IT-MAIS) and (ESP) were used to evaluate the development of auditory skills, besides the MUSS to evaluate. Results: The number of active electrodes that did not cause any non-auditory sensation varied from three to nineteen. All of them were programmed with SPEAK strategy, and the pulse widths varied from 100 to 300 mu s. Free-field thresholds with warble tones varied from very soft auditory sensation of 70 dBHL at 250 Hz to a pure tone average of 45 dBHL. Speech perception varied from none to 60% open-set recognition of sentences in silence in the adult population and from no auditory sensation at all to a slight improvement in the IT-MAIS/MAIS scores. Conclusion: We observed that ABI may be a good option for offering some hearing attention to both adults and children. In children, the results might not be enough to ensure oral language development. Programming the speech processor in children demands higher care to the audiologist. (C) 2011 Elsevier Ireland Ltd. All rights reserved.