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Copyright of Journal de Ciencia e Ingeniería is the property of Corporacion Universitaria Autonoma del Cauca and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Two refined genetic decompositions (DGs) are proposed, as a result of the application of the APOS Research Cycle, which describe mental structures and mechanisms for the concept of value and eigenvector in two case studies. The first DG0 models the prior knowledge that high school students (14 - 16 years old) must achieve in R2 order to build this concept in the university --this model is based on vector rotation and the concept of scalar multiple--. The second DG1 models in R2 the construction of eigenvalue and eigenvector in firstyear university students and shows how to rely on secondary education to structure that concept from relationships between the linear transformation and the scalar multiple vector as a generator of a line. The data analysis allows to validate the DG's and outline a cognitive path for learning the concept of eigenvalue and eigenvector in R2. [ABSTRACT FROM AUTHOR]

Copyright of Tecnología y Ciencias del Agua is the property of Instituto Mexicano de Tecnologia del Agua (IMTA) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Canonical Correlation Analysis (CCA) is an exploratory method of Multivariate Analysis, it studies the relationship between two sets of quantitative variables observed in the same set of individuals. It obtains new variables that are linear combination of the original variables of the two groups, such that the correlation between the projections of the data of this new variables is maximum. There are several proposals to determine canonical correlations and canonical vectors using techniques of numerical linear algebra, that is, in the formulation of Lagrange, CCA becomes a generalized eigenvalues and eigenvectors problem, assuming that the variance-covariance matrices are invertible. On the other hand, Genetic Algorithms (GA) are adaptive methods used to solve global optimization problems. When the invertibility condition is not satisfied by the variance-covariance matrices, we propose in this paper, use GA to solve the problem of CCA directly from the definition. We test the proposal with problems reported in the literature and also presents a real application of CCA to data of soil carbon in the area of Teziutlan, Puebla. [ABSTRACT FROM AUTHOR]

Copyright of Revista de Ciencias is the property of Universidad del Valle and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In general, the complexity of phenomena in sciences makes researchers feel obligated to face problems where multiple variables and big volumes of information are presented. Those problems require advanced in order to decipher the concepts and tools for its treatment. For this reason, multivariate techniques were developed long ago, but only the computer evolution and several software packages have caused the power of the multivariate statistics to become important. The problem of the displacement of people from the countryside to cities is a reason for consolidating the concepts and the principal component application technique (PCA). This article explains PCA technique while prefacing the applyed multivariate analysis. In order to study ACP, one first needs the fundamentals of matrix algebra concepts. When developed and then applied in a specific simulation, there is a way to carry and practice the theory related to the technique treated in this article. On the other hand, the simulation development using this technique needs to use other concepts associated with PCA which are explained and interpreted from the analysis of results obtained in the different processes. The analysis of this article points to one conclusion. In spite of the government taking a role for the displaced persons well-being, there is an absence of major efforts that leads to these problematic solutions. [ABSTRACT FROM AUTHOR]