15 resultados para rational points

em Brock University, Canada


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Appendix: On the conduct of the government of United States towards the Indian tribes: p.[129]-139.

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There is substantial research linking meaning-making ability and psychological well-being in the context of turning point events. Still, an important research question remains: whether individuals who report meaning-making and psychological well-being were already better adjusted psychologically, prior to the experience of their turning point. In addition, the role of meaning-making on academic achievement and parental relationship quality has received little empirical attention although both variables have been shown to be positively associated with positive adjustment among adolescents. This longitudinal study examined differences in psychological well-being, academic achievement, and parental relationship quality between adolescents who reported meaning-making (lessons or insights) and those who reported no meaning-making within their turning point narratives. Participants were 803 (52% female) grade 12 adolescents, 26% (N = 209) of whom had reported experiencing a turning point. Participants also completed measures on the outcome variables (psychological well-being, academic achievement, and parental relationship quality) 3 years prior, when they were in grade 9. MANOVA results indicated that, of the participants who experienced a turning point, adolescents who reported meaning-making reported significantly higher psychological wellbeing and more positive parental relationship quality than adolescents who reported no meaningmaking. Importantly, these two groups did not differ on the outcome variables prior to their experience of a turning point event when they were in grade 9. Academic achievement scores did not differ significantly between adolescents who reported meaning-making and those who reported no meaning-making. These findings highlight the importance of meaning-making in relation to positive adjustment subsequent to a turning point among adolescents.

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Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].