Amaral, P., and P. Barahona. "
On Optimal Correction of Inconsistent Linear Constraints."
Principles and Practice of Constraint Programming, CP'2002. Ed. Pascal Van Hentenryck. Vol. 2470. Lecture Notes in Computer Science, 2470. Springer, 2002. 33-46.
AbstractIn practice one has often to deal with the problem of inconsistency between constraints, as the result, among others, of the comple\-xi\-ty of real models. To overcome these conflicts we can outline two major \mbox{actions}: removal of constraints or changes in the coefficients of the model. This last approach, that can be generically described as ``model corre\-ction" is the problem we address in this paper. The correction of the right hand side alone was one of the first approaches. The correction of both the matrix of coefficients and the right hand side introduces non linearity in the constraints. The degree of difficulty in solving the problem of the optimal correction depends on the objective function, whose purpose is to measure the closeness between the original and corrected model. Contrary to other norms, the optimization of the important Frobenius was still an open problem. We have analyzed the problem using the KKT conditions and derived necessary and sufficient conditions which enabled us to unequivocally characterize local optima, in terms of the solution of the Total Least Squares and the set of active constraints. These conditions justify a set of pruning rules, which proved, in preliminary experimental results, quite successful in a tree search procedure for determining the global minimizer.
Lima, M. M. R. A., F. M. Braz Fernandes, and R. C. C. Monteiro. "
Study of the crystallization of a borosilicate glass."
Key Engineering Materials. 230-232 (2002): 157-160.
AbstractThe crystallization of a commercial borosilicate glass powder has been studied in the temperature range 750-900°C. Crystal growth was investigated by high temperature XRD and cristobalite precipitation was identified. Glass devitrification exhibited a characteristic incubation period that decreased with increasing temperature: 25-30 min at 750°C, 9-12 min at 775°C, 5-10 min at 810°C, and 0-5 min at 840°C. Cristobalite is an unfavorable transformation product in terms of thermal expansion behavior. The precipitation of cristobalite in sintered glass compacts was confirmed by dilatometric analysis, where the increase in thermal expansion coefficient due to the presence of cristobalite and its transition from the tetragonal to the cubic phase were verified. Correlation between the XRD results and the dilatometric data from sintered glass compacts showed the partial dissolution of cristobalite when the glass was heated at the highest temperatures.