Efraimidis, I., Gaona, J., Hernandez, R., & Venegas, O. (2017). On harmonic Bloch-type mappings. Complex Var. Elliptic Equ., 62(8), 1081–1092.
Abstract: Let f be a complex-valued harmonicmapping defined in the unit disk D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which, roughly speaking, states that for. analytic log. is Bloch if and only if. is univalent.
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Gaona, J., Hernández, R., Guevara, F., & Bravo, V. (2022). Influence of a Function’s Coefficients and Feedback of the Mathematical Work When Reading a Graph in an Online Assessment System. Int. J. Emerg. Technol. Learn., 17(20), 77–98.
Abstract: This paper shows the results of an experiment applied to 170
students from two Chilean universities who solve a task about reading a graph
of an affine function in an online assessment environment where the parameters
(coefficients of the graphed affine function) are randomly defined from an ad-hoc
algorithm, with automatic correction and automatic feedback. We distinguish two
versions: one of them with integer coefficients and the other one with decimal
coefficients in the affine function. We observed that the nature of the coefficients
impacts the mathematical work used by the students, where we again focus on
two of them: by direct estimation from the graph or by calculating the equation of
the line. On the other hand, feedback oriented towards the “estimation” strategy
influences the mathematical work used by the students, even though a non-negligible
group persists in the “calculating” strategy, which is partly explained by the
perception of each of the strategies.
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