Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Comitês de Classificadores para o Reconhecimento Multibiométrico em Dados Biométricos Revogáveis

This work discusses the application of techniques of ensembles in multimodal recognition systems development in revocable biometrics. Biometric systems are the future identification techniques and user access control and a proof of this is the constant increases of such systems in current society. However, there is still much advancement to be developed, mainly with regard to the accuracy, security and processing time of such systems. In the search for developing more efficient techniques, the multimodal systems and the use of revocable biometrics are promising, and can model many of the problems involved in traditional biometric recognition. A multimodal system is characterized by combining different techniques of biometric security and overcome many limitations, how: failures in the extraction or processing the dataset. Among the various possibilities to develop a multimodal system, the use of ensembles is a subject quite promising, motivated by performance and flexibility that they are demonstrating over the years, in its many applications. Givin emphasis in relation to safety, one of the biggest problems found is that the biometrics is permanently related with the user and the fact of cannot be changed if compromised. However, this problem has been solved by techniques known as revocable biometrics, which consists of applying a transformation on the biometric data in order to protect the unique characteristics, making its cancellation and replacement. In order to contribute to this important subject, this work compares the performance of individual classifiers methods, as well as the set of classifiers, in the context of the original data and the biometric space transformed by different functions. Another factor to be highlighted is the use of Genetic Algorithms (GA) in different parts of the systems, seeking to further maximize their eficiency. One of the motivations of this development is to evaluate the gain that maximized ensembles systems by different GA can bring to the data in the transformed space. Another relevant factor is to generate revocable systems even more eficient by combining two or more functions of transformations, demonstrating that is possible to extract information of a similar standard through applying different transformation functions. With all this, it is clear the importance of revocable biometrics, ensembles and GA in the development of more eficient biometric systems, something that is increasingly important in the present day