Resumo: Este artigo busca principalmente propor um modelo de gramática que descreva e explique o processo de aquisição da lateral silábica do inglês por aprendizes brasileiros. Pretendemos responder às seguintes questões: 1) Qual gramática está sendo adquirida? Mais especificamente: qual é a gramática que licencia a forma [ɫ̩ ] na língua inglesa de falantes nativos (bem como suas variantes)? 2) Quais são as principais etapas pelas quais a gramática da interlíngua do aprendiz brasileiro no processo de aquisição de [ɫ̩ ] passa? 3) Como explicar a variação na interlíngua durante todo o processo de aquisição? É possível prever as variantes que irão emergir no processo de aquisição de [ɫ] juntamente com suas frequências e estabelecer os limites da variabilidade? Para responder tais questões, fazemos uso da Teoria da Otimalidade em sua versão Estocástica e seu Gradual Learning Algorithm (BOERSMA & HAYES, 2001). Nosso modelo foi embasado e testado por dados empíricos de um estudo realizado por nós assim como de outros autores.
The Bohnenblust-Hille inequality and its variants have found applications in several areas of Mathematics and related fields. The control of the constants for the variant for complex m-homogeneous polynomials is of special interest for applications in Harmonic Analysis and Number Theory. Up to now, the best known estimates for its constants are dominated by (1 +) m , where > 0 is arbitrary and > 0 depends on the choice of. For the special cases in which the number of variables in each monomial is bounded by some fixed number M, it has been shown that the optimal constant is dominated by a constant depending solely on M. In this note, based on a deep result of Bayart, we prove an inequality for any subset of the indices, showing how summability of arbitrary restrictions on monomials can be related to the combinatorial dimension associated with them.
A computer application, dealing with numbering systems, is presented. This central subject is discussed both as an object for studying and as an integrating theme and an anchor point for several topics belonging to mathematics curricula for ages nine to seventeen. The interest and the importance of such an instrument are discussed, from both the points of view of contents and processes. A general overview of the type of user interface and user interactivity is presented. Some aspects, which characterize the computer as a special instrument to use if and when adequate, are highlighted. The intended positioning of this application concerning pedagogical, didactical, and methodological aspects is referred to. The teacher role is emphasized. Some suggestions of approaches and activities are made explicit and a reference is made to some pilot in-field experiments.
In his pioneering work in the field of Inductive Inference, Gold (1967) proved that a set containing all finite languages and at least one infinite language over the same fixed alphabet is not learnable in the exact sense. Within the same framework, Angluin (1980) provided a complete characterization for the learnability of language families. Mathematically, the concept of exact learning in that classical setting can be seen as the use of a particular type of metric for learning in the limit. In this short research note we use Niyogi's extended version of a theorem by Blum and Blum (1975) on the existence of locking data sets to prove a necessary condition for learnability in the limit of any family of languages in any given metric. This recovers Gold's theorem as a special case. Moreover, when the language family is further assumed to contain all finite languages, the same condition also becomes sufficient for learnability in the limit.
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