Representations of gender in the writings of St. Francis Xavier: an interdisciplinary approach

Francis Xavier’s Letters and Writings are eloquent narratives of a journey that absorbed the Saint’s entire life. His experiences and idiosyncrasies, values and categorizations are presented in a clear literate discourse. The missionary is rarely neutral in his opinions as he sustains his unmistakable and omnipresent objective: the conversion of peoples and the expansion of the Society of Jesus. Parallel with this objective, the reader is introduced to the individuals that Xavier meets or that he summons in his epistolary discourse. Letters and Writings presents us with a structured narrative peopled by all those who are subject to and objects of Xavier’s apostolic mission, by helpful and unhelpful persons of influence, and by leading and secondary actors. What is then the position of women, in the collective sense as well as in the individual sense, in the travels and goals that are the centre of Xavier’s Letters and Writings? What is the role of women, that secondary and suppressed term in the man/woman binomial, a dichotomy similar to the civilized/savage and European/native binomials that punctuate Xavier’s narratives and the historic context of his letters? Women are not absent from his writings, but it would be naïve to argue in favour of the author’s misogyny as much as of his “profound knowledge of the female heart”, to quote from Paulo Durão in "Women in the Letters of Saint Francis Xavier" (1952), the only paper on this subject published so far. We denote four great categories of women in the Letters and Writings: European Women, Converted Women, Women Who Profess another Religion, and Women as the Agents and Objects of Sin, the latter of which traverses the other three categories. They all depend on the context, circumstances and judgements of value that the author chooses to highlight and articulate.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Analysis of the Van der Pol oscillator containing derivatives of fractional order

In this paper a modified version of the classical Van der Pol oscillator is proposed, introducing fractional-order time derivatives into the state-space model. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, using phase portraits, spectral analysis and bifurcation diagrams. The fractional-order dynamics is illustrated through numerical simulations of the proposed schemes using approximations to fractional-order operators. Finally, the analysis is extended to the forced Van der Pol oscillator.