The active control of sound is analyzed in the framework of the mathematical theory of optimal control. After setting the problem in the frequency domain, we deal with the state equation, which is a Helmholtz partial differential equation. We show the existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure. Two optimization problems are successively considered. The first one concerns the choice of phases and amplitudes of the actuators to minimize the noise at the sensors' location. The second one consists of determining the optimal actuators' placement. Both problems are then numerically solved. Error estimates are settled and numerical results for some tests are reported.

This article describes an unsupervised strategy to acquire syntactico-semantic requirements of nouns, verbs, and adjectives from partially parsed text corpora. The linguistic notion of requirement underlying this strategy is based on two specific assumptions. First, it is assumed that two words in a dependency are mutually required. This phenomenon is called here corequirement. Second, it is also claimed that the set of words occurring in similar positions defines extensionally the requirements associated with these positions. The main aim of the learning strategy presented in this article is to identify clusters of similar positions by identifying the words that define their requirements extensionally. This strategy allows us to learn the syntactic and semantic requirements of words in different positions. This information is used to solve attachment ambiguities. Results of this particular task are evaluated at the end of the article. Extensive experimentation was performed on Portuguese text corpora.